This guide divides the game into part based (more or less) on which of the goals in the "Goals" tab have been accomplished so far.
Note that this guide was mostly written based on a playthrough which was very active and did not use offline progress. The times given are thus fairly close to minimum possible times. However, this playthrough was done before achievements were added, so the achievement bonus makes it possible to go slightly faster.
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This part of the game is fairly simple. Start by clicking the "Main" button to go to the main tab, if you haven't already. Then buy a Generator 1 for the cost of stars. Other generators will become affordable over time. You can hold down M to buy max of all generators. The way generators work is very simple. Each generator produces the one before it, except the first which produces stars. Buying more of a generator increases a multiplier to its production, by ^( / ), which is x, per purchase.
Generator initial costs: ^(generator number^) stars
Generator cost increases per purchase: (^generator number)x stars
It doesn't matter very much in what order you buy generators, but generally buying a generator you don't have any of is best, and otherwise cheaper and lower generators are better than higher ones. Buying max will generally automatically buy generators in this order (first buying generators you don't have any of, then repeatedly buying the cheapest generator possible).
The autobuyer tab is also useful at this point. You can buy "slow" autobuyers for stars, and they will each automatically buy a certain generator every (which is why they are called "slow"). They are automatically set to buy max, and you should probably keep them there because then, if they can buy more than of a generator when they trigger, they will do so (if set to buy singles they will only buy ). You should generally buy an autobuyer as soon as you have bought all generators with the same price or a lower price.
Once you get stars, several things will happen more or less at once. Firstly, you can buy the last generator, your first Generator 8. There is no Generator 9, so this is somewhat significant. Secondly, you can buy a boost. This will multiply all your generator multipliers by when bought. Thirdly, after buying Generator 8, you will be able to sacrifice. It doesn't matter very much for what multiplier you do this the first time, but I would recommend at least x, and getting the boost with cost stars.
When you sacrifice, you'll be asked if you're sure you want to. You should say yes. This is a measure to stop accidental sacrifices at bad times for it. Turn it off in the options tab (in the confirmations row) when you feel that the safety of not accidentally sacrificing stops being worthwhile. This applies to other confirmations too.
So, you've sacrificed. This resets all Generator 1-7 amounts, but they keep their multipliers, and Generator 8 actually has a slightly increased (x) multiplier. Thus, it should only take roughly for you to get back to the same star production you had before. After this, keep playing as before. There'll be another boost at stars. Note that in general boosts are the most worthwhile things to buy, since they give a multiplier to all generators.
Sacrifice formula: (log(stars when sacrificing) / ) sacrifice multiplier
At stars, you will be able to prestige. The slow Generator 8 autobuyer also costs stars, so unless you're very active you probably want to buy that autobuyer first. However, after buying that, prestige as soon as you can.
So, you've prestiged. This resets all Generator 1-8 amounts and multipliers, and your stars. However, you now have a roughly x multiplier to all generators, which will let you get far more quickly to where you were before. You also keep your slow autobuyers. Keep playing as before, perhaps sacrificing slightly later, at perhaps x (though it barely matters). Eventually you'll be able to prestige again. In theory, the optimal prestige powers amounts to prestige at are roughly , , , , and , but you may want to prestige slightly less often so that you have to buy generators and boosts less, especially if you are idle. Consistently prestiging for x or x is not that bad.
If you are idle, it might be worth pushing on your second prestige to stars to unlock the slow boost autobuyer, the last slow autobuyer. This will give you roughly prestige power, or a x prestige multiplier if you first prestiged for prestige power.
Prestige formula: (stars when sacrificing^ / ) prestige power
Note that prestige power gain (and sacrifice multiplier gain, for that matter) is based on highest stars since last prestige (or since last sacrifice), so buying something right before prestiging or sacrificing won't decrease the gained multiplier, but will stop that gained multiplier from going up for some time as stars increase to their previous maximum value.
Keep prestiging as described above (for the above amounts, or x or x). Sacrifice once in each prestige, to after prestiging (or when progress feels like it's starting to slow). If you're close to stars (if you have more than , perhaps) it's probably best not to prestige, because stuff happens at stars. Specifically, stars will stop increasing. Also, the main tab will vanish, and be replaced with a message saying "The universe has collapsed due to an excess of stars." (I guess that's why stars stopped increasing.) Also, a new button will appear, saying "Infinity: Gain 2 infinity points", with additional statistics on it. Press this button, and infinity, as soon as it appears; unlike with sacrifice and prestige, there's nothing to be gained from waiting at this point.
So, you've infinitied. This resets everything prestige resets, and also resets prestige power. However, you keep your slow autobuyers. New tabs called "Infinity" and "Normal Challenges" also unlock. On the Infinity tab, you can see that you have infinity points and infinity (infinities are basically a count of how many times you've infinitied). Buy an Infinity Generator 1 for the infinity points you just got. Note that infinity generators (IGs) have the same initial costs, cost increases, and multiplier per purchase as the generators you already know from pre-infinity (for clarity, in this guide the pre-infinity generators are sometimes called normal generators, though sometimes they are called generators when it is (hopefully) clear); they just cost IP instead of stars. Infinity will reset infinity stars to infinity generator amounts to however many you've bought, but will not reset their multipliers.
There will be something on the autobuyer tab that appears to let you turn the infinity autobuyer on (checked) or off (unchecked). It indeed does, but since the infinity autobuyer is locked it doesn't do anything whether it's on or off yet. It doesn't really matter whether you turn it on or off right now; by the time you unlock it you'll be changing its other settings a lot too. In general, if an autobuyer does something that resets things in the way that (as you just saw) infinity does, it will be possible to turn it off before unlocking it, so it doesn't reset things right after it's unlocked and before it can be turned off. This is also why the above "Turn newly unlocked autobuyers on when unlocked" setting exists.
You can do Normal Challenge 1 right now. If you want to do so, you should read below about normal challenges and Normal Challenge 1 in particular. Do another infinity, whether or not you do it in Normal Challenge 1, generally following the parts of the guide above this (except that you don't need to unlock slow autobuyers, since they're already unlocked). It'll be a lot quicker (probably at least x quicker), since you'll have a x multiplier to normal generators from having produced infinity points (the formula for this multiplier is ( + total infinity points / ), capped at ), and there'll be an increasing multiplier to normal generators from infinity stars, produced by your Infinity Generator 1. Due to this infinity being quicker, you don't need to wait as long to sacrifice; generally you should sacrifice once each prestige, when the number of stars you need to prestige is roughly x your current stars.
After you infinity for the second time, you'll have unspent infinity points, which you can't buy anything with. Do the same thing again but slightly quicker. Now the multiplier from total IP is x and since you have infinities rather than , infinity stars will be produced x faster (infinity generators are all multiplied by min(, infinities / ), meaning that more infinities make them stronger up to ), giving roughly a x additional multiplier to generators. After you infinity for the third time, you'll have IP and be able to buy Infinity Generator 1 again. Now you're ready to start doing normal challenges.
Normal challenges are much like normal infinities, but they have special conditions to make them harder and give you an autobuyer (or make one of your autobuyers trigger every tick) on completion. Also, all generators are multiplied by ^(completed normal challenges / ). To do a normal challenge, go to the Normal Challenges tab and click its "Start challenge" button. In theory any of the normal challenges could be done immediately, but some are much easier than others. Also, some challenges (1, 2, and 12) start out similar to a normal infinity and don't get easier as you progress by as much as the other normal challenges. These are marked with "Consistent" because they take a more consistent amount of time with progress than the others. I found 1 easy and 2 and 12 hard, but other people have different views which may be more correct.
Below is information on each normal challenge (including strategy), followed by a description of general strategy.
Normal Challenge 1: Consistent. If you could somehow do it as your first infinity, it would be faster than a normal first infinity. As a second infinity, it's slightly slower than a normal infinity, but not by much. Later, it gets noticeably slower compared to a normal infinity. After you have of each generator the only generators worth buying are Generator 1 and (to a small extent) Generator 8. If you're fairly active, you might want to turn some of your autobuyers off and buy Generators 1 and 8 manually due to this. (Boosts are still worth buying though.) Also, don't sacrifice in this challenge because it's useless.
Normal Challenge 2: Consistent. This challenge is somewhat slow, and doesn't speed up as much with progress as normal infinities and most challenges do. The important thing for this challenge is not to be buying things constantly (so you can't always be buying max), because buying almost anything resets the generator multipliers and they take a while to recover. At this point, buying things roughly every is good. You can do Normal Challenge 2 very early if you want (buying things less frequently, maybe even only once per minute). You can buy things on some interval by setting autobuyers to trigger every (in which case you probably want to synchronize your slow and fast autobuyers), or do it manually.
Normal Challenge 3: Easy. The only hard part of this is the very start, when you don't have any generators higher than Generator 1. However, due to the very small multiplier on Generator 1 (starting at ), this will be the case for a few minutes at the start, which you just have to mostly wait for. Buying Generator 1 a second time for stars will let you get Generator 2 sooner, but buying it a third time for stars won't, so buy it twice and not a third time. Once you get stars and buy Generator 2 it should be fairly hard to even notice you're in a challenge. After you first prestige in Normal Challenge 3, there'll be a short wait until you can get Generator 2 again, but this time it should be less than a minute. It's worth noting that overnight, you can do Normal Challenge 3 at any point, since its increasing multiplier to Generator 1 will have the same effect as an additional x multiplier to all generators for every (a bit more than ) you wait. After or so this is enough to easily get you to infinity.
Normal Challenge 4: Easy. This challenge doesn't have much special strategy, but you might want to wait to make a purchase of a higher generator (any generator other than Generator 1, but especially the highest few) until you can buy many at once (more explicitly, get roughly times more stars than last time you bought things), since when you buy a higher generator you'll have to wait for all the ones below it to reach their previous levels again before you reach your prior star production.
Normal Challenge 5: Medium. This challenge starts out reasonable but gets harder due to you "missing" more purchases. It doesn't have any special strategy.
Normal Challenge 6: Hard. This challenge might seem not that bad at first, but it gets a lot harder later due to you missing generator multipliers. It doesn't have any special strategy, though note that you can't sacrifice due to not getting Generator 8.
Normal Challenge 7: Hard. This challenge doesn't take too long (it's only a bit harder than Normal Challenge 5 if you do it right) but it requires autobuyers to be off and has some strategy. Don't feel worried about doing prestiges; you can do prestiges even for x and you'll have a lot of purchases left over if you follow the advice here. For all prestiges but your last, buy only of each generator (you can buy as many boosts as you want). For your last prestige (this is best to do when you have over stars), turn the prestige autobuyer off (or otherwise make sure you don't prestige), buy as many Generator 8 as you can, then buy as many Generator 1 as you can. If you have leftover purchases, buy as many Generator 2 as you can. You should then wait until you can infinity.
Normal Challenge 8: Medium. This challenge is actually a bit faster than a normal infinity for most of the first prestige, but then gets slower at the end. It doesn't have any special strategy.
Normal Challenge 9: Medium. This challenge is on the easy side of medium, and, like the other medium challenges, gets harder at the end. It doesn't have any special strategy.
Normal Challenge 10: Hard. This challenge is almost like a different game. Buy of each generator (it's all you can buy), then sacrifice. Repeat (it'll probably take repetitions or so before you can infinity and finish the challenge, though it gets quicker with more infinity stars). Once you can sacrifice each time, only wait a few seconds to do so; waiting longer is basically a waste of time (and not waiting at all is fine).
Normal Challenge 11: Medium. As you'd probably expect, this challenge gets harder at the end. It doesn't have any special strategy.
Normal Challenge 12: Consistent. This is like pre-infinity, but faster and with better automation. It doesn't have any special strategy; just do what you did first infinity. It might seem like this would be a good early challenge. However, actually infinity stars speed up a normal infinity quite a lot compared to Normal Challenge 12, and so you can do several normal infinities in the time it'd take you to do Normal Challenge 12. Furthermore, Normal Challenge 12 is sped up somewhat by the multiplier to normal generators based on total infinity points. Thus, Normal Challenge 12 is best to do either last or because you want to be able to do infinities automatically.
In this paragraph, challenge orders within each sentence are suggestions and not following them probably won't make anything much harder. Do Normal Challenge 1 (if you didn't do it already as your second infinity), Normal Challenge 3, and Normal Challenge 4 in separate infinities. Then do normal infinities (each of which is roughly long if you are active). Spend your IP on an Infinity Generator 2. Then do Normal Challenges 5, 8, 9, and 11. Spend IP on the first infinity upgrade, increasing the multiplier per boost from x to x. Optionally do some more normal infinities now if you want. Do Normal Challenges 2, 6, 7, 10, and 12, and then, having completed all normal challenges, break infinity in the Infinity tab.
For autobuyers, you probably want to sacrifice for multiplier x, prestige for multiplier x, and, if you do Normal Challenge 12 earlier than suggested here, infinity whenever possible, at least before breaking infinity (multiple settings lead to this).
So, you've broken infinity. You can now get more infinity points from each infinity, if you get more stars. At the very start, you want to do slightly long infinities just to find out how many IP to infinity for so that you get the most IP/sec (infinity points per second), then do shorter infinities in each of which you get that many IP. (Of course, with this guide, finding out yourself how many IP to infinity for is mostly unnecessary.) Once IP/sec starts going down, it generally won't go back up in that infinity, except sometimes if you are about to be able to buy another boost (so that might be worth checking).
You still, throughout this channel (except in very special circumstances such as trying to get achievements), want to set the sacrifice autobuyer to multiplier x and set the prestige autobuyer to multiplier x. Other nearby settings work, but far higher (above x) or lower (below x) settings are probably bad.
Note that you cannot go beyond stars in normal challenges even if infinity is broken, so don't try to, for example, spend months in Normal Challenge 3 to get exponential infinity point gain. Also note that although you can now view the Infinity Challenges tab, it is not useful for a while.
IP formula: stars^
The order to buy things in is, most importantly, new infinity generators, second-most importantly, infinity upgrades (with the second being better than the first when they have the same cost), and least importantly, infinity generators you already have (these are so unimportant that even if they cost x the price of a new infinity generator or an infinity upgrade, you shouldn't buy them).
Here are some example infinity point gain statistics (yours might be different due to having a different number of total IP or infinities). First get IP per infinity with IP/sec going from roughly (right after breaking infinity) to roughly . After buying the first infinity upgrade for IP (increasing the per-boost multiplier to , which is a lot more useful than the first time now that you can get more boosts), get IP per infinity with IP/sec going from roughly to roughly .
After buying Infinity Generator 3 (which, to repeat, you should do before buying the first infinity upgrade for IP), you'll notice that IP/sec stops really going down at all (it might occasionally go down a little, but when you get your next boost it will mostly go back up). Do a single infinity for roughly , getting IP. Buy the first infinity upgrade again. Now (you can do this slightly later or earlier) start doing infinities for IP until you have infinities (to increase infinity generator multipliers). This should take roughly per infinity at first, decreasing to . After that, again do a single long infinity, this time for roughly and for IP. The first two infinity upgrades should both have that cost; they're roughly equally good but the second is slightly better, so buy it. Now do another infinity for roughly , but still for IP, and buy the first infinity upgrade.
At this point you're on your own, because a long list of exact infinities seems like too much detail. Generally try to make sure that after every infinity, with the IP you got, you unlock an infinity upgrade, unlock a new infinity generator, or can make a lot (e.g., ) infinity generator purchases. On the other hand, if you're getting more than x total IP per infinity at this point, your infinities are probably too long. You may want to get a bit more IP than the price of whatever you want to purchase, so that you can also buy some cheap infinity generators. Infinities will get longer at first, getting as long as to (how long your longest infinity is depends on how much more IP you try to infinity for each time), but past IP infinities will get a bit shorter again, more specifically, to long. The infinity autobuyer isn't that useful in this part, but if you know how much IP you want to infinity for, then you can set it to that.
At stars, which you can reach in roughly from IP, Infinity Challenge 1 should become unlocked and thus possible to start. Don't start it until you get the first infinity upgrade costing IP and the second infinity upgrade costing IP. Note that after buying the second infinity upgrade for IP, it will be maxed and you will not be able to buy it again its effect should now be that generators are multiplied by (infinity stars)^, rather than the original (infinity stars)^. Anyway, you can now start Infinity Challenge 1, so do that. The next section of the guide becomes visible when you complete Infinity Challenge 1, so information on how to do so is in this section (it is also repeated in the next section).
Infinity challenges (or ICs) are much like normal challenges, except they require more stars to infinity than a normal infinity (you cannot go beyond their star requirement in them whether or not infinity is broken), and after completing them you get some new bonus to something rather than getting an autobuyer and get a multiplier to infinity generators of ^(completed infinity challenges / ) rather than a multiplier to normal generators. Infinity challenges can generally be grouped into the easy ones with no special strategy and the hard ones with special strategy. Unlike the previous normal challenges, they unlock in a particular order, which is also the order you should complete them in.
Infinity Challenge 1: Hard. This is a bunch of normal challenges combined (Normal Challenges 2, 3, 4, 5, 6, and 7), and its strategy is mostly taken from Normal Challenge 7, so follow the strategy given above for that challenge. The differences are that you want to spend at least before prestiging (to build up infinity stars and thus do fewer prestiges, letting you save more purchases for the last prestige), you want to spend at least in each prestige (again, to do fewer prestiges; time in current prestige can be viewed in the Statistics tab, but estimating it should also work), your last prestige should instead be when you reach over stars (because of the goal of being far higher than the goal for Normal Challenge 7), and that at the end you should buy Generator 6 rather than Generator 8, because Generator 8 does not exist due to Normal Challenge 6. Despite Normal Challenge 2 making boosts reset multipliers, boosts are worth buying as soon as you can afford them. You don't have to worry about sacrifice because, due to Normal Challenge 6, you can't do it. Infinity Challenge 1 should take to . It's perhaps worth noting that you can complete this challenge eventually just by buying a Generator 1 and waiting, since it includes Normal Challenge 3, but this will take a day at least.
Infinity challenges (or ICs) are much like normal challenges, except they require more stars to infinity than a normal infinity (you cannot go beyond their star requirement in them whether or not infinity is broken), and after completing them you get some new bonus to something rather than getting an autobuyer and get a multiplier to infinity generators of ^(completed infinity challenges / ) rather than a multiplier to normal generators. Infinity challenges can generally be grouped into the easy ones with no special strategy and the hard ones with special strategy. Unlike the previous normal challenges, they unlock in a particular order, which is also the order you should complete them in.
It's also important to note that as in the previous channel, when you're not in an infinity challenge, you want to set the sacrifice autobuyer to multiplier x and set the prestige autobuyer to multiplier x. Since some infinity challenges will require turning the prestige autobuyer off, it's also important to remember to turn it back on after completing those infinity challenges.
Infinity Challenge 1: Hard. This is a bunch of normal challenges combined (Normal Challenges 2, 3, 4, 5, 6, and 7), and its strategy is mostly taken from Normal Challenge 7, so follow the strategy given above for that challenge. The differences are that you want to spend at least before prestiging (to build up infinity stars and thus do fewer prestiges, letting you save more purchases for the last prestige), you want to spend at least in each prestige (again, to do fewer prestiges; time in current prestige can be viewed in the Statistics tab, but estimating it should also work), your last prestige should instead be when you reach over stars (because of the goal of being far higher than the goal for Normal Challenge 7), and that at the end you should buy Generator 6 rather than Generator 8, because Generator 8 does not exist due to Normal Challenge 6. Despite Normal Challenge 2 making boosts reset multipliers, boosts are worth buying as soon as you can afford them. You don't have to worry about sacrifice because, due to Normal Challenge 6, you can't do it. Infinity Challenge 1 should take to . It's perhaps worth noting that you can complete this challenge eventually just by buying a Generator 1 and waiting, since it includes Normal Challenge 3, but this will take a day at least.
The Infinity Challenge 1 reward uncaps the multiplier to normal generators based on total IP, which, at this point, gives normal generators at least an additional x multiplier. This means that your next few infinities will be very quick; for example, you can now get enough IP to buy Infinity Generator 6 for the first time ( IP) in a infinity that is long (which is a reasonable thing to do strategically if you want). Infinities are now so short that they are a bit limited by autobuyers. In this part of the game, try to infinity for roughly x total IP each time (though it's OK to infinity earlier if that would let you get a new infinity generator that you don't have yet). You can do roughly this (definitely close enough) with the infinity autobuyer by setting its mode to "X times best of last ten" and its input to , though you'll still have to buy infinity upgrades (well, the one of them that isn't yet maxed) and infinity generators. Infinities will get slightly longer over time, going roughly from to , until you unlock Infinity Challenge 2. When you unlock Infinity Challenge 2, infinity and then start it.
Infinity Challenge 2: Easy. Sacrifice formula is stars^, but since prestige is square-rooted there's a fairly big overall nerf. The challenge still doesn't require any special strategy, though. However, it does take roughly .
The Infinity Challenge 2 reward increases the sacrifice formula to stars^, if it's bigger than the old formula (which it usually is). This is equivalent to almost a x multiplier to each normal generator. This will, as before, make your next few infinities far quicker. Also, due to your extra infinity generators making infinity stars increase faster and thus making longer infinities better, start to infinity for x IP rather than x. The length of infinities will increase from (right after IC2 completion) to , until you unlock Infinity Challenge 3. Infinity Challenge 3 is somewhat hard, so it might be worth getting somewhat more IP before starting it, even after you unlock it.
Infinity Challenge 3: Hard. Be very careful about when you prestige; turn the prestige autobuyer off (though you can leave all others on). Prestige for at least , , and prestige power in your first prestiges, in that order; after that, you won't be able to prestige again. It can take up to (mostly spent in the first prestige), but it's shorter if you got more IP before starting it.
Compared to previous IC rewards, the IC3 reward is rather weak. Infinities will still be roughly to long until you unlock IC4 (which should only take a few more infinities).
Infinity Challenge 4: Hard. This infinity challenge is best done with your autobuyers set to trigger only every , and with your prestige autobuyer set in such a way that you gain a significant multiplier each time (setting its mode to time and its input to is good); it then takes roughly . You can slightly speed it up by manually prestiging somewhat earlier for the first few prestiges, or by manually buying things quicker at the start of each prestige, which makes it somewhat shorter.
Since the IC4 reward is roughly linear with time in infinity ( + seconds in infinity / ), it rewards longer infinities. Thus, it is now best to infinity for times best of last ten rather than times. Infinities will still be to long (though remember that you're making roughly twice as much progress per infinity) until you unlock IC5.
Infinity Challenge 5: Easy. This infinity challenge doesn't have any special strategy. The infinity challenge condition means in practice that every prestige starts with a few useless seconds, so you might think that setting your prestige autobuyer to or something like that is good because it will stop you from doing a lot of useless short prestiges, but in reality you can leave it at x and the challenge will take roughly as long as it would otherwise, because you still have to wait for infinity stars to build up. This is a rather fast infinity challenge, taking only roughly .
The IC5 reward is, initially, slightly worse than the IC3 reward, so it doesn't really change much. Continue to infinity for x. Infinities will still be to long until you unlock IC6, in or more infinities.
Infinity Challenge 6: Hard. This infinity challenge requires you to turn your prestige autobuyer off. In this description of IC6 strategy, "prestige formula" refers to the formula for prestige power shown in the main tab (so initially ^, then ^ after you first prestige, then ^ again, and so on). In your first prestige, when the prestige formula is normal (^), get stars, then prestige. Having, for example, times more or less stars than when you prestige is not bad, but having times more or less stars is bad. Prestiging with fewer stars than recommended is bad because you'll have less prestige power than expected, and prestiging with more stars than recommended is bad because it will be hard to prestige again. Right now, prestiging with stars should be fairly easy because your production is slow enough that you won't get to this many stars instantly, but after further resets (such as eternity), when you come back to this challenge with more production, you might have to turn some autobuyers off to prestige with stars. In your second prestige, when the prestige formula is weaker (^), get stars and prestige. In your third prestige, when the prestige formula is normal (^), prestige at stars again. In your fourth prestige, when the prestige formula is weaker (^), you won't be able to prestige again, but you should be able to finish the infinity challenge fairly quickly. This challenge takes , and with this strategy most of that is spent in the second prestige.
The IC6 reward is actually decently strong, somewhat stronger than the IC1 or IC2 rewards were on completion. It won't speed up infinities as much, though, because of the IC4 reward still making long infinities better. Still, infinities should only be roughly to long until you unlock IC7, in or more infinities.
Infinity Challenge 7: Easy. Prestige power is far more important than boosts, which is why this challenge is a nerf. This challenge doesn't require any special strategy, and takes roughly .
The IC7 reward is fairly small; it's slightly larger than the IC5 reward was, but not much larger (it's roughly a x multiplier to normal generators). It's interesting to note that it actually gets smaller as you progress, not just in comparison to your stars but overall. Still, infinities should only be roughly long until you unlock IC8, in or more infinities.
Infinity Challenge 8: Hard. This infinity challenge doesn't take too long but has strategy. First, turn all your autobuyers off, then manually buy each of Generator 1 through Generator 7, then buy max of Generator 8. Then, without turning autobuyers on yet, set autobuyers to buy singles of Generators 1 through Generator 7 and boosts, buy max of Generator 8, sacrifice off or set to some huge unreachable multiplier (like ; the point of this is to not sacrifice at all, so either turning it off or setting it to a multiplier you'll never reach works), and prestige set to x multiplier. Then turn autobuyers on. Once you have IC8 purchases, set your non-prestige autobuyers as if you were playing normally, and either turn your prestige autobuyer off (prestige manually when progress slows down) or set it to . Alternatively, once you have IC8 purchases, set your non-prestige autobuyers as if you were playing normally, and set your prestige autobuyer to x. Either way, you should now be able to complete the challenge without using all your purchases, and without changing the prestige autobuyer. This challenge takes roughly . Remember to change your prestige autobuyer back to x after completing the challenge. It's not clear if doing this challenge is actually worthwhile, given how close eternity is.
The IC8 reward is roughly as strong as the IC7 reward. Infinities should only be roughly to long until you can eternity, in or more infinities.
Unlike stars when you could infinity, IP don't cap at . However, getting enough more to get more than eternity points isn't worth it yet, so eternity for eternity points as soon as you can. You can get to this point from the start of infinity challenges in roughly .
So, you've eternitied. This resets basically everything. You keep your slow autobuyers, and that's basically it. However, with your eternity points (EP) you can, and should, buy an Eternity Generator 1. Eternity generators (EGs) are like normal generators and infinity generators except that they cost eternity points. Eternity stars have two effects: a multiplier and a power. Note that you start with eternity stars at the start of each eternity. Eternity stars and eternity generators reset on eternity to the same extent infinity stars and infinity generators reset on infinity.
Multiplier from eternity stars: (eternity stars)x.
Power from eternity stars: + log(log(eternity stars)) /
You won't want to get more than EP per eternity for a while, but just for reference, here's the EP formula.
EP formula: (total IP this eternity)^
The starting benefits from milestones are below, in the hopes that they will be convenient.
Milestone formulas: ^(min(, eternities)) starting stars, ^(min(, eternities / )) starting IP, min(, eternities)^ starting infinities
The second eternity is much like the first, except far quicker, and generally following the guide above works. Following are the important differences, together with other important things to note.
You should do your first infinity in Normal Challenge 12, because the condition does nothing and you'll get an autobuyer and a small multiplier for it. You don't need to unlock slow autobuyers again, since they're already unlocked. Normal Challenge 1 is comparatively harder, because the multiplier from eternity stars only applies to generator (albeit ^); you may thus want to do Normal Challenge 1 as a medium-difficulty challenge rather than an easy challenge, and do an extra normal infinity instead so you still have Infinity Generator 2 before starting the medium-difficulty challenges. Normal Challenge 2 is a tiny bit more annoying due to not being quicker by as much as the rest of the game is; you may want to do it last, and to do more normal infinities before doing it, but you will be able to buy things more often (every is fine). total infinities is enough to max the multiplier to normal generators from total IP, which helps for that. Right after breaking infinity, the best IP per infinity is somewhat higher; for example, IP on your first infinity after breaking infinity is reasonable. Don't forget to get infinities; this isn't a difference, but it's one of the easier things to forget because not doing it slows down progress rather than stopping it (these infinities will probably be far quicker than before, though, which is a difference). Infinity Challenge 1 doesn't require as much waiting before prestiging; should be more than enough. More generally, almost every infinity challenge is far quicker. For the sake of speed, it may be best to infinity and start an infinity challenge immediately after unlocking it rather than waiting for your infinity autobuyer's requirement.
After Infinity Challenge 1, due to how quick infinities are, it's better to set prestige to than to x. However, note that whenever you set the prestige autobuyer or another reset autobuyer (such as the infinity autobuyer) based on time, if you go offline, ticks will be longer and so the autobuyer may trigger every few ticks, which may not let production build up enough. So if you go offline, you may want to adjust your reset autobuyers to trigger less often or instead be based on multiplier.
Due to eternity stars, setting your infinity autobuyer to x best of last ten is good even just after Infinity Challenge 1, for the rest of the eternity. If you want, you can do slightly better manually early on by doing slightly longer infinities, because of how powerful Infinity Challenge 1 is (also note what was said above about starting an infinity challenge immediately after unlock). Infinity Challenge 4 is not far quicker; it's not worth doing and should be skipped. Because you start with stars, Infinity Challenge 5 doesn't have as much of a delay at the start of every prestige, so you can leave the prestige autobuyer at and it'll be fine. Infinity Challenge 8 is not far quicker because its speed depends on autobuyer speed, and definitely should be skipped.
Note that at this point, if your playstyle is relatively idle, it is possible to get EP by waiting another few hours. If you do this, it's suggested to also get another EP by waiting another few hours, which will end up letting you get Study 3 faster than you otherwise would. It's also suggested to do IC4 and IC8 now, using the strategies from your first eternity. This section of the guide, however, will assume you don't do this and instead get only EP.
Make sure to buy a theorem (in the Studies tab) for stars and to buy another for IP; it's not crucial that you do this now, but you'll have to do it in one of the next eternities (counting this one) and there's no reason not to do it now. Generally, from now on, you should buy theorems with stars and IP as soon as they become affordable, even if this isn't stated explicitly.
Overall, your second eternity can be as short as to .
It is best to spend your next EP (including the you just got) on theorems, for EP and EP (it doesn't really matter whether you buy both theorems at once, or buy the first earlier and the second later). This will give you total theorems, which will let you buy Study 3, which will speed up eternities a lot. So don't buy Eternity Generator 1 again until you have total theorems.
Your third eternity is a lot like the second, except that, from the -eternity eternity milestone, you start with all challenges (but not infinity challenges) completed, with all fast autobuyers, and with infinity broken, and since eternity generators are all multiplied by min(, eternities / ), eternity stars will produce x as fast. The strategy is similar to that for second eternity, except that you don't need to do challenges, and there's thus no reason to do your first infinity in Normal Challenge 12. Remember to set your prestige autobuyer back to x until you complete IC1. You still want to do some early infinities for IP, perhaps until infinities and total IP. Once you're done with those early infinities, you can (though this is not strictly necessary) infinity a few times for to IP per infinity, then do more quick infinities to get up to infinities (infinity length will get down to roughly by the end of this). Infinity Challenge 5 now has basically no delay at the start of each prestige.
Overall, your third eternity can be as short as to .
Your fourth eternity is almost the same as the third, except that, from the -eternity eternity milestone, you can buy an Infinity Generator 1 before you infinity. Again, remember to set your prestige autobuyer back to x until you complete IC1. This eternity will be roughly the same length as the previous one.
Now you can finally buy another theorem for EP and buy Study 3. This will make eternities a lot quicker. Getting infinities is now unnecessary. Also, the -eternity eternity milestone automatically completes ICs, which means you don't need to do them yourself and is thus very helpful. Initially it only completes the first ICs, so you might still have to do IC5 and IC7. You can set your prestige autobuyer to and your infinity autobuyer to x best of last ten, or try to slightly improve on this with manual prestige and infinity. You should still eternity for EP. This eternity should take roughly (maybe slightly quicker), mostly limited by autobuyers and (if you prestige and infinity manually) manual speed.
Now keep doing eternities much like the last. The -eternity eternity milestone gives you some infinities (initially ), which helps a bit but not that much. When you have eternities, you can (and should) get another EG1. The -eternity eternity milestone makes sacrifice not reset generators, which prevents some lag. It also lets you set the sacrifice autobuyer to x, as you should do. At this point, eternities are roughly long. The -eternity eternity milestone is just autobuyers (on by default) and thus is not much of a speedup. The -eternity eternity milestone lets you set the prestige autobuyer to prestige for a x multiplier, which is a very big speedup. You can also set the infinity autobuyer to infinity since total. (That is, set it to the value and the mode "Time since gain was total"; "Time since gain was total" is a helpful autobuyer mode that infinities some amount of time after gained IP reaches total IP.) You'll still need to buy infinity generators until you get autobuyers for them, though. Eternities should now be roughly to long. When you have eternities, you can, and should, buy EG2. After roughly to from eternities, you'll have eternities and thus will have completed all eternity milestones.
In this section of the game, you'll start to have several studies at once and to need to determine which studies are best. Generally, a multiplier to infinity generators is times better than the same multiplier to normal generators, and a multiplier to eternity generators is slightly better than (the highest eternity generator you've bought any of) times better than the same multiplier to infinity generators. Of course, the studies that multiply normal generators generally have the biggest multipliers, and those that multiply eternity generators generally have the smallest multipliers, so determining which is best requires some mental arithemetic (and of course, multipliers should be compared logarithmically; a x multiplier is only x as good as a x multiplier to the same thing, since is ^).
First, turn off your eternity autobuyer. It's good in general, but there are advantages to doing a somewhat long eternity now. It gives less EP/second, but it makes Study 3 stronger and lets you get more theorems. Getting to IP should be enough to get another theorem with stars, get another theorem with IP, and noticeably increase Study 3's multiplier without taking too long ( to ), so do that. Note that you should buy the theorems with stars and IP as soon as you can afford them, as stated above. Then start doing quick eternities for EP again. In addition to this being efficient for EP/second, it makes EGs slightly stronger via more eternities, and gives you more starting benefits (in particular starting IP), which makes eternities even quicker.
As for what to spend your EP on, first buy the first eternity upgrade once, then start saving for theorems with EP. After buying a theorem for EP and another theorem for EP, you can buy Study 4 to speed up quick eternities even more.
At some point soon (you could do this immediately, or make it slightly faster by getting more eternities first), you should try to do another longer eternity to get more theorems. For this longer eternity, you'll want Studies 2 and 3, rather than 3 and 4, so respec your studies and buy Studies 2 and 3. You should be able to get more theorems with stars and also another theorem with infinity points, for total theorems, fairly quickly. After roughly (right before the second theorem bought with stars) you should switch the infinity autobuyer to since total, since IP gain will start to slow down. (Remember, this means to use the "Time since gain was total" mode, as explained at the end of the "Eternity to completing all eternity milestones" previous guide section.) Overall this eternity should take roughly . Remember to set your eternity autobuyer back to EP, and also you'll want to respec and buy Studies 3 and 4. Additionally, you can now set the infinity autobuyer to . Furthermore, soon you'll be able to buy another theorem for EP. Do so, and buy Study 2 (in addition to Studies 3 and 4, which you already have).
Eternities are useful enough that you should try to get of them right now. They should only take roughly each. Buy EG2 again, then buy EG1 as it becomes affordable. From now on, advice about buying eternity upgrades and generators is similar to that about buying infinity upgrades and generators. The third and second upgrades start out good (the third especially so) but get worse per purchase; the first starts out bad but gets better per purchase (though it can only be purchased times, at which point its effect is ^, making the per-purchase eternity generator multiplier x).
Eternities will start to be long once you have roughly of them. This makes it even easier to get to eternities.
Once you have eternities, keep doing quick -EP eternities, and save EP to buy another theorem for EP. Once you can buy that theorem, buy it (giving you total theorems), and do another longer eternity with Studies 1, 2, and 3, and with your infinity autobuyer set to . As before, switch the infinity autobuyer to after . You should be able to, within roughly from the start of the eternity, buy another theorem with stars and more theorems with IP, for a total of theorems. You can now buy Study 4, so do that. Stay in this eternity until you can buy another theorem with stars, for a total of theorems.
Now you can do slightly longer eternities for maximum EP/second. Set your infinity autobuyer to since total and your eternity autobuyer to EP. You should get roughly EP/second by doing this. Save EP for EG3 ( EP), after buying which you should get EP/second, then for the first eternity upgrade for the second time ( EP). Then buy all eternity generators costing up to EP in any order you want. By the end of this, you'll be getting roughly EP/second.
Now save EP to buy another theorem with EP. After buying that theorem, do eternities for EP (and infinities for IP with the mode being amount) until you have eternities, to make Study 7 stronger. For these eternities, use Studies 3, 4, and 7. Each eternity should be roughly to long. With the EP you're getting, buy the second eternity upgrade (which is very good), then the first eternity upgrade (which is not as good), and then eternity generators as they become affordable.
After these eternities, change the infinity autobuyer to since total, turn the eternity autobuyer off, and buy Studies 5, 6, and 7. You'll be doing another longer eternity, since longer eternities are now the best way to get more EP/second.
You will soon get more than boosts and thus start producing boost power. Each boost reached in the current eternity above boosts (that is, max(0, boosts reached this eternity - ) boosts)) produces boost power per second, so boost power gain is max(0, boosts reached this eternity - ) * ) per second. Losing boosts due to prestige or infinity does not decrease boost power production. Boost power resets on eternity (as does boost power production), but not on infinity. Boost power provides a multiplier to boosts based on its amount ( + log(amount)). You also get theorems (which you keep on eternity) at certain thresholds of boost power. Boost power makes long eternities good and is eventually a major reason that they become better.
Buy theorems with stars and IP as they become affordable. When you get total theorems, buy Study 8. Roughly after the start of the eternity, you should be able to eternity for EP. Do that, and buy the third eternity upgrade (which is at this point even better than EG4). If you have a small amount of extra EP, buy cheap eternity generators.
Do another longer eternity, with the infinity autobuyer set to since total again. After roughly , you should be able to again eternity for EP. Do that, and buy EG4. Do another eternity for EP (which should take roughly ), and buy the first eternity upgrade and another theorem for EP.
In your next eternity, you should get EP, which will take roughly . During this eternity, you'll get another theorem with IP, for a total of theorems. Spend the EP you get on unlocking the Eternity Producer. You can reach this point roughly after getting all eternity milestones.
Studies to use so far:
| Total EP (roughly) | Total theorems | Studies | Notes | |
| 3 | You should have this before getting all eternity milestones | |||
| 3, 4 | For quick eternities ( EP each) | |||
| 2, 3 | For getting more theorems | |||
| 2, 3, 4 | For quick eternities | |||
| 1, 2, 3 | For getting more theorems | |||
| 1, 2, 3, 4 | In same eternity as previous | |||
| 3, 4, 7 | For quick eternities | |||
| 5, 6, 7 | After eternities (long eternities are now best for EP) | |||
| 5, 6, 7, 8 | In same eternity as previous |
The Eternity Producer produces eternities, and gives a multiplier to eternity generators based on their amount. Upgrades for it (to produce more eternities and increase the multiplier) are generally fairly minor: worse than an eternity upgrade with the same cost, but better than an eternity generator. Note that with more eternities (from, for example, waiting overnight), progress will be significantly faster and the time it takes to do things after getting a large number of additional eternities will likely be less than the time given below.
Do another long eternity (roughly ) to get another theorem with stars and another extra theorem from boost power, increasing your total theorems to . As before, set the infinity autobuyer to since total. Now do an eternity (roughly long) for EP with Studies 5, 6, 8, and 10. Buy the second eternity upgrade (rather than the first). At this point, you should replace Study 10 with Study 9 instead. Do another eternity for EP, which should take roughly , and buy the first eternity upgrade. Do another eternity for EP, which should take roughly , and buy EG5.
From now on, you can choose when to do eternities yourself. Generally try to get between x and x your total EP in each eternity, with smaller multipliers like x generally being better early and larger multipliers like x generally being better late. If you're about to be able to get a theorem, wait for it. Generally, almost all eternities should be less than .
Once you have theorems, you should switch to using Studies 3, 5, 6, 7, and 8 (that is, losing 9 and getting 3 and 7); you can afford them now, and 3 and 7 are each almost as strong as 9 is. (You'll get theorems when you buy the theorem costing EP, unless you've already gotten another theorem from boost power.) While trying to get EP (or, slightly earlier, EP), there's a small wall and so you'll probably need to do a long eternity (); during this eternity you should be able to get a theorem for boost power, perhaps by making the eternity somewhat longer (). Getting this theorem (and the theorem for EP) will let you buy Study 9 in addition to Studies 5, 6, 7, and 8, instead of Study 3; Study 9 is somewhat better than Study 3 at this point, so this is good. After roughly EP, eternities should become a lot faster than they were immediately before (they should now be to long), and you should be able to get as far as buying the second eternity upgrade for EP in roughly . Once you buy the second eternity upgrade for EP, you should do an eternity with Studies 5, 6, 8, and 9 and unlock Eternity Challenge 1 when possible. After unlocking Eternity Challenge 1, start it. You can reach this point in roughly from unlocking the Eternity Producer.
The next section of the guide becomes visible when you complete Eternity Challenge 1 for the first time, so information on how to do so is in this section (it is also repeated in the next section).
Eternity challenges (or ECs) are somewhat like challenges and infinity challenges. There are several important differences, however. Eternity challenges require a certain amount of IP to eternity and complete the challenge, rather than a certain amount of stars to infinity and complete the challenge. They have infinity-challenge-like rewards that make various things stronger, but they can each be completed up to times, having a higher goal amount of IP each time and getting a stronger reward for each time completed. Finally, they have a requirement (depending on times completed) and a cost in theorems (fixed for each challenge) to unlock, and must be explicitly unlocked to be entered. Note that you can respec studies in an eternity challenge if you want. You will get the theorems you paid to unlock an eternity challenge back when you complete it or respec your eternity challenge (which will lock it again).
You can do EC1 the first time (EC1x1) at EP, unlocking it with Studies 5, 6, 8, and 9. Once you unlock it, respec your studies and buy Studies 7, 8, 10, and 12. Within EC1x1, you should infinity for x best of last ten rather than, for example, every . Unless you are speedrunning (and thus have a low eternity count), this challenge will likely take less than to complete (possibly as short as ); even if you are speedrunning, it will likely take under .
Studies to use in this phase:
| Total EP (roughly) | Total theorems | Eternity Challenge | Studies | Notes |
| 5, 6, 7, 8 | ||||
| 5, 6, 8, 10 | ||||
| 5, 6, 8, 9 | ||||
| 3, 5, 6, 7, 8 | ||||
| 5, 6, 7, 8, 9 | ||||
| EC1x1 | unlock 5, 6, 8, 9 complete 7, 8, 10, 12 |
Eternity challenges (or ECs) are somewhat like challenges and infinity challenges. There are several important differences, however. Eternity challenges require a certain amount of IP to eternity and complete the challenge, rather than a certain amount of stars to infinity and complete the challenge. They have infinity-challenge-like rewards that make various things stronger, but they can each be completed up to times, having a higher goal amount of IP each time and getting a stronger reward for each time completed. Finally, they have a requirement (depending on times completed) and a cost in theorems (fixed for each challenge) to unlock, and must be explicitly unlocked to be entered. Note that you can respec studies in an eternity challenge if you want. You will get the theorems you paid to unlock an eternity challenge back when you complete it or respec your eternity challenge (which will lock it again).
To recap, you can do EC1 the first time (EC1x1) at EP, unlocking it with Studies 5, 6, 8, and 9. Once you unlock it, respec your studies and buy Studies 7, 8, 10, and 12. Within EC1x1, you should infinity for x best of last ten rather than, for example, every . Unless you are speedrunning (and thus have a low eternity count), this challenge will likely take less than to complete (possibly as short as ); even if you are speedrunning, it will likely take under .
Switch back to infinities that are long and Studies 5, 6, 7, 8, and 9 after completing EC1x1. You should be able to get EP and buy EG8 with it in an eternity between and long. EG8 will make eternities somewhat faster (). Buying the theorem costing EP (which gives you total theorems), you can try using Studies 2, 5, 6, 8, and 9 (that is, replacing 7 by 2) if you want, or similarly, Studies 3, 5, 6, 8, and 9; these studies may give you x to x the EP you would get otherwise, but they shouldn't make much of a difference.
When (slightly later) you get total theorems, replace Study 7 (or Study 2 or 3, if you were using one of those rather than 7) by Study 10, making your studies be 5, 6, 8, 9, and 10. Once you get roughly EP, you can do EC2x1 (EC2 for the first time). Unlock it with Studies 5, 6, 7, 8, and 9, and complete it with Studies 6, 8, 9, and 10. Unlocking and completing it should each take less than . After completing EC2x1, switch back to Studies 5, 6, 8, 9, and 10. At this point, your eternities should generally be for between x and x total EP. Getting EP is somewhat hard (it requires an eternity that is long), but once you get that much EP you can do EC1x2 (EC1 for the second time). Unlock with 5, 6, 7, 8, 9 (which should take roughly ), and complete with 8, 10, 11, and 12 (if you already have eternities, you can use 8, 9, 10, and 12 instead and thus not have to wait for 11 to build up). As before, infinity for x best of last ten within EC1x2. EC1x2 will take roughly to complete.
Next, for maximum speed, you should actually do EC4x1. EC3x1 has a slightly lower unlock requirement and cost than EC4x1, but is significantly harder (though both have similar requirements for completion). I do regret that EC4x1 comes before EC3x1, though in general completion x of EC4 is harder than completion x of EC3. For EC4x1, you should get total EP (via a eternity roughly long), and unlock and complete with 5, 6, 7, 8, 9. When doing EC4x1, wait before your first infinity to let boost power and eternity stars build up, and then do infinities that are long. You should easily be able to complete EC4x1 in roughly . Then do EC3x1. Unlock with 5, 6, 7, 8, 9, and complete with 3, 8, 9, 12. In EC3, unusually for an EC, longer infinities give less IP per time than shorter infinities, so it is very important to set the infinity autobuyer to some mode which can do short infinities, such as fraction of peak log/sec. This applies to all EC3 completions. ( fraction of peak log/sec is a decent mode for the infinity autobuyer elsewhere, but in this specific case I am editing the guide (written before this mode existed) to suggest it due to its importance.) EC3x1 should take at most roughly , though it is faster if you have more eternities; it will take only to if you have eternities. (In this case, it may be better to do it first.)
After doing EC3x1 and EC4x1 (whatever order you do them in), you'll have a burst of progress; it's now better to do eternities for x to x in general, though your first eternity after EC3x1 and EC4x1 might give you even more EP than that (your eternities should be at least long). At roughly total EP (at which point progress should still be rather fast, with eternities lasting less than ) do EC1x3, unlock 5, 6, 8, 9, 10, complete 3, 8, 9, 10, 12, infinity autobuyer x. EC1x3 should take roughly . With some eternities to in length (the later ones being longer), you should be able to get to total theorems at roughly EP, at which point you can buy Study 7. Once you get EP ( total theorems), several more ECs become possible, specifically EC1x4 and EC3x2. You can do these in either order; doing EC1x4 first is probably slightly faster, but the times are comparable, and once you do one you should do the other without getting more EP first. When you do EC1x4, unlock 5, 6, 8, 9, 10, complete 3, 8, 9, 10, 12, infinity x. EC1x4, if you do it first, should take to . When you do EC3x2, unlock 5, 6, 8, 9, 10, complete 3, 7, 8, 9, 12, infinity fraction of peak log/sec (as with EC3x1). EC3x2, if you do it second, should take to . In general, even-numbered ECs are harder than odd-numbered ECs, which is why EC3x2 can be done before EC2x2. You will now have eternity challenge completions, which will allow you to produce boost power faster.
After doing EC1x4 and EC3x2, you'll have another burst of progress; your first eternity might give you x EP in . In fact, eternities from now on will often take only . Once you get EP, do EC2x2, unlock 5, 6, 8, 9, 10, complete 6, 8, 9, 10, 12. It should take only to complete; it's only being done now as opposed to earlier because progress was so fast. You should now have total theorems; replace Study 7 by Study 12, for 5, 6, 8, 9, 10, 12. At roughly EP (you might need an eternity long to get this much EP), do EC3x3, unlock 5, 6, 8, 9, 10, complete 3, 7, 8, 9, 12, infinity fraction of peak log/sec again. The production of boost power helps a lot in this challenge. EC3x3 should take to . At this point, eternities will get somewhat longer, getting as long as to before you get EP. When you get EP, you can do EC4x2, unlock () 1, 5, 6, 7, 8, 9, and complete () 3, 5, 6, 7, 8, 9, (for completion) first infinities for and IP (each roughly ), following infinities . When you get EP, do EC2x3, unlock 5, 6, 8, 9, 10, 12, complete 2, 3, 6, 8, 9, 10 (). When you get EP, do EC3x4, unlock 5, 6, 8, 9, 10, 12, complete 3, 4, 7, 8, 9, 12 ().
After EC3x4, change your studies to 1, 2, 3, 5, 6, 8, 9. (Note that heuristics on which studies to use may have suggested using 1 and 2 before this point; this is slightly worse than expected, for unclear reasons that aren't currently known.) At this point, progress is so fast that you may want to do eternities long if you can gain x EP with them; from this point on, every eternity challenge completion will be a rather large benefit to progress, and progress will slow down somewhat directly before the next eternity challenge completion. At EP, do EC2x4, unlock 1, 3, 5, 6, 8, 9 (), complete 3, 6, 8, 9, 10, 12 (). At EP, do EC5x1, unlock 1, 3, 5, 6, 8, 9, complete 1, 2, 3, 4, 5, 6, 8 (). At EP, do EC6x1, unlock whatever (you have the unlock requirement already), complete 3, 5, 6, 8, 9, 10 (). You can get here within roughly from starting EC1x1.
After EC6x1, you'll have EC completions, which will give a huge multiplier (x initially) to eternity gain. You'll soon (in to ) be able to gain permanence (or slightly more). Do so. Your first priority should be getting permanence quicker, so get the first permanence upgrade so that you can get permanence x faster. When you can next get permanence in roughly , get the fourth permanence upgrade so you can get permanence roughly x faster. Then get permanence (which takes roughly ) and buy the second and third permanence upgrades. While you're waiting for permanence, you can gain some EP. After buying all the permanence upgrades for the first time, you can wait to gain permanence until you can gain enough to buy each upgrade once; it's unclear if this is the most efficient thing to do but it's easier than gaining permanence more frequently. Roughly after buying all the permanence upgrades for the first time, you should be able to get EP and total theorems. When you do, do EC4x3, unlock and complete 1, 2, 3, 5, 6, 8, 9, infinity . EC4x3 should be very easy. When you get a theorem for EP giving you total theorems, buy Study 4, making your studies be 1, 2, 3, 4, 5, 6, 8, 9. Once you buy each permanence upgrade times (so the cost of each is permanence), switch your studies to 1, 5, 6, 8, 9, 10, 12; this is better now since the third permanence upgrade is making third-row studies stronger.
Once you get EP, at which point you should have theorems and current permanence upgrade costs should be at least per upgrade, do EC5x2, unlock and complete 1, 2, 3, 5, 6, 8, 9 (completing takes ). Once you get EP, with permanence upgrade costs at least , do EC7x1, unlock whatever, complete 5, 6, 8, 9, 10, 12 (). Once you get EP, with permanence upgrade costs at least , do EC5x3, unlock and complete 1, 3, 5, 6, 8, 9, 10 (this isn't optimal for unlocking but unlocking is very easy so it doesn't matter, completing takes ). Once you get theorems, buy Study 7, to make your studies be 1, 5, 6, 7, 8, 9, 10, 12.
This is a decent place to get the theorem requiring boost power, if you don't have it from a long run. This is because that theorem makes it easier to do EC6x2. It will take a single eternity of length at least roughly to get this theorem. Once you get EP, with permanence upgrade costs at least (though with the extra theorem study setup, costs may be needed), do EC6x2 (whether or not you have the theorem from boost power). Studies for it are unlock whatever, complete 3, 5, 6, 8, 9, 10, 12 () with the theorem or 5, 6, 8, 9, 10, 11, 12 () without it. Note that this guide was written assuming you didn't have this theorem, so other things may also be easier for a while if you have it.
Once you get total theorems (which, if you got the boost power theorem, will happen right after completing EC6x2), replace Study 7 by Study 2, to make your studies be 1, 2, 5, 6, 8, 9, 10, 12. Once you get EP, with permanence upgrade costs at least , do EC5x4, unlock and complete 1, 3, 5, 6, 8, 9, 10 (both quick). Once you can unlock EC7x2 ( EP), with permanence upgrade costs at least , do EC7x2, unlock whatever, complete 5, 6, 8, 9, 10, 11, 12 (). At roughly EP, replace Study 2 by Study 11 (because eternities are longer than they were before), to make your studies be 1, 5, 6, 8, 9, 10, 11, 12. At this point, since you have Study 11, it's reasonable to do longer eternities that still gain a lot of EP, such as, for example, an eternity long for x EP.
Once you have EP (permanence upgrade costs will probably be at least but it doesn't matter), do EC8x1, unlock 9, 10, 11, 12, complete 1, 2, 3, 4, 5, 6, 7, 8 (). Note that it was useful to get EP before EC8x1, even though eternity generators are disabled, because of Eternity Upgrade 2, Study 3 (this depends on total stars, but total EP and total stars are closely related), and the Eternity Challenge 7 reward. Doing EC8x1 with much less EP than recommended here will likely take a long time.
You now have EC completions and gain IP without needing to infinity, so you can turn your infinity autobuyer off. You can also now view the chroma tab, but it won't be useful for a while. Do EC4x4, unlock and complete whatever (EC4x4 is so easy that you don't need any studies). Replace Study 11 by Study 2 again, since now that you don't need to infinity eternities are shorter (your first few eternities after completing EC8x1 and EC4x4 can be less than ), making your studies be 1, 2, 5, 6, 8, 9, 10, 12. At roughly EP, however, eternities get long enough that it is again better to replace Study 2 by Study 11, making your studies be 1, 5, 6, 8, 9, 10, 11, 12. Once you get EP, with permanence upgrade costs at least , do EC6x3, unlock whatever, complete 5, 6, 8, 9, 10, 11, 12 (). Replace Study 11 by Study 2, because eternities are quick. Once you get EP (which should take at most ), with permanence upgrade costs at least (as before), do EC7x3, unlock whatever, complete 3, 5, 6, 8, 9, 10, 12 (less than ). At roughly EP, switch back from Study 2 to Study 11 because eternities are longer. If you don't have the theorem requiring boost power yet (from just before EC6x2 or from elsewhere), this is a good place to get it; it's fairly quick to get and it helps a little. Once you get EP, with permanence upgrade costs at least , do EC7x4, unlock whatever, complete 3, 5, 6, 8, 9, 10, 12 (). You should now have total theorems. Switch your studies to 1, 2, 3, 5, 6, 8, 9, 10, 12. When you get total theorems, switch to 1, 2, 5, 6, 8, 9, 10, 11, 12 because eternities are getting longer and you can afford it. Once you get EP, do EC8x2, unlock 9, 10, 11, 12, complete 1, 2, 3, 4, 5, 6, 7, 8 ().
Fairly soon, you should get enough EP ( EP) to unlock chroma. Do it. You should have completed all ECs times, except for EC6 ( times) and EC8 ( times). You can get here in roughly from having EC completions, or from starting EC1x1.
Studies to use in this phase:
| Total EP (roughly) | Total theorems | Permanence upgrade costs | Eternity Challenge | Studies | Notes |
| 5, 6, 7, 8, 9 | |||||
| EC1x1 | unlock 5, 6, 8, 9 complete 7, 8, 10, 12 |
Infinity autobuyer x best of last ten | |||
| 5, 6, 7, 8, 9 | As before | ||||
| 5, 6, 8, 9, 10 | |||||
| EC2x1 | unlock 5, 6, 7, 8, 9 complete 6, 8, 9, 10 |
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| 5, 6, 8, 9, 10 | As before | ||||
| EC1x2 | unlock 5, 6, 7, 8, 9 complete 8, 10, 11, 12 |
Infinity autobuyer x, takes , complete with 8, 9, 10, 12 if you have eternities | |||
| 5, 6, 8, 9, 10 | As before | ||||
| EC4x1 | unlock and complete 5, 6, 7, 8, 9 | First infinity , then ; could swap with EC3x1 | |||
| EC3x1 | unlock 5, 6, 7, 8, 9 complete 3, 8, 9, 12 |
Infinity autobuyer fraction of peak log/sec, gets faster with more eternities, do immediately after EC4x1 (or even before) | |||
| 5, 6, 8, 9, 10 | As before | ||||
| EC1x3 | unlock 5, 6, 8, 9, 10 complete 3, 8, 9, 10, 12 |
Infinity autobuyer x | |||
| 5, 6, 8, 9, 10 | As before | ||||
| 5, 6, 7, 8, 9, 10 | |||||
| EC1x4 | unlock 5, 6, 8, 9, 10 complete 3, 8, 9, 10, 12 |
Infinity autobuyer x; could swap with EC3x2 | |||
| EC3x2 | unlock 5, 6, 8, 9, 10 complete 3, 7, 8, 9, 12 |
Infinity autobuyer fraction of peak log/sec, do immediately after EC1x4 (or even before) | |||
| 5, 6, 7, 8, 9, 10 | As before | ||||
| EC2x2 | unlock 5, 6, 8, 9, 10 complete 6, 8, 9, 10, 12 |
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| 5, 6, 8, 9, 10, 12 | |||||
| EC3x3 | unlock 5, 6, 8, 9, 10 complete 3, 7, 8, 9, 12 |
Infinity autobuyer fraction of peak log/sec | |||
| 5, 6, 8, 9, 10, 12 | As before | ||||
| EC4x2 | unlock 1, 5, 6, 7, 8, 9 complete 3, 5, 6, 7, 8, 9 |
Unlock is a bit slow for an EC unlock (), first infinities , then | |||
| 5, 6, 8, 9, 10, 12 | As before | ||||
| EC2x3 | unlock 5, 6, 8, 9, 10, 12 complete 2, 3, 6, 8, 9, 10 |
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| 5, 6, 8, 9, 10, 12 | As before | ||||
| EC3x4 | unlock 5, 6, 8, 9, 10, 12 complete 3, 4, 7, 8, 9, 12 |
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| 1, 2, 3, 5, 6, 8, 9 | |||||
| EC2x4 | unlock 1, 3, 5, 6, 8, 9 complete 3, 6, 8, 9, 10, 12 |
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| 1, 2, 3, 5, 6, 8, 9 | As before | ||||
| EC5x1 | unlock 1, 3, 5, 6, 8, 9 complete 1, 2, 3, 4, 5, 6, 8 |
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| 1, 2, 3, 5, 6, 8, 9 | As before | ||||
| EC6x1 | unlock whatever complete 3, 5, 6, 8, 9, 10 |
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| 1, 2, 3, 5, 6, 8, 9 | As before | ||||
| EC4x3 | unlock and complete 1, 2, 3, 5, 6, 8, 9 | ||||
| 1, 2, 3, 5, 6, 8, 9 | As before | ||||
| 1, 2, 3, 4, 5, 6, 8, 9 | |||||
| 1, 5, 6, 8, 9, 10, 12 | |||||
| EC5x2 | unlock and complete 1, 2, 3, 5, 6, 8, 9 | ||||
| 1, 5, 6, 8, 9, 10, 12 | As before | ||||
| EC7x1 | unlock whatever complete 5, 6, 8, 9, 10, 12 |
||||
| 1, 5, 6, 8, 9, 10, 12 | As before | ||||
| EC5x3 | unlock and complete 1, 3, 5, 6, 8, 9, 10 | ||||
| 1, 5, 6, 8, 9, 10, 12 | As before | ||||
| 1, 5, 6, 7, 8, 9, 10, 12 | |||||
| EC6x2 | unlock whatever complete 5, 6, 8, 9, 10, 11, 12 |
Can instead complete with 3, 5, 6, 8, 9, 10, 12 if you have theorems due to a theorem from boost power | |||
| 1, 5, 6, 7, 8, 9, 10, 12 | As before | ||||
| 1, 2, 5, 6, 8, 9, 10, 12 | |||||
| EC5x4 | unlock and complete 1, 3, 5, 6, 8, 9, 10 | ||||
| 1, 2, 5, 6, 8, 9, 10, 12 | As before | ||||
| EC7x2 | unlock whatever complete 5, 6, 8, 9, 10, 11, 12 |
||||
| 1, 2, 5, 6, 8, 9, 10, 12 | As before | ||||
| 1, 5, 6, 8, 9, 10, 11, 12 | |||||
| EC8x1 | unlock 9, 10, 11, 12 complete 1, 2, 3, 4, 5, 6, 7, 8 |
EP is useful in EC8x1 for Eternity Upgrade 2, Study 3, and EC7 reward | |||
| EC4x4 | unlock and complete whatever | Do immediately after EC8x1 | |||
| 1, 2, 5, 6, 8, 9, 10, 12 | |||||
| 1, 5, 6, 8, 9, 10, 11, 12 | |||||
| EC6x3 | unlock whatever complete 5, 6, 8, 9, 10, 11, 12 |
||||
| 1, 2, 5, 6, 8, 9, 10, 12 | |||||
| EC7x3 | unlock whatever complete 3, 5, 6, 8, 9, 10, 12 |
||||
| 1, 2, 5, 6, 8, 9, 10, 12 | As before | ||||
| 1, 5, 6, 8, 9, 10, 11, 12 | |||||
| EC7x4 | unlock whatever complete 3, 5, 6, 8, 9, 10, 12 |
||||
| 1, 2, 3, 5, 6, 8, 9, 10, 12 | |||||
| 1, 2, 5, 6, 8, 9, 10, 11, 12 | |||||
| EC8x2 | unlock 9, 10, 11, 12 complete 1, 2, 3, 4, 5, 6, 7, 8 |
||||
| 1, 2, 5, 6, 8, 9, 10, 11, 12 | As before |
Chroma works as follows. Chroma builds up over time in an eternity and resets on eternity, getting times closer to the cap every (cap / ( * buildup speed)) seconds. Alternatively, as a formula, chroma is given below.
chroma = cap * ( - ^(- * time in eternity * buildup speed / cap)).
Since chroma builds up over an eternity, it is best to wait for it to build up when you unlock it, though you can gain permanence while waiting. In the eternity that you unlock it, you should try to get chroma and thus grey. This will take roughly . After this, you should be able to do quick eternities each gaining you a lot of EP, and it is thus best to replace Study 11 by Study 3, making your studies be 1, 2, 3, 5, 6, 8, 9, 10, 12. At roughly EP, it's best to switch back to Study 11. Only a few eternities later, at EP, it's best to do a long eternity for some additional grey. You should try to get grey, which will take roughly . After that, keep gaining more EP. Once you get EP, do EC8x3, unlock 9, 10, 11, 12, complete 1, 2, 3, 4, 5, 6, 7, 8 (). Then do EC6x4, unlock and complete whatever (it's so easy to complete that you don't need any studies).
You should soon be able to get EP to unlock purple, without any very long eternities. Unlock purple, start producing purple, and do an eternity long enough to let you get purple (which should take roughly ). Note that from here on, specific amounts of colors to get and orders in which to get them are largely suggestions (though you may have trouble getting EP if you get less than suggested). If you're getting one color right after getting another, you should get orange (which you unlock later) first and purple first except for orange, but apart from that it's mostly up to you. Anyway, after getting some purple, you should quickly be able to get EP, at which point you can do EC8x4, unlock 9, 10, 11, 12, complete 1, 2, 3, 4, 5, 6, 7, 8 (). Now you will have all eternity challenges done, which gives you autobuyers for the things you'd otherwise buy every eternity with EP. You should be able to get here from unlocking chroma in .
When you have EP, you should do another long eternity to get grey, which takes roughly . Even though you have more grey than purple at this point, grey is more useful and thus more worth producing.
You should soon be able to get EP to unlock orange. Unlock orange, start producing orange, and do an eternity long enough to let you get orange (which should take roughly ). Then get purple (which should also take roughly ). Then keep gaining EP. From here on eternities should be roughly as long as it takes to make Study 11 cap, which is currently roughly but will decrease with additional EP and thus additional eternity stars. You can in fact set your eternity autobuyer to time and get more EP automatically, due to your eternity generator autobuyers and other similar autobuyers. When you get EP, you should get grey (which should take ). Then keep gaining EP until EP, at which point you should do another longer eternity to get grey (which will take roughly ).
It will be somewhat hard to get EP to unlock cyan (permanence upgrade costs will probably be ). Roughly when you unlock cyan, you should get enough theorems to buy Study 3, so do that. You should be able to get here from completing all eternity challenges in .
When you unlock cyan, first get cyan, which should take roughly . Then keep getting EP. Once you get EP, get orange (which takes roughly ) and then cyan (which takes roughly another ). Then keep getting more EP. When you get EP, then get grey (). Then keep gaining EP. When you get EP, get orange (), then purple, and then cyan (both also each). At EP, get grey, which should take roughly . When you get EP, get of orange, purple, cyan, and grey in that order, each taking roughly .
When you get EP, unlock green and start producing it. Buy Study 4 and Study 7 as they become affordable. After you buy them, you'll be able to buy fourth-row studies. For now, buy only Study 16. Once you've bought Study 16 at least once, create a study preset at the bottom of the Studies tab and call it "Chroma". You'll always want to use this preset for gaining chroma. Once the next theorem from green is within of the chroma cap, or is over the chroma cap, stop producing green. Then create a preset and edit its studies to 1,2,3,4,5,6,7,8,9,10,11,12&s9,10,9,0. This preset will buy roughly the same amount of Studies 13, 14, and 15, except it will be slightly more willing to buy Study 14. Call this preset "Push". You'll always want to use this preset when you're trying to gain EP rather than chroma (well, as long as you have at least theorems, which you do).
At EP, get of each color, in the order orange, purple, green, cyan, grey ( for each). Remember to use the Chroma preset and turn your eternity autobuyer off. Then use Push to gain more EP. At EP, gain of each color, again in the order orange, purple, green, cyan, grey ( to each). At EP, produce of each color ( to for each). At , get of each color ( each). You should soon be able to complexity for complexity points. Do so as soon as you can. You should be able to get to this point from unlocking cyan in roughly , or from unlocking chroma in roughly .
Studies to use in (and just before) this phase (pre-green):
| Total EP (roughly) | Total theorems | Eternity Challenge | Studies | Notes |
| 1, 2, 5, 6, 8, 9, 10, 11, 12 | ||||
| EC8x2 | unlock 9, 10, 11, 12 complete 1, 2, 3, 4, 5, 6, 7, 8 |
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| 1, 2, 5, 6, 8, 9, 10, 11, 12 | As before | |||
| 1, 2, 3, 5, 6, 8, 9, 10, 12 | Use this after getting grey | |||
| 1, 2, 5, 6, 8, 9, 10, 11, 12 | ||||
| EC8x3 | unlock 9, 10, 11, 12 complete 1, 2, 3, 4, 5, 6, 7, 8 |
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| EC6x4 | unlock and complete whatever | Do immediately after EC8x3 | ||
| 1, 2, 5, 6, 8, 9, 10, 11, 12 | As before | |||
| EC8x4 | unlock 9, 10, 11, 12 complete 1, 2, 3, 4, 5, 6, 7, 8 |
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| 1, 2, 5, 6, 8, 9, 10, 11, 12 | As before | |||
| 1, 2, 3, 5, 6, 8, 9, 10, 11, 12 | At this point you should have extra theorems from boost power |
So, you've complexitied. As with eternity, this resets basically everything. You keep your slow autobuyers, and that's basically it. However, you do have complexity points (ℂP) and Complexity Challenge 1 (ℂC1) completion. Complexity challenges will become more relevant and thus more discussed later. For now you can ignore them.
With your ℂP, you can, and should, buy a Complexity Generator 1. Complexity generators (ℂGs) are like previous generators except that they cost complexity points. Complexity stars have a single effect, which makes complexity challenge rewards stronger. Note that you start with complexity stars at the start of each complexity. Note also that before you eternity you have eternity stars, but they don't do anything until you eternity. Complexity generators reset on complexity as eternity generators do on eternity.
Multiplier to complexity challenge rewards from complexity stars: (log(complexity stars)^)x.
You won't want to get more than ℂP per complexity for a while, but just for reference, here's the ℂP formula.
ℂP formula: (total EP this complexity)^
In addition to affected complexity generator multipliers, complexities do two other things. They let you automatically complete an EC tier every / min(, complexities) seconds, and they multiply chroma buildup speed and permanence gain by ^(min(, complexities)^) (this also decreases the required eternities to gain permanence).
Note that the automatically completed EC tier will be a tier of the first EC you do not yet have completions of, regardless of which ECs you can unlock, which EC is currently unlocked, or which EC if any you are currently in.
The second complexity is so much quicker than the first that it feels qualitatively different in many areas, but much of the pre-complexity guide still applies. You should assume the pre-complexity guide applies unless an alternative is presented, or more accurately and generally, assume that you should do whatever you should have done in the previous complexity. So if something is mentioned to have changed in third complexity and nowhere else, you should do it in the old pre-complexity way for the first and second complexities and in the new way for all others.
The first infinity is much like the first infinity of the second eternity, except even faster, especially after you prestige. After you infinity, buy things in the same order as before, but do infinities before doing any challenges. At this point all the challenges should be very easy. Some of the challenges are hard in the sense that they might take ; Normal Challenge 2 and Normal Challenge 7 are hard only because they still require autobuyers to be off, Normal Challenge 3 is hard due to remaining slow initially, and Normal Challenge 10 is hard because it still requires a lot of sacrificing.
When you complete all the challenges, break infinity. Set the sacrifice autobuyer to x and set the prestige autobuyer to . With infinities roughly long, you should reach IC1 in less than . Before starting IC1, do infinities for IP until you get infinities. IC1 still requires you to turn autobuyers off, but you don't need to wait to prestige at all. You should be able to unlock IC2 in roughly ; do it when you can unlock it. It should be fairly easy. Don't do IC3 or IC5 as soon as you can unlock them. When you can unlock IC5, do IC3 and IC5. For IC3, turn the prestige autobuyer off and don't worry that much about when you prestige, since IC3 is easy now. For IC5, set the prestige autobuyer to (on, of course). Don't do any more ICs until you can eternity, in roughly . When you can eternity, don't do so immediately. Instead, do IC6 (following the above strategy, but it should be quicker; you may need to turn the boost autobuyer off in your first prestige to avoid getting too many stars), and do IC7 (which should be very easy). Buy a theorem with stars and a theorem with IP. When you get IP, do IC8, but you only need purchases if you prestige manually a few times after building up purchases rather than using the prestige autobuyer. Now do IC4, with autobuyers set to trigger every and prestige autobuyer set to . IC4 should take roughly . You should now have done all ICs.
Set prestige autobuyer to and infinity autobuyer to x best of last ten. You should be able to get another theorem with stars and another theorem with IP in or less, giving you total theorems. Buy Study 3. When you can get EP, do so, and buy EG1 and a theorem with EP. It should take roughly from complexity to get here.
Now that you have Study 3, eternities are very fast. First infinity and all the challenges, even Normal Challenge 7, can be completed by maxing all a few times. IC1 is both easy and the only IC worth doing. Keep your infinity autobuyer at x best of last ten. Do eternities for EP until you have eternities. When you get eternities, you no longer have to do IC1 yourself. When you get eternities, make the sacrifice autobuyer x. When you get eternities, make the prestige autobuyer x and the infinity autobuyer . You should mostly save up for EG2 in this phase. These eternities will decrease in length from to .
After you get eternities, set the infinity autobuyer to since total, turn the eternity autobuyer off, and do a longer eternity. Even if you can't buy any theorems with EP, you should easily be able to get theorems. When you do, buy Study 2. Eternity when it will increase your current EP to , which is enough to buy total theorems with EP ( which is already boughts, , , ) and you have at least theorems not bought with EP. This should take roughly . Then do another longer eternity like the previous, with Study 1 in addition to Studies 2 and 3 this time. You should be able to get total theorems and over EP on eternity, at which point you should eternity, get another theorem with EP, and buy Study 4.
At this point, set your infinity autobuyer to and your eternity autobuyer to EP. Each eternity will take roughly . At roughly eternities they'll take only ; then change the infinity autobuyer to IP. When you get eternities, do another longer eternity like those before. Eternity when you can get EP, which should take roughly . Buy EG3. Now do another longer eternity. Set your infinity autobuyer to after . Eternity when you can gain at least EP and have at least boost power, which should take roughly . Buy the second eternity upgrade with the EP you get. Now do an eternity to gain EP (), and spend them on a theorem. You should now have theorems.
As a general heuristic, at this point (including in later complexities) you should often buy studies in the order 5, 6, 8, 9, 10, 12, 1, 2, 3, 11, 4, 7. There were enough cases where this would lead to no progress pre-complexity that it wasn't mentioned there, but if you don't want to do experimentation or calculation, it should usually be enough in this phase of the game, despite still usually not being optimal. (This hasn't been tested fully, so beware; it might completely fail somewhere.)
Generally from here on, you'll want to aim for getting extra theorems with boost power a lot later than according to the pre-complexity guide, meaning you may have a few fewer theorems than the pre-complexity guide suggests at any given point. Get eternities rather than . After you first get EP, do another eternity to get another theorem with IP and roughly EP so you can get theorems.
Roughly when you unlock the Eternity Producer, you will automatically complete EC1x1, which will give you another theorem. It'll also make progress significantly quicker. However, progress will slow down somewhat; the eternity after which you get EG7 will take roughly and will give you a theorem for getting boost power, if you don't have that theorem already. The eternity after which you get EG8 will take roughly (which is slightly longer than the eternities leading up to EG8). It should take roughly from eternity to get EG8, or equivalently from complexity.
You'll only have total theorems for EC2x1 so you'll need to do 5, 6, 8, 9 for unlock. After completing EC2x1, you should have theorems, and should use studies 3, 5, 6, 8, 9 due to 3 being slightly better than 7 (largely because 7 has not reached its cap). At roughly EP, it is worth doing a longer eternity in which you try to get an extra theorem from boost power, so that you can get total theorems. Set your infinity autobuyer to . Getting this theorem will take roughly . After you get it, switch to 5, 6, 8, 9, 10 and set your infinity autobuyer back to .
At this point, you should almost have another EC tier autocompletion, but it will complete EC1x2 if you do nothing, and you'll be able to complete EC1x2 soon yourself. So, you should turn EC autocompletion off until you complete EC1x2. The EC autocompletion timer will keep counting down, but if it hits it will just store an EC autocompletion that will be used when you turn EC autocompletion back on. You should do both EC1x2 (complete 8, 9, 10, 12) and EC4x1 at total EP, one right after the other. After EC1x2 but before EC4x1, you should turn autocomplete back on and thus automatically complete EC1x3. You should wait to do EC3x1 until EP, wait to do EC1x4 and EC3x2 until EP, wait to do EC3x3 until EP, wait to do EC2x3 until EP, and wait to do EC3x4 until EP.
After doing EC2x4, you'll be close to getting another autocompletion, which will be of EC4x3 if you don't do anything. It's worth putting this autocompletion off a bit so it's of EC4x4, by turning autocompletion off. If you can't afford Study 10 for EC6x1, use Study 2 instead (so 2, 3, 5, 6, 8, 9). You should now have EC completions. It takes from EG8 to get here, or from complexity.
At this point you should be gaining boost power quickly enough that it's worth getting another theorem from boost power ( to ). Generally you should from now on use the EP requirements given in the guide for EC tiers, not the permanence upgrade requirements. After doing EC4x3, turn autocompletion back on; it will autocomplete EC4x4. Wait to do EC6x2 until EP and permanence upgrade costs, and use 3 instead of 11 for EC6x2 (so use 3, 5, 6, 8, 9, 10, 12). You'll soon have the option of Study 2 or Study 11; since progress is faster, you almost always want to pick Study 2, even when the pre-complexity guide suggests Study 11. Use 3 instead of 11 for EC7x2 (so use 3, 5, 6, 8, 9, 10, 12). After EC7x2, due to EC4x4 autocompletion you'll have EC tiers completed.
Do EC7x3 as soon as you can unlock it ( EP) and wait to do 6x3 (which can also be done with 3, 5, 7, 8, 9, 10, 12 at this point) until you've done EC7x3. Soon you'll get another EC tier autocompletion; if you don't do anything it will give EC6x4, which is a very good EC tier to have, so let it happen. When you get theorems, use studies 1, 2, 3, 5, 6, 8, 9, 10, 12 and keep them even when you could swap 3 for 11; your eternities won't generally be long enough that you'd want to do that. You'll automatically complete EC6x4 after completing EC8x2, and EC6x4 should allow you to easily unlock chroma. It takes from EC completions to get here, or from complexity.
You'll generally need to get chroma later (in terms of EP) now than pre-complexity, and it will be roughly x faster. You can get to EP with a very small amount of grey, and even somewhat beyond it, but at roughly that point you should do a longer eternity to get grey (roughly ). At EP, do a longer eternity to get grey (). You can do EC8x4 long before it is autocompleted. After doing EC8x4, get purple (). Typical eternities at this point should be roughly long. At EP, you should get grey (). When you get total theorems, buy Study 4, making your studies 1, 2, 3, 4, 5, 6, 8, 9, 10, 12. When you unlock orange, get orange, then purple, and then grey ( each). At EP, get grey, as you did pre-complexity ( to ). When you get total theorems, swap Study 4 for Study 11, making your studies 1, 2, 3, 5, 6, 8, 9, 10, 11, 12. Study 11 is still fairly weak but it's better than Study 4.
When you unlock cyan, first get cyan, which should take roughly . Then keep getting EP. At first you should do eternities that are long, going up to when after only you get less than x EP per eternity. At EP, get of each color in the order orange, purple, cyan, grey ( to each). At EP, get of orange, purple, cyan, grey ( to each). When you unlock green, start producing green as you did pre-complexity, using the Chroma preset. Getting chroma of each color is now so quick that you should do it whenever you can't get x EP in . Eventually you should be able to complexity again for ℂP, with far less trouble than the first time. You can get here in from unlocking chroma, or from complexity.
At this point, you can either complexity, or get ℂC1x2, which requires stars. Though the guide was written from a perspective of ℂC1x2 not being optimal, ℂC1x2 seems optimal now (due either to game changes since the guide was written or to that perspective just having been wrong). If you've been playing very actively and gotten here in something close to the time suggested by the guide, this may be somewhat hard (take ). However, if this complexity has taken more like , then, due to having more complexity stars, it may take less than to get to ℂC1x2, which is then clearly worthwhile.
Note that whatever you do, it's very important to disable buying of boosts, either just before or just after you complexity, so that you're in ℂC2. This is described more below, but it's important enough that it deserves its own paragraph so that it's easier to notice.
If you really don't like waiting, you don't absolutely need to get ℂC1x2. However, otherwise, you should get it. It will allow you to easily get "Forever isn't too long", get more ℂC2 completions, and complexity again (even getting ℂC1x3) in roughly . An important note is that this section of the guide was written without ℂC1x2 yet and hasn't yet been rewritten (except for a few small parts), so if you want to follow the guide exactly, you might not want to get ℂC1x2 yet. If you scroll down to the fourth complexity description (starting with "You should be able to figure out how to do a complexity now"), it's much like the third complexity with ℂC1x2 is. I'm sorry.
In any case, after getting ℂC1x2, there's nothing else worth trying to get, so complexity.
Now you have complexities and can start doing complexity challenges. Complexity challenges are very different from the previous types of challenges. They have star requirements and do not require you to infinity, eternity, or complexity for completion. They can be completed any number of times (though they get harder each time), like eternity challenges without the limit of completions each. Most importantly, however, each complexity challenge has a condition rather than being entered explicitly. For as long in a complexity as you observe the condition, you stay in the complexity challenge, and once you break the condition you exit the complexity challenge. Now that you have complexities, you should get some completions of ℂC2, which has the condition that you can't buy boosts. In the Complexity Challenges tab you can disable buying of boosts, and you should do this.
You get complexity achievements for getting certain amounts of progression in complexity challenges. Complexity achievements have various types of rewards of varying significance. Right now you'll want the first two complexity achievements, "One per generator" and "Forever isn't too long". (Without ℂC1x2, which is what this section of the guide was originally written for, "Forever isn't too long" will take roughly due to EC1 autocompletions, so may not be worth getting and was thus not originally recommended. Specifically, without ℂC1x2, EC1 autocompletions are required for "Forever isn't too long"; this will let you get Study 3 and make "Forever isn't too long" easy.)
The early part of the third complexity will be somewhat slower than that of the second due to you not buying boosts. However, the strategy is generally similar before breaking infinity. You can now do Normal Challenge 9 immediately without losing anything since you're not buying boosts anyway. It helps that boosts are helpful later in an infinity and the later part of an infinity is already fast. Otherwise, behaving as for your last complexity until you break infinity works. When you break infinity, you'll notice that progression slows down. You'll want to set the prestige autobuyer to x rather than second. This likely goes without saying but the first infinity upgrade is basically useless at this point. You should get IP (and ℂC2 completion) roughly after complexity. At this point, get infinities, and then keep getting more IP. From here on, progression will feel much like it was between and IC1 in first eternity, except somewhat faster. Roughly when you unlock IC1, you'll autocomplete EC1x1, which will make it far easier to unlock IC1 if you haven't done that yet and to complete IC1. You should get completions of ℂC2, and with them "One per generator", roughly after your first ℂC2 completion or after complexity.
Getting to eternity is fairly straightforward; you can skip IC4 and IC8, but not IC6. IC7 does nothing except a small boost to infinity generators, which you can ignore, so you don't need it.
After getting to eternity, since you then get "Forever isn't too long", you can exit ℂC2 by re-enabling buying of boosts in the Complexity Challenges tab. You'll have ℂC2 completions. Notably, instead of exiting ℂC2 at this point, you can get automatic EC completions here to get a lot of extra completions of ℂC2 (e.g., roughly ℂC2x40). This will take a long time (many hours), due to needing to wait for the EC automatic completions and remain in ℂC2, but it will make the next few complexities a lot easier. If you'll be going to sleep anyway, this is almost certainly worth doing. The advice in the rest of this part of the guide isn't adapted for this many ℂC2 completions, though. Generally, if you do this, you should try to get more ℂC completions than the guide recommends.
If for some reason, such as stepping away for a few minutes, you got a lot more stars and IP after becoming able to eternity but before exiting ℂC2, you may have completions instead, or more. These few extra completions may slightly speed up this complexity overall. So if you want, you can try to get them, perhaps by doing a few more eternities to be able to afford Study 3. However, they're not necessary; their effect is fairly minimal at this point.
From here on the third complexity is much like the second, except faster. Set your prestige autobuyer back to . You can skip IC4. You have "extra" theorem from EC1x1, which helps in getting studies slightly. After eternities, you should be able to progress far faster than in second complexity. Your eternities should generally be between and , and they should each give significantly more EP than the last (except when you do quick eternities to get eternities, which you should do at roughly total EP). There's no need to get more than eternities before the Eternity Producer. You'll generally want your infinity autobuyer at seconds rather than due to how quick progress is. The eternity in which you get EG7 is somewhat long, being roughly . When you get EG7, you should be close to getting your second EC autocompletion; it's fine to keep autocomplete on and get EC1x2. You can get EG8 roughly after exiting ℂC2, or after complexity.
You may not have the theorem for boost power yet. If you don't, do an eternity that's as long as needed for you to get it (probably roughly ). At EP, change your infinity autobuyer to seconds. Do EC4x1 at EP as you did second complexity, but you should wait to do EC3x1 until EP, EC1x3 until EP, and EC1x4 and EC3x2 until EP. Complete EC3x1 with 3, 7, 8, 9, 12, since you can afford Study 7 now.
You will soon get a third EC autocompletion. You're close to doing EC2x2 yourself and progress is fast, so you should turn autocompletion off. Do EC2x2 at EP, EC3x3 at EP, and EC2x3 at EP. After doing EC4x3, you can turn autocomplete back on and autocomplete EC4x4. Due to how quickly you're going, you may get less permanence with the same EP, making third-row studies worse compared to first-row studies; you should use studies 1, 2, 3, 5, 6, 8, 9, 10 when you can afford them. After completing EC5x3, you should have a fourth EC autocompletion coming soon; turn EC autocompletion off so you can use it when it's more helpful. Do EC6x2 at EP, and switch to 1, 2, 5, 6, 8, 9, 10, 12 after completing EC6x2. After doing EC6x3, you can turn autocomplete back on and autocomplete EC6x4. You can unlock chroma roughly after getting EG8, or after complexity.
At this point you should be able to figure out roughly when to get chroma. You'll probably want to do it somewhat less than you did second complexity. You can reach the point where you can complexity roughly after unlocking chroma, or after complexity.
However, rather than complexitying at that point, you should try to get ℂC1x2 (if you didn't before). This requires stars, or EP. You should get ℂC1x2 roughly after being able to complexity, or after complexity. (Commentary: Aren't you glad you got ℂC1x2 and this only took ? Also, you can get ℂC1x3 now, included in the given time estimate.) At this point, complexity for ℂP again.
You should be able to figure out how to do a complexity now, especially since ℂC1x2 will make it a lot easier. Buy another ℂG1 for 4 ℂP. Enter ℂC2 again as before. From IC1 on, ℂC2 will be much like first complexity but somewhat quicker. Between unlocking IC4 and unlocking IC5 you should get EC1x1, which should help. Skip IC4, IC7, and IC8. After you eternity, you will get "Forever isn't too long". This will make it so you have more eternities, for a total of . This will make it easy to get eternities while still in ℂC2. You should be able to get theorems and then ℂC2 completions without much trouble. Once you get ℂC2 completions, exit ℂC2. (Note: You may have already got this many in your third complexity, in which case it isn't worth getting them now. In fact, getting "Forever isn't too long" in your third complexity necessarily gives you enough ℂC2 completions that it's not clearly worth getting more now.)
You will get EC autocompletions before you complete all EC tiers. The game is now fast enough that it doesn't matter that much if or when you use them. Towards the end of this complexity, you might notice that you can get chroma even when you use the "Push" preset, and thus switching between Chroma and Push can be replaced by just using Push all the time. You should complexity once you get ℂC1x3. This requires stars, or EP. However, read the following paragraph first. This complexity should take roughly .
You now have complexities. This will let you do ℂC3. ℂC1x3 will also let you do a few more tiers of ℂC2. (Later comment: This is true but I'm not sure it's worth the extra time.) So disable buying boosts (do this before you complexity, since otherwise you'll buy boosts before you can disable them) and disable unlocking the Eternity Producer. Technically you could leave unlocking the Eternity Producer enabled and you would remain in ℂC3 until you actually unlock it, but it is good to remove the risk of accidentally unlocking it.
You start with eternities, so there's no need to do eternities to get automation. Once you get ℂC2 completions, exit ℂC2, that is, re-enable buying boosts. Unlocking the Eternity Producer should remain disabled, though. Note that once you have EC completions, you will still get a multiplier to eternity gain, but it won't help you get permanence because gaining permanence requires the Eternity Producer to be unlocked. You'll get an EC autocompletion; EC4x4 is a good choice to use it on (since otherwise you won't complete EC4x4 in ℂC3 at all) but you don't need to use it at all, and if you do use it it's not too important where. You should get "Actually a boost" naturally, at roughly EP.
After roughly in complexity, you can reach EP, ℂC3x9, and ECs 4/4/4/3/3/1/1/0 (EC1x4, EC2x4, ..., EC7x1, no EC8) or possibly 4/4/4/4/3/1/1/0. At this point, do eternities as quickly as possible (infinity for IP, eternity whenever possible). After roughly , you will get "Time after time". The default setting of the permanence autobuyer ( times last) is good.
You could now exit ℂC3 by re-enabling unlocking the Eternity Producer and then actually unlocking the Eternity Producer. However, you could also continue ℂC3, to get "After a hurricane". For this, you'll want to get your ECs to 4/4/4/4/4/2/1/0, which will require an EC4 auto-completion (which you may have gotten already) and manually doing EC5x4 and EC6x2. You then need to wait for the autocompletion of EC6x3. After that, you can progress and get chroma (thus getting "After a hurricane") just before autocompleting EC6x4. Alternatively, you can wait longer to autocomplete EC6x4, which may be a few minutes slower than progressing, but which you can do without being active. This will also give you ℂC3x17, though you can (likely) continue in ℂC3 until you could complexity (ℂC3x33) if you want. Unlocking chroma in this way takes roughly the time of or EC autocompletions, which is or at this point (though it's shorter if you're about to get an EC autocompletion).
In any case, however many ℂC3 completions you got, complexity when you can gain ℂP, at EP. You will still only have ℂC1x3 (not ℂC1x4). This should take roughly , or (likely) longer if you got more ℂC3 completions.
You now have complexities. This complexity should be fairly straightforward. You shouldn't try to get any complexity challenge completions. EC1 and EC3 are at this point far harder than the other ECs compared to their original difficulty (so EC3 is still easier than EC2 and EC4 in general, and EC1 is still the easiest, just not by as much). You'll get EC autocompletion and it doesn't matter much where you use it. Complexity when you can gain ℂP; this may feel harder than it did last complexity because you have fewer complexity stars due to getting to the end of your complexity more quickly. This complexity should take roughly .
You now have complexities and complexity points. Save for ℂG2 rather than buying ℂG1 again. Also, enter ℂC4. Also, turn EC autocomplete off if it's on, since you'll be trying to get "Broke every stone" this complexity. Even though you don't have chroma, you should be able to do EC8x3, EC6x4, and EC8x4 as soon as you can unlock them. This will give you "Broke every stone", which will be very convenient for doing ECs in the future. Note that if you really like doing ECs via autocompletions, getting "Calm EC" at complexities will automatically give you "Broke every stone", because you'll not have unlocked chroma yet. However, "Broke every stone" is convenient enough that it's almost certainly better to get it now (at complexities).
At EP, you should be able to easily get "No rest" by entering EC2 after roughly . After this point, do eternities which are long. later, or equivalently after complexity, you should get ℂC4x7. At this point, exit ℂC4. (People have pushed forward and gotten Shadeless in this complexity, but it takes a while and though Shadeless is wonderful quality of life, I can't recommend it unless you're fairly idle.) Don't try for ℂC1x4, since it's still somewhat too hard. Complexity when you can gain ℂP. This complexity should take roughly .
You now have complexities and complexity points. This complexity should be fairly straightforward. At this point you can change the initial part of the Push preset (before &) to 5,6,8,9,10,12,1,2,3,11,4,7. From now on (including in later complexities) this version of the Push preset should be enough to get you through the early part of a complexity, except in some hard complexity challenges such as the upcoming ℂC6. However, using it in some ECs will make them harder. You can either load the preset and respec whenever you can buy a new study, or load only when you can buy the next study in the list; if you constantly load the preset without respeccing, you may buy a later study (for example, Study 7) while unable to afford an earlier one, which is a short-term boost but will be bad eventually if you don't respec.
You shouldn't try to get any complexity challenge completions. You should consider "Broke every stone" mostly as not forcing you to unlock ECs and letting you do some later ECs slightly early; you still can't generally do ECs much earlier or complete an EC multiple times at once (sometimes you can complete the last tiers of an EC together, though). This complexity should take roughly .
You now have complexities and complexity points. Do ℂC5. Note that by this point in the game, manual infinities might be faster than using the infinity autobuyer due to being easier to adjust. You should be able to get ℂC5x2 (possibly even ℂC5x3) in roughly (or possibly faster), at which point you should exit ℂC5. After only roughly more you should get ℂC1x4, and you should then complexity. This complexity should take roughly .
You now have complexities and complexity points. Spend ℂP on ℂG2. You can now easily get more completions of several complexity challenges. This complexity, do ℂC4. You could also do ℂC3 at this point, but "Shadeless" is such wonderful quality of life and raising the chroma cap is so valuable that ℂC4 is good to do first. Once you complete all ECs, due to not being able to get chroma you can mostly just do eternities that are to long ( initially, then when progress gets slow). You should get ℂC4x13 in , giving you "Shadeless", and ℂC4x14 less than later. Exit ℂC4. You should then get 3 ℂP less than after exiting ℂC4. This complexity should take roughly .
You now have complexities and complexity points. Do ℂC3. Get eternities early (once eternities take less than ). In the last few complexities you've been able to rely on the Eternity Producer, but you can't do that here. After roughly EP, because you can't get permanence upgrades (permanence requires the Eternity Producer), third-row studies are useless to an extent comparable to how useless Study 7 is (most are slightly better than Study 7, though Study 11 is slightly worse). You should be able to unlock chroma, giving you "After a hurricane" and complexity achievements, in roughly . After EP, you should be able to do eternities that are long. (Just after EP you might want to intermittently do eternities that are long for chroma, but by EP, should be enough for chroma.) You can get very far in ℂC3, but progress will slow down slightly just before ℂC3x36, roughly when you get "3 * 7 * 11". Do eternities that are long at this point until you get ℂC3x36. When you get ℂC3x36, exit ℂC3 and complexity (or complexity and then exit). This complexity should take roughly .
You now have complexities and complexity points. Don't do any complexity challenges for this complexity. Progress will be very quick. Complexity as soon as you can get 3 ℂP. This complexity should take roughly .
You now have complexities and complexity points. Spend ℂP on ℂG1, since you're not really saving ℂP for anything right now. Disable buying studies (or in other less precise words, enter ℂC6). Turn EC autocompletion off if you have it on, since you'll be trying to get "Calm EC". Note that you'll get enough eternities to gain permanence even before completing EC tiers, and if you leave the game for a few hours you may have more permanence than expected, which may let you do certain EC tiers earlier than you otherwise could. The third permanence upgrade is useless while you're in ℂC6 since you can't buy studies, so so you can turn its autobuyer off if you want, but doing so is not that helpful and the benefits are perhaps outweighed by the fact that you might forget to turn the autobuyer back on.
The following sentence gives the order you should do EC tiers in and how much EP you should do them at. Do EC2x1 at EP, EC4x1 at EP, EC1x1 at EP, EC3x1 at EP, EC1x2 at EP, EC2x2 at EP, EC1x3 at EP, EC3x2 at EP, EC1x4 at EP, EC3x3 at EP, EC2x3 at EP, EC4x2 at EP, EC3x4 at EP, EC2x4 at EP, EC5x1 at EP, EC6x1 at EP, EC4x3 at EP, EC5x2 at EP, EC5x3 at EP, and EC7x1 at EP. Doing EC6x1 and thus getting EC tiers should take roughly , and doing EC7x1 and thus getting EC tiers and "Calm EC" should take roughly more, or equivalently total.
After getting "Calm EC", you will have all ECs complete. This will allow you to get ℂC6x12 almost immediately. Do a long eternity to accumulate boost power and thus get "Power beats knowledge". This eternity will be roughly long. Once you get "Power beats knowledge", you should be able to get ℂC6x13 almost immediately. Once you get ℂC6x13, exit ℂC6 and buy studies again. In this complexity you should try to get ℂP and ℂC1x5, both of which require almost exactly the same amount of progress. To do this, your eternities may need to be long right before ℂP. After getting ℂP and ℂC1x5 but before you complexity, disable buying boosts. This complexity should take roughly .
You now have complexities and complexity points. You'll be getting a lot of ℂC2 completions. Remember to unlock the Eternity Producer when possible (which is almost immediately due to "Calm EC"). The good studies are 2, 3, 4, 6, 7, 8, 9, 10, 12. Studies 1 and 5 are useless in ℂC2, and Study 11 is too slow. Thanks to "3 * 7 * 11" uncapping Study 7 and making it stronger, though, Study 7 is decent. Get ℂC2x60, which you can do in roughly , then exit ℂC2. Remember to unlock chroma and colors of chroma as it becomes possible to do so. As you did last complexity, get ℂP. The extra ℂC2 completions should make this far easier. Turn off theorem autobuyers right before you complexity, because next complexity you'll be trying to get "Thousand-theorem twilight". This complexity should take .
You now have complexities and complexity points. Enter ℂC4 (that is, disable unlocking chroma). Note that you can buy studies, and will still get theorems from several sources (boost power, EC completions, ℂC6). You just can't buy theorems. 5, 6, 7, 9, 10 are good studies to use up until EP, at which point you should switch to 1, 5, 6, 9, 10 (replacing 7 by 1). At EP, switch to 1, 5, 6, 9, 11 (replacing 10 by 11). When you can buy Study 2, do so, making your studies be 1, 2, 5, 6, 9, 11. (You should have this by when you get EP, within roughly .) Just before you get "Thousand-theorem twilight", your eternities may need to be roughly long. Getting "Thousand-theorem twilight" should take roughly .
When you get "Thousand-theorem twilight", you'll have complexity achievements. The remaining ones are "More colorful than a potato", "Forgot something", "Nonzero-color theorem", and "On the other side". Turn your theorem autobuyers back on. You'll have ℂC4x16. ℂC4x17 is too hard to get to be worth it, so exit ℂC4. At EP, which is also where you can get ℂP on complexity and ℂC1x5, you can unlock the new color, which is red. Do so. Note that the multiplier softcap is the number shown near the bottom of the main tab above which normal generator multipliers are reduced. It's initially , which you reached even before complexity, but red will increase it (which also makes the softcap have less of an effect when it does apply). Red may seem weak now, but it will get much stronger with more red and more eternities.
You'll be able to get much farther this complexity than before. Set your eternity autobuyer to , and increase it to at ℂP gained on complexity. Wait to complexity until you get ℂC1x8, at which point you should gain ℂP. This complexity should take .
You now have complexities and complexity points. Buy ℂG1 again. Enter ℂC6; in this complexity you'll be trying to get "Nonzero-color theorem" (but not yet "On the other side"). Remember to unlock the Eternity Producer. Initially, eternity every , and more often in roughly the first when even very short eternities can be good. You should reach EP in at most roughly . After reaching EP, set the eternity autobuyer to . At EP, set the eternity autobuyer to . You should be able to unlock chroma after roughly . Unlock chroma but do not yet exit ℂC6. Turn the eternity autobuyer off, get grey, then turn the eternity autobuyer back on. You should get ℂC6x18 roughly after complexity. When you get ℂC6x18, exit ℂC6.
Unlocking red should now be easy; it should take at most from exiting ℂC6 if you eternity manually. When you unlock red, set the eternity autobuyer to . Get ℂC1x11. Before you complexity but after you get ℂC1x11, disable buying boosts in preparation for the next complexity. You will get at least ℂP from this complexity, and maybe depending on if you eternity after ℂC1x11 and, if you do, how much EP you eternity for. The guide will assume you got ℂP, and it is not important. This complexity should take .
You now have complexities and complexity points. Buy ℂG1 again; you're not really saving up for anything right now. Since you disabled buying boosts, you should now be in ℂC2. Advice is similar to the last time you did ℂC2, except that you should buy Study 11 when you can, and at that point it will be somewhat useful. Set the eternity autobuyer to . Once you get EP, set the eternity autobuyer to instead, for the sake of making Study 11 stronger.
You should be able to unlock chroma after roughly , giving you "More colorful than a potato". However, grey, which is the only color that will be unlocked initially, is useless at this point. You should still stay in ℂC2 to get "Forgot something", though. You should get total theorems roughly after complexity). Once you get total theorems, respec studies and buy every study other than a single third-row study (such as Study 12) to get "Forgot something". Then exit ℂC2 with ℂC2x66. If you don't yet have ℂC2x66, instead wait until you get it, which should be easy, and then exit ℂC2.
Set your eternity autobuyer back to . Colors of chroma now unlock automatically due to "More colorful than a potato", so you don't need to manually unlock them. Complexity for ℂP. This complexity should take .
You now have complexities and complexity points. Enter ℂC5 before you eternity; if you eternity before entering ℂC5, you will likely buy EG8 automatically first. Unlocking red is easy, even in ℂC5. Get ℂC5x8, and then exit ℂC5 and complexity. This complexity will give ℂP. This complexity should take .
You now have complexities and complexity points. Enter ℂC6. Set the eternity autobuyer to . In this complexity, you will try to get "On the other side" and thus complete all complexity achievements. Unlocking chroma should be easy. As before, when you unlock chroma, turn the eternity autobuyer off, get grey, then turn the eternity autobuyer back on. Chroma production may sometimes apparently stop for a few seconds. This is because of the permanence autobuyer causing you to lose eternities. Since "After a hurricane" makes chroma faster with more eternities and chroma buildup speed is retroactive, losing eternities will temporarily decrease chroma. This has been going on in the past and happens outside of ℂC6 also; it is just easier to notice now.
When you unlock purple, turn the eternity autobuyer off and get chroma, giving you grey and purple in the same eternity due to "Shadeless". Then turn the eternity autobuyer back on. After roughly in this complexity, you should get "On the other side" and thus complete all complexity achievements.
In case you get "On the other side" earlier than suggested here, it makes "Forgot something" and "3 * 7 * 11" very easy, since both "Forgot something" and "3 * 7 * 11" can then be gotten with the theorems you have from the previous complexity. Also, only buying theorems in your current complexity stops you from getting "Thousand-theorem twilight", so "Thousand-theorem twilight" is also easier.
This section of the game (from complexity to completing all complexity achievements) should take roughly .
Here's a shorter-form description of when to get each complexity achievement, if you're using this guide and playing relatively actively. Note that a given complexity challenges doesn't generally help in getting more tiers of itself (exceptions being ℂC1 and ℂC3). Also, exact numbers of each complexity challenge usually don't matter; it's fine if you have one fewer (with the main exception being ℂC1, which is very important).
| Order ( to ) | Complexities | ℂC completions (ℂC1/ℂC2/ℂC3/ℂC4/ℂC5/ℂC6) | Complexity Achievement | Notes |
| ///// | One per generator | Straightforward, fairly soon after IC1 | ||
| ///// | Forever isn't too long | You can get this with complexities by waiting or already having ℂC1x2 | ||
| ///// | Actually a boost | You don't need to do anything special to get this | ||
| ///// | Time after time | Do quick eternities; this will take roughly | ||
| ///// | Broke every stone | Remember to turn EC autocompletion off so you can get this | ||
| ///// | No rest | If you aren't close to this with in EC2, come back later with more EP | ||
| ///// | Shadeless | Note that you should now have ℂG2 also. This complexity achievement can be done earlier, but unless you're fairly idle it's not recommended. | ||
| ///// | After a hurricane | Straightforward | ||
| ///// | 3 * 7 * 11 | Straightforward, but requires pushing a little | ||
| ///// | Calm EC | See guide above for which EC tiers to do and when to do each EC tier | ||
| ///// | Power beats knowledge | Build up boost power in a single eternity that's long | ||
| ///// | Thousand-theorem twilight | Turn theorem autobuyers off. Use studies 1, 2, 5, 6, 9, 11 for most of complexity (including the end); see above for advice for the start | ||
| ///// | Nonzero-color theorem | Straightforward | ||
| ///// | More colorful than a potato | Straightforward | ||
| ///// | Forgot something | Third-row studies are most expensive so skip one of those | ||
| ///// | On the other side | You can get this earlier if you're patient, and it helps with "Forgot something", "3 * 7 * 11", and "Thousand-theorem twilight" if you do, but overall unless you're idle I don't think it's worth it |
After getting "On the other side", exit ℂC6 with roughly ℂC6x22 (but the exact number of completions is not important). Change "Push" to 1,2,3,4,5,6,7,8,9,10,11,12&s9,10,9,3. This allows buying Study 16 when it is very cheap, which will increase total fourth-row study purchases and thus increase the chroma cap slightly.
Complexity for ℂP again, and then enter ℂC2. Do ℂC2x76, ℂC3x38, and ℂC4x17, each in its own complexity and each roughly between and . You aren't doing ℂC5 because it's weak, and you aren't doing ℂC6 because you just did it.
Note that at this point, due to Study 16 and its effect being raised to a power, chroma will basically always cap almost instantly.
From this point on, new complexity generators are of course the most important thing to buy with ℂP, and otherwise it's best to buy the cheapest complexity generator (or the highest one you've bought, if you can buy it and it costs the same amount of ℂP as others).
Do a complexity for more ℂP. Set the eternity autobuyer to . Once you can get ℂP on complexity, which should happen roughly after complexity, do a long eternity to build up boost power. This increases your highest boost power, which slightly increases complexity generator multipliers (the ℂG1 multiplier might increase roughly x). is a good amount of boost power to get, and will take roughly to reach.
After getting boost power, turn the eternity autobuyer back on. Unlike in previous complexities, ℂP per second will keep going up. Complexity for ℂP (which you can use for ℂG3), which should take roughly in complexity (counting the time spent building up boost power).
Do another complexity for ℂP, getting ℂP in .
Do ℂC2x82, ℂC4x19, ℂC5x11, and ℂC6x33, each in its own complexity, of course, and each roughly between and long, except for ℂC6x33 which will take . You can't get enough new ℂC3 completions for ℂC3 to be worthwhile.
Some general complexity challenge advice follows. ℂC1 and ℂC4 are generally the best ℂCs (ℂC6 becomes good later, once it gives you total theorems, but it isn't good yet). In ℂC4, your progress will always stall quickly, so if you can get a completion of ℂC4 in , do it, and if not, it's probably practically impossible without more progress. For the other ℂCs, getting to completions and taking to when you try each is good. This roughly means that you should do most ℂCs once or twice per squaring of stars (or, roughly equivalently, of ℂP). Once ℂC6 becomes good, even completion of it is worthwhile, though.
Now, turn the complexity autobuyer on (setting it in such a way that it will always complexity) and set the eternity autobuyer to . This will let you do complexities that are long, which will improve complexity generator multipliers. If you want, you can try instead setting the eternity autobuyer to or time past peak log/sec, which may make complexities a few seconds shorter. Either way, you should attempt to reach complexities at this point. At complexities you should be able to shorten eternities to and still complexity in eternities, decreasing the length of each complexity to . Note that with more ℂP you could do complexities that were far quicker, but getting more ℂP and then more complexities would be slower overall.
After getting complexities, go back to doing complexities for ℂP, with eternities long. Each complexity should be for x to x total ℂP. Each new complexity generator will increase ℂP gain a lot.
At this point, Study 14 is by far more useful than the other fourth-row studies; the main benefit from other fourth-row studies is their small increase to the chroma cap. Change your Push study preset to 1,2,3,4,5,6,7,8,9,10,11,12&s3,10,3,3 to further prioritize Study 14.
Complexities will increase in length from to . At ℂP, you should again do a longer eternity to get boost power, getting boost power in to at the end of a complexity. Unlock powers as soon as you have ℂP.
This section of the game (from completing all complexity achievements to unlocking powers) should take roughly .
Powers have randomness. Thus, this section and the next section of the guide cannot reasonably give exact strategy. It will instead bring up all the considerations for you to take into account, and say what you want to do no matter what.
Some general explanation of things you'll probably want to know about powers follows. You can equip up to powers at once, and if you want to change your choices for some reason you can unequip your equipped powers (and can later re-equip them if you want). To unequip powers, you need to do a complexity reset or to complexity. You can have multiple powers of the same type equipped, but if you do, their multipliers combine as + (a - ) + (b - ) where a and b are their individual multipliers (if there are ), or + (a - ) + (b - ) + (c - ) where a, b, and c are their individual multipliers (if there are ). In other words, they combine additively rather than multiplicatively.
The multiplier of a power is generally its strength times its rarity, but there is an additional multiplier for each type of power other than normal which only depends on the power's type (and other properties of the state of your game, but not directly other properties of the power itself). Powers of the same type can be compared by their multiplier (or equivalently their strength times their rarity); a higher multiplier is always better. Stored powers (powers you have but which are not equipped) are sorted by type, and vertically within each type with the best on top. There's no reason to have more than powers of the same type, so if you do the worst one will be deleted (for the same amount of power shards as if you deleted it).
Turn the eternity autobuyer off. Its only use at this point is in ℂC3 for getting eternities (since in ℂC3 you don't produce eternities automatically).
You start with of each of the types of power. The best powers to use initially are NIC (normal, infinity, complexity), since an eternity power takes a long time to build up and with NIC you can make progress quickly. Complexities only long should let you get to ℂP. Do ℂCs again after ℂG7 (just after unlocking powers) or after ℂG8, if you haven't done them recently.
Some more general complexity challenge advice follows. Since you don't have to eternity, the amount of time to spend on a ℂC is now only instead of to . You can try to do a ℂC for longer than at the start of a complexity and, when you're done with the ℂC, exit it and start a normal complexity. This means that ℂGs can still build up while you're in the ℂC. However, the risk of forgetting to leave the ℂC, especially for some ℂCs that aren't that hard, makes this technique usually not worth it in my opinion. (There will, after roughly , be a warning if you spend a long time in a complexity challenge.)
It is very important, for the sake of red (which is stronger with more eternities and which is very important), to get eternities in ℂC3. So, when in ℂC3, either manually eternity several times roughly every , or eternity every with the eternity autobuyer. Note that eternities depend on the effect of purple, which increases a lot over a complexity, so just getting eternities at the start of ℂC3 will not suffice.
Going back to the topic of powers, all the power upgrades are very important. They are much more important to buy than complexity generators, with the exception of the first purchase of ℂG8. However, they only apply to new powers you get, so they aren't generally useful immediately. Generally, you should turn power gain off until you get the strength upgrade for ℂP (and of course turn it back on after getting that upgrade), unless your first randomly generated power (which you can see as your initial "next power") has rarity under (making it likely not worth using anyway). In general, up to ℂP, if you're about to get a power upgrade right after you get a power, turn power gain off until you get the upgrade.
On the topic of ℂP gain, getting between x and x total ℂP every complexity is good. If you recently got something helpful for ℂP, like a very good power or (later) a ℂC4 completion, you might want to complexity for a higher multiplier than x right after getting it (and, in the case of a power, equipping it), if you can reach a higher multiplier in . If you suddenly get a good new power (significantly better than your current powers), you'll probably want to complexity and equip it, even if you don't gain much ℂP from doing so.
If you are using an eternity power, the above paragraph's suggestion of x to x ℂP is too low. Indeed, at least for this section of the guide, playstyle when using an eternity power is very different than it is otherwise. If you use an eternity power, it is best to do much longer complexities (hours initially, going down to roughly by the end of this section), because an eternity power takes time to build up.
Obviously this extra complexity length means you need a lot more ℂP each complexity for this to be worthwhile. Indeed, if you are active and do not have an eternity power that is extremely good (for example, higher multiplier than your other powers), using an eternity power is only near as good as not at the end of this section (after ℂP). Before that, an eternity power is bad. However, if you are idle and only want to look at the game every hour, or if you are doing an overnight complexity, or if you have an extremely good eternity power, or (in some cases) if you're at a wall and want to do something to get past it, an eternity power is likely the right choice.
Going back to early progression in this section of the game, in getting to ℂP, your longest complexity should be at most. This of course assumes you are not using an eternity power. At this point, the best powers for ℂP are normal powers, with infinity powers somewhat worse, eternity powers as discussed above, and complexity powers a lot worse than infinity powers but still better than eternity powers for short runs. Basically, as soon as you get powers that are either normal or infinity that all have multiplier at least , you should use those for ℂP (unless you are using an eternity power, or your powers of other types are very good).
At this point you should probably create a power preset (called "Push" in this guide, but I guess you can call it something else if you want) for complexities in which you get ℂP. Note that "probably" here depends on your style of play, and mostly not on the game's random number generator; this power preset will change, or additional ones will be added, several times before finality. However, despite that, I found having a power preset to be convenient. As with a study preset and the Studies tab, you can create a power preset at the bottom of the Powers tab. Either create the preset when you have your ℂP gain powers (primarily normal and infinity) equipped, or create a new preset and make it the powers abbreviations you want equipped, where N, I, E, and C are normal, infinity, eternity, and complexity respectively. Power presets are stored in the save (which doesn't handle unicode well) and most keyboards don't have ℂ, which is why C is used instead. You might try to make a power preset NNN when you don't have normal powers; in this case the game will equip as many normal powers as you do have when you load the preset (it won't throw an error, or suddenly create normal powers out of nowhere and equip them).
Now that you're generally not using your complexity power, you should still use it (or them, if you've gotten more than ) sometimes to get more complexity stars. Now, you're probably wondering what you're going to use those complexity stars for. After all, you'll lose them when you complexity and go back to using the Push preset. But to answer that, we need to talk about "On the other side". And if you thought the other parts of complexity were complicated, just you wait.
The way "On the other side" works is you keep bought theorems, but you also keep each type of extra (non-bought) theorem. For example, if you somehow get "On the other side" before "Calm EC", you'll start every complexity with theorems from EC completions anyway. Theorems from ℂC6 are a type of extra theorem, and how many you have depends on two things, which are ℂC6 completions and complexity stars (because complexity stars make ℂC6 stronger). So getting more complexity stars increases extra theorems from ℂC6. Since you keep extra theorems, you keep these theorems even after switching to another preset. Now, these theorems might not let you buy another study, but "Nonzero-color theorem" increases the chroma cap linearly based on theorems (it multiplies the chroma cap by ( + theorems / )). So more theorems are very helpful. Note that increasing the chroma cap is mostly helpful because of the effects of purple and red.
Whenever you gain more ℂP (and thus more complexity generators) or more ℂC6 completions, you can quickly get a large number of extra theorems by using complexity powers. So for best results, you would briefly switch to complexity powers every time you gained ℂP or ℂC6 completions. Doing this is a large speedup but not mandatory.
If you've used complexity powers recently, you'll probably need to use them again to get anything from a ℂC6 completion, since the extra ℂC6 completions aren't so strong that ℂC6 will give more extra theorems than it gave with complexity powers.
Of course, if you just complexitied, you should buy complexity generators before or while using complexity powers, not after. If you first switch to complexity powers, then switch back, and then buy complexity generators, you won't get the extra theorems that would have come from having higher complexity generator multipliers and thus more complexity stars while your complexity powers were equipped. This might seem somewhat intuitive, but you (or at least I) can easily mistakingly buy complexity generators afterwards.
There's not much use to using your complexity powers for that long. The complexity star gain from waiting doesn't give many more theorems. seconds in a complexity with complexity powers should be enough.
If you don't yet have complexity powers, also use your other powers with highest product of strength and rarity when using complexity powers. Since complexity powers get an extra multiplier based on strength and rarity of equipped powers, this will maximize that extra multiplier.
Once you have complexity powers, you should create a preset called "Complexity" which is CCC, to make it easier to equip your complexity powers.
Complexities in this phase will generally be about long, shorter when you get a good new power and longer if you are using an eternity power (in this pre-galaxy phase, is almost a minimum length if you're using an eternity power).
If you're playing actively, you probably won't be using eternity powers much, so feel free to delete any that aren't especially good (higher total multiplier than your normal and infinity powers). In general, if you're sure you won't use a power, you can delete it. However, since powers are automatically deleted when you have enough better powers, this doesn't give you too many extra power shards compared to using power shards from automatically deleted powers, except very early on (your first powers or so).
The most important power shard upgrades to buy are those for powers you use the most of. However, you should generally keep all power shard upgrade costs for power types you use at all within a factor of of each other (in this phase, those power types are likely at least everything but eternity, and also eternity if you're idle).
Crafting powers is sometimes useful, especially if you feel like fewer than expected of the random powers you're getting are good. Crafting lets you create powers of a given type and rarity, for a cost in power shards. In this phase of the game, crafting is on average slightly less efficient than waiting for random powers, but of course this depends on which random powers you're going to get. Generally, crafting normal powers is best in this part of the game, but right before unlocking galaxies crafting an infinity power becomes perhaps slightly better (especially if you're not using any infinity powers), and if you're very idle crafting an eternity power might be worth it.
As suggested by the suggestions above for what types of power to craft, when you're trying to get more ℂP, NNN (all normal) is generally best (unless you're using an E (eternity power) as described above), with NNI becoming good near galaxy unlock or if you get a great infinity power, and NII or III being good if your infinity powers are extremely good compared to your normal powers. For more context, I gets better compared to N as you get more complexity points, and roughly ℂP is the break-even point, where at the same strength and rarity, NNN and NNI are roughly the same and NII and III are slightly worse.
IEC and NEC are good powers to use if you're using an eternity power, since the C gives you more complexity stars and makes the E build up faster. As said above, this usually becomes good at roughly ℂP.
In ℂC4 specifically, NNC or (if you have no good C) NNN is good. Note that ℂC4 completions are very important. It may be worth creating a preset.
The Oracle is a very useful feature, even though it only gives you information. It lets you know roughly what your game state will be in the future. It has two main usages. One usage is comparing sets of powers without actually doing long complexities with then (this is especially important for eternity powers since they take time to become good and you don't want to waste that time if in fact they're not good). The other usage is seeing what powers you're going to get and when, so you can plan accordingly and can avoid getting a great new power just after starting a long run, or randomly getting a power similar to one that you just spent a lot of power shards crafting.
You should have the alert option on so that you can press O on another tab (like the powers tab) and get a brief description of the consequences of your powers. Note that with enough ticks, the Oracle might take a few seconds to work (it will show a progress bar on the top of the screen during this time), but the more ticks you're using the more accurate the predictions will be ( ticks is usually enough, though).
After ℂP, the game largely consists of waiting for good enough powers (either via random generation or via crafting) to unlock galaxies. You'll probably need powers with rarities to to unlock galaxies. Even a increase in rarity in power is noticeable.
How long unlocking powers to unlocking galaxies takes is variable, but is a typical amount of time.
Unlocking galaxies gives you autobuyers for complexity generators and power upgrades, so you don't need to buy those manually anymore. Due to needing to use CCC for theorems, however, auto-complexity is still not good.
More importantly, galaxies increase the chroma cap over time by raising it to a power, which starts at and increases over each complexity to some cap based on how many galaxies you have. There are three main impacts this has on play. The first effect is to make long complexities better. This may make IEC better than whatever powers you're using. On the other hand, it might not. Use the Oracle to find out (using an amount of time roughly equal to the time galaxies take to cap). The second effect is to encourage getting more galaxies, which is almost but not exactly the same as making more general progress. CCC is good for getting galaxies because it gives you more total complexity stars, and IEC gains the additional advantage that your additional total eternity stars may give you another galaxy. Using more than E is not worth it, however, because you then can't get as much EP which generally more than cancels out the additional power to EGs.
The third effect of galaxies on gameplay is the decision of how many galaxies to dilate. The galaxy power on chroma increases quicker the more dilated galaxies you have; the speed multiplier is ( + dilated galaxies)^. However, dilated galaxies don't count towards increasing the cap, so if you dilate all your galaxies, then galaxies don't increase the chroma cap at all. (Thus dilating all your galaxies is a bad idea.)
Note that, if you get another galaxy during a complexity, your setting for dilated galaxies will determine if it gets dilated or not. If a new galaxy gets dilated, the galaxy effect power will increase faster, which will apply retroactively in your current complexity, likely causing a sudden jump in the galaxy effect power. On the other hand, if a new galaxy does not get dilated, the cap for the galaxy effect power will increase, potentially causing the galaxy effect power to suddenly increase to the new cap if it was already at the old cap.
Generally dilating roughly a quarter () of your galaxies, rounded down, is good if you're active. If you're idle or doing an overnight run, dilate fewer galaxies. (But once you have galaxies or so, you should basically always dilate at least galaxy no matter what.)
It's worth noting that after the first few galaxies, each galaxy increases the time for the galaxy effect power to reach its cap by more than the last (which is why dilating galaxies becomes basically necessary).
Galaxies also increase the strength of new powers somewhat, but this doesn't affect gameplay much qualitatively.
As for how long complexities should be, once you unlock galaxies you generally want to get the galaxy effect to its cap in each complexity. After roughly ℂP, if you're using an eternity power (as you probably are), you probably want the eternity power extra multiplier to cap at x also. (Ideally the galaxy effect and your eternity power cap at about the same time, but this is not very important.)
This does not apply in challenges, which you should generally only be in for to , even if galaxies don't cap that quickly (as they almost surely won't). Since complexities with challenges are shorter, it might be better to use NNI, NII, or III for challenges. However, further along (perhaps at ℂP), as eternity powers build up faster due to more complexity stars, IEC may be better in complexity challenges.
Note that after ℂP, the eternity power extra multiplier will cap before the galaxy effect caps. If the galaxy effect caps first, you are probably dilating too many galaxies and should probably try dilating fewer.
Powers to use for getting ℂP are IEC initially, switching to IIE (or IEE if you have no good I or only one good I) at roughly ℂP. For ℂC4, it's best to use NCC after roughly ℂP (when you unlock galaxies) and to use CCC after roughly ℂP.
How long unlocking galaxies to finality takes is variable, but is a typical amount of time (yes, roughly the same as for unlocking powers to unlocking galaxies).
So, you've finalitied. As with eternity and complexity, this resets basically everything. You keep your slow autobuyers, and that's basically it. However, you do have finality points (FP) and finality shards.
You may have noticed that you hit a star hardcap right before you reached finality. That star hardcap is there to stay. There's no way to get rid of it or push it back, and the rest of the game is about reaching it quicker and quicker.
With your FP, you can, and should, buy a Finality Generator 1. Finality generators (FGs) are like previous generators except that they cost finality points. Finality stars have the effect of multiplying all previous generators (normal, infinity, eternity, and complexity) by ^(log(number of finality stars)^). This is very strong early in each prestige layer, but is hard to notice in later parts of each prestige layer because all the generator multipliers are so big that this extra multiplier is comparatively small. In practice, this means that the FG multiplier speeds up early eternity in an easy-to-notice way (roughly up to unlocking the Eternity Producer) and also speeds up early complexity (roughly up to unlocking powers), but between the Eternity Producer and complexity and between power unlock and finality, finality stars won't do much.
Note that the finality star per-purchase multiplier depends on finalities; it's ^(min(, max(, finalities^)) / ). This starts at the usual ^( / ) but can increase up to eventually. This is in addition to the multiplier to finality generators of min(, finalities / ).
Fortunately, there are other benefits given by finality. The most notable are finality shard upgrades. You get times your finalities shards each finality (so , , etc.), with the only (unimportant) exception being that you instead get twice that many shards on finalities divisible by (this is unimportant because by finalities, finalities will be very fast; it's only included to make certain numbers line up). There are finality shard upgrades, described below. The first can be bought up to times; the other can only be bought up to times.
Power to non-finality generator multipliers: This raises all multipliers of non-finality generators to the power of + times bought / . This is very noticeable in eternity after roughly EP. In powers it becomes slightly harder to notice, but is still important. For comparison, the effect this has on normal generators (which is most of its effect) is equivalent to a normal power with strength and rarity (before power shard upgrades).
Finality point gain on finality: This has a messy formula. At first it's just more per purchase, but it eventually becomes a lot stronger and reaches when it caps. This is the only way to get additional FP per finality. It's mostly worthwhile when it'll give you a new finality generator you have none of yet.
Multiplier to eternity and permanence gain: The formula for this is ( + times bought)^. This is mostly noticeable between eternity and chroma. It makes eternity milestones a lot easier to deal with, and since it multiplies eternities and permanence it basically acts as a ( + times bought)^x multiplier to permanence. Still, before you get far into chroma this becomes harder to notice.
Multiplier to chroma buildup speed: The formula for this is also ( + times bought)^. This is useful when chroma is slow, which is during your first few complexities of your first few finalities but never again. This is probably the weakest of the upgrades, overall.
Multiplier to chroma cap: The formula for this is ( + times bought / )x. When you first unlock chroma, this is probably less helpful than "Multiplier to chroma buildup speed", but unlike "Multiplier to chroma buildup speed" it keeps doing something throughout. Its effect on chroma cap is significantly less than that of galaxies, though (note that galaxy raises the chroma cap to the power of , which is a lot stronger because it's a power rather than a multiplier).
Multiplier to power gain speed: The formula for this is, yet again, ( + times bought)^. This is probably the most important finality shard upgrade. It's true that it only affects things once you have powers, but at that point not much else is doing anything (mostly "Power to non-finality generator multipliers" and "Multiplier to chroma cap") so powers can be very slow without this.
Increase to strength of new powers: The formula for this is +(times bought / ). This upgrade works similarly in practice to "Multiplier to power gain speed", but is weaker early. This is true both early in each finality, since power strength varies a lot right after you unlock powers anyway and getting more chances is thus more valuable than a small increase, and early overall, since a x (from the first purchase of "Multiplier to power gain speed") or x ( / , from the second) multiplier to power gain are both really strong and "Increase to strength of new powers" can't compete much.
Multiplier to galaxy effect buildup speed: The formula for this is, as you might expect by this point, ( + times bought)^. This is less important than the power finality shard upgrades but still important near the end of each finality. Note that if you don't want to wait as long for galaxies, you can just dilate another galaxy even without this upgrade; this isn't as true for powers, which is what makes this upgrade weaker.
In addition to their effects, finality shard upgrades give you bonuses based on how many you've bought (counting multiple purchases of the same one as multiple). You get stars at the start of each prestige, infinity, eternity, complexity, and finality, with that number of starting stars squaring for every upgrades. You also get starting IP, EP, and ℂP equal to the number of each you could get with your starting stars ( if you don't have enough starting stars for that). You also get ^min(4, upgrades bought / ) (rounded down) complexities at the start of finality. Lastly, you get starting complexity achievement for every upgrades (going left-to-right, top-to-bottom) and extra galaxy for every upgrades.
The way this all ends up playing out is that early on, you want finality shard upgrade bonuses as strong as possible so you can start with more complexity achievements. This means not buying any upgrade more than time more than any other upgrade. The numbers of extra complexity achievements you can thus get are , , , , , . After finalities you can get exactly of every finality shard upgrade, which gives you all complexity achievements to start with (this is the from the previous sentence).
If you replay the game, you can import "replay mode" in the save import prompt to see all tabs from the start, if you want (and you can import it again to undo this). This is at a random point in this section to make it slightly harder to find. This mode spoils things, of course, if you haven't played through the game, but if you're reading this you're probably not too worried about that.
Before you have finalities, you won't start with Calm EC (and before you won't start with Broke Every Stone). This is annoying, but there are two other things that ameliorate it. One is finality milestones. The first finality milestone halves the requirements for complexity challenges, meaning you only need complexities to do ℂC6 and get Calm EC (and only for Broke Every Stone). The second finality milestone, in addition to permanently automating complexity generators and power upgrades (but not power shards upgrades), removes complexity requirements for complexity challenges entirely.
However, even with the finality milestone for 2 finalities, it's still wise to first do a normal first complexity, then do a second complexity where you get ℂC2, ℂC3, and ℂC4 completions (likely getting Broke Every Stone, and stopping each when it starts to feel at all hard) and also perhaps some more ℂC1 completions (though you'll also have some of these from your first complexity), and only then go for Calm EC which should then be pretty easy. Note that in general, if a complexity challenge feels hard you should do other ones first.
With all of this, you'll still be doing eternity challenges roughly times (some of which will be cut short by getting Calm EC). Most of these times will just be frantically clicking. If you're more idle, the other thing that ameliorates not having Calm EC is improvements to automatic EC completion. You now automatically complete an EC tier every / min(, finalities) seconds, and the automatic completions from complexities are x faster (every / min(, complexities) seconds, which helps once you have any complexities). This will also help a lot when you have complexities and finality. It's not that worth planning out your EC automatic completions, but you'll likely get or at least before you complete any ECs manually.
Strategy is pretty straightfoward; it's like before, except you should keep going if things feel fast. For example, your complexities right before powers can be for more than x ℂP. As for powers and galaxies, dilating more galaxy and using NII or III longer (even after unlocking galaxies) and IEC longer are good strategies; it's worth using the Oracle or intuition to see when to switch powers. Note that eternity power extra multiplier isn't sped up by anything yet, which makes power sets with E comparatively weaker (because you won't be waiting as long).
The finality you do with finality will be split between first few complexities (mostly frantic clicking, with some waiting in first complexity) and powers (mostly waiting). It can take as short a time as roughly ( for first complexity, for first complexity to unlocking powers, for unlocking powers to finality).
Finality times can be as short as roughly (as previously stated), , , , , , after which speedups are largely due to finality milestones automating things that would have taken time to click. Descriptions of the effects of finality milestones will be given below.
With finalities, you get a milestone removing complexity challenge requirements and automating complexity generators and power upgrades (as discussed above). With finalities, you get a milestone giving you ℂP, which lets you get effects from complexity challenge completions even before doing a complexity. This isn't too significant (it might help you get more ℂC1 completions in your first complexity though).
With finalities, you get a milestone letting you keep ℂC completions. The number you can keep is ^(min(, finalities) / 2), rounded down. Of course you can't keep more than you have, so the min with does nothing since you can't get completions. Anyway, this will help a lot early on. You don't have to do too much to take advantage of it. Technically after you keep all your ℂC completions you can try to reach the star hardcap in every challenge but ℂC4, but this won't happen for a while and won't be too helpful anyway.
The milestones for through finalities are fairly self-explanatory. Once you automatically gain permanence every second you can turn your permanence autobuyer off, which reduces lag a little. Once you unlock study list auto-load you can constantly load Push. Unlocking autobuyers for power shard upgrades is a bit of quality of life (it does mean you might have fewer shards to craft powers with but at this point crafting powers isn't too helpful). Always having EP generation makes getting to powers less painful.
At this point (in fact, at finalities), you'll have capped all but finality shard upgrades. You should try to keep those roughly even. You can try to focus on the second one if you're near a new finality generator and could get it with, say, x more finality points, and focus on the first otherwise, but it's not that important.
The milestones for through finalities and for and finalities are fairly self-explanatory. The milestone for finalities might be a bit confusing but it basically just serves to remove the need for swapping in CCC, so there's no real reason to use CCC (except in ℂC4); you get the theorems you would have gotten from CCC even without using it. The milestone for finalities means you only have to swap powers manually if you want different types of powers equipped. For the milestone for finalities, IEC are good equipped powers to load.
Once you get finalities, you can set your complexity autobuyer to roughly seconds, set your dilated galaxies to in "seconds to reach cap" mode (or however many seconds to reach cap your complexity autobuyer is), and turn your finality autobuyer on. Finalities should initially take roughly long. Keep buying finality generators and finality shard upgrades.
The milestone for finalities will help a little; it will make your eternity power and galaxies slightly faster due to giving them a few seconds of free time. Specifically, it gives finalities^ seconds, thus starting at when the milestone unlocks, and capping at at finalities. The milestone for finalities will help significantly more; once you get finalities, you can turn your complexity autobuyer off. Finalities should be roughly long with it off. Soon starting bonuses of stars/IP/EP/ℂP will become significant and make finalities faster.
At finalities, you'll max out all finality shard upgrades, which will make your starting benefits of stars/IP/EP/ℂP the same as their values at the star hardcap. This lets you finality immediately and is for fairly clear reasons thus the end of the game. This part of the game (finality to end) takes roughly (roughly of which is spent in second finality and of which is spent beyond).