Previous: Theory 9 to Endgame
The custom theory guides assume you have read the page on stepwise variables
Disclaimer: This is a simplified version of the guide. The guide will skip over things, and is not completely optimal. Click here for a more polished, in-depth, and optimal guide.
When discussing strategy, this section may use more jargon then the rest of the guide. If you are confused, please check out the discord server and ask.
This section of the guide will briefly discuss strategy for custom theories. You have been warned
The complexity ratings given is a rating on how approachable each CT is. For example basic theory \(\dot{\rho} = c_1c_2\) would be given a rating of 1/5. Complexity rating takes into account both difficulty of comprehending the math, and difficulty of executing the strats. Difficulty of execution is NOT activity. A theory that requires you to press a button every 5 minutes is very easy to execute, but also very active
The following table is a guide only
| Score | Math description | Execution Description |
| 1 | Math uses only simple functions (T4) | Mostly/All Idle (EFSNAX) |
| 2 | Math uses more complex functions, but is reducible to a hard rule and can be simplified/ignored (WSP) | Simple d strats. No MS (WSPd) |
| 3 | Math uses more complex functions that must be interacted with. Generally explainable, creates simple progressions (CSR2) | Mod 10 strats, simple MS (T2MS) |
| 4 | Math uses more complex functions that must be interacted with, that creates more complex progressions (RZ) | Long step mod 10 strats, complex MS, with more difficult thresholds (CSR2XLII) |
| 5 | Math uses very complex functions that must be interacted with. Creates complex progressions (FP) | Esoteric strategy, hard MS, exponentiation (T3MS) |
Most theories are complexity 2 minimum. 3 is normal. 4 is high. Many theories have optional strats with an execution complexity of 4
There are a lot of custom theories out now. A total of 9 have been released! WSP, SL, EF, CSR2, FI, FP, RZ, MF and BaP. A natural question is, which one should I play? The guide aims to help you answer that question
Firstly, there is no right answer! You can play whichever CT you want to play, and we encourage you to play around and find out what CTs you like
the most. However if you are looking for some guidance, here is a quick rundown of each CT, gameplay wise.
Personally, I recommend starting with some lower complexity theories, some good idle theories (to overnight) and ideally some fast early game
theories
For those trying to play optimally, CTs are not effected by R9, and thus the greedy method is optimal
Execution complexity refers to the complexity of the optimal strategies. Forced Execution complexity includes only non-optional strats + active
Math complexity is not what it looks like! Sometimes, theories can look intimidating, but are actually not that bad if you sit and think about it
Math complexity also include a bit of a hidden element about how difficult a strat is to DERIVE. This may be based off of hidden factors such as variable cost functions, so math complexity may not reflect the above
Activity is how active the theory is considered as a whole.
Example: SL has this scary looking equation \(\frac{x}{\sqrt[x]{x!}}\). In a vacuum this would be difficult to analyse. However, a quick google search (or guide search) reveals that this is an approximation for the value e, and with a bit of experimentation, one can determine how quickly it converges. Thus, it is given a score of 2, as it is difficult to being with, but can be simplified
| CT | Sim Completion time | Math Complexity | Execution Complexity | Forced Execution Complexity | Activity\(^{[0]}\) |
| WSP | 4y 333d | 3 | 2 (WSPd) | 2 (WSPd) | Active |
| SL | 288d | 2 | 4 (SLMS) | 2 (SLstopA) | Idle |
| EF | 132d | 2 | 1 (EF) | 1 (EF) | Idle |
| CSR2 | 1y 73d | 3 | 4 (CSR2XLII) | 2 (CSR2d) | Active |
| FI | 264d | 4\(^{[1]}\) | 3 (FIMSd) | 2 (FId) | Idle |
| FP | 103d | 4 | 3 (FPMS) | 3 (FPmod10) | Active |
| RZ | 67d | 4 | 2 (RZMSd) | 2 (RZ) | Idle |
| MF | 189d | 1 | 4 (MFd) | 4 (MF) | Active |
| BaP | 151d | 2 | 3 (BaPMSd) | 1 (BaP) | Idle |
\(^{[0]}\)Many active theories have idle sections, many idle theories have active sections. Do not take as gospel. Considered post full milestones if applicable
\(^{[1]}\)FI's milestone route and milestone effectivity is difficult to derive
Complexity
WSP is relatively simple theory (Complexity 2/5). Gameplay-wise, WSP is quite simple, using only d strats with optional MS. The math contains a scary looking
product but can be generally simplified to more \(\chi\) = more \(\rho\)
Speed
WSP takes 4 years and 333 days to complete, making it the slowest theory in the game. WSP is slow to start, with the very earlygame being somewhat
of a timewall but very good early game, with tau/hour
jumping after the first few milestones, peaking at 12 at 1e250 rho and staying above 1 until 1e660. 1e660 can be achieved in 3 days active.
WSP is 15 days to 1e900, 30 days to 1e1000, 68 days to 1e1100, 158 days to 1e1200 and so on
Activity
On average WSP has a consistent active-idle ratio of 1.3, and has pub multi's around 8. It reaches 8h of pub time at 1e825 rho. It is an active
theory
Conclusion
Overall, WSP is a good beginner theory, and is quite fast in the early game. You should play it early, but don't expect to complete it. Like, ever
Complexity
SL is a mostly simple theory (Complexity 3/5). Gameplay-wise SL has only d strats and semi-optional MS. The semi-optional MS swaps between 3 states, making
it relatively difficult to perform. SL contains a lot of cumulative variables and thus has strong coasting strats. The math contains many intertwined
cumulative variables, making it look intimidating on first glance, but can be easily broken down
Speed
SL takes 288 days to complete, making it the 3rd slowest theory to complete. SL has a fairly normal decay amount, with it's tau/hour peaking at 19
in the first publication, and dropping to 1-2 at around 1e60, where it stays, jumping around with milestones until finally falling below 1 at 1e440
SL takes 25 days to reach 1e900, 37 days to 1e1000, 54 days to 1e1100, 78 days to 1e1200, 112 days to 1e1300 and so on
Activity
SL has no good active strats and when MS is not an option has an active-idle ratio of near 1. Pre-1e300 when SLMS is an option, it is a very active
theory. Post 1e300, or if you choose not to do SLMS, SL is a very idle theory. It has multiple cumulative variables, meaning it does well idle. It
has an average pub multi around 8. It reaches 8h pubs at 1e750 (14 days in) and from then on can be a good overnight.
Conclusion
SL is a good beginner theory and a good choice for a theory you can idle. The MS is not the most friendly, but is a good way of learning or
practicing your MS skill, which will are important if you want to play efficiently, and is a fun part of the game. You should play it early, but
don't expect to complete it for a long time
Complexity
EF is a relatively simple theory (Complexity 1.5/5). Gameplay-wise, EF has 3 different currencies that are generally separate, with R and I used to purchase \(a_12\).
Other than those 2, all the variables are simply multiplied together, with \(sin^2(t)\) and \(cos^2(t)\) which can be thought of as 1/2 on average.
Mathematically, the theory is mostly just multiplication and competing variables, which make it look more complex then it actually is
Speed
EF takes 132 days to complete making it one of the completable theories. It has a rho/tau conversion of 1.6, meaning that whilst rho will appear to
grow slowly, the theory is faster then it looks. EF starts off fast but very quickly falls below 1 at 1e25 for the 1e50 timewall. Surpassing that
time well rates will again jump to 7 falling back down and jumping back up as new milestones are unlocked. This theory survives of milestones.
This continues until 1e200 where the rates fall below 0.5 for the last time and stays between 0.2 and 0.05 tau/hour for the rest of the theory
Activity
EF has many cumulative variables and no MS. This makes it a very good idle theory with and average active/idle ratio of 1.06ish.
Pub's before milestones generally have long publication times with 28 -> 30, 33 -> 50 having pub times over 8h hours. The timewall at 1e50 is
actually helpful here as the publications leading up to it can be overnighted for little to no time loss. Whether a publication is overnightable
depends on where you are in the theory compared to the relatively frequent milestones, so they have to be checked on a case by case basis
with the theory sim.
Conclusion
EF is a decent beginner theory, although it's incredibly slow start means that I would not recommend it to new players. If you are trying to play
optimally, EF's timewall at 1e50 is decent for a few overnights without significant timeloss, as EF generally will have to be pushed past 1e50 at
some point. You will have to play it at some point, and if you are looking for an early idle theory it can provide, but I would hold off playing EF
for a bit, and not play it first
Complexity
CSR2 is a decently simple theory in my opinion (2.5/5). CSR2 is what I like to call the quintessential CT. I find CSR2 the perfect inbetween from main theories to custom theories. It introduces much of the
complexity of custom theories. Whilst it does have some complexity in its recurrence relation and a more difficult MS strat, the doubling strats are
quite straightforward and the strategies are nothing new. The MS is on the more difficult and complicated side, so may not need to be attempted,
although it is 2x faster, making it semi-optional
Speed
CSR2 takes 1 year and 73 days to complete, making it the 2nd slowest theory to complete. It has a fairly normal decay rate in early game, staying
above 1 tau/hour and spiking to about 4 at each milestone. The theory spikes to 16 at 1e80 and stays very strong for the next 100 rho. It stays above
5 tau/hour until 1e250, and first drops below 1 at 1e600. This makes it an extremely strong theory earlygame, at the level of WSP. Lack of endgame
milestones make decay start post 500, and thus like WSP it falls off far before the cap
CSR2 takes 2d 12h to 1e500, 26d to 1e1000, 45d to 1e1100, 80d to 1e1200, 139d to 1e1300 and so on
Activity
CSR2 has no cumulative variables. Before 1e500 it is very active, with MS semi-optional MS strats (CSR2XLII is 2x better than CSR2d). If you do not
do MS, CSR2 is still active but with a much kinder ratio (1.17 active/idle ratio). However, CSR2 has bad post optimal pub multi decay and does not
get 8h pubs until 1e1100 which is very late into the theory with rates well below 0.1. CSR2 is definitely an active theory and definitely should not
be considered if you are looking for an idle theory
Conclusion
In my opinion, CSR2 is the quintessential CT. It is active, but in doing so you have to interact with the doubling strats. Its equations and
strategies feel reminiscent of the main game, and it is a great bridge to move into CTs. I recommend playing CSR2 as one of your first CTs,
especially if you are willing to push it past 1e80. With optional MS, you don't have to do it. If you are a beginner, I recommend trying the MS, but
remembering it is optional, as CSR2XLII is a very difficult strat
Complexity
FI is a more complex theory, especially in it's milestone route, which may not be reflected in complexity but definitely will cause anyone going in
blind a headache (3/5). FIMS uses q stacking instead of variable ratios, which is generally a simpler method, and also uses a very weird one time per
pub milestone swapping strategy. All in all, FI strategy is easy to execute, but hard to derive
Math-wise, FI's fractional equation is complicated, but can be generally simplified with some understanding of the idea behind them. It makes the
milestones hard to evaluate however, especially since FI has milestones that actively hurt your progress
Speed
FI takes 248 days to complete, making it the 4th slowest theory in the game. It's decay rate is nothing special, spiking at important milestones
staying at an average of 1 until 1e650 where it starts to drop. FI takes 9 days to 700, 30 days to 1000, 61 days to 1100, 108 days to 1200, etc.
Activity
FI is a very idle theory. The MS is has an active/idl ratio of 1.22 and without MS it is as low as 1.02. FI has pubs consistently over 8h from 1e150
rho, making it one of the best theories to overnight. FIMS is also relatively easy and idle (though it is still MS)
Conclusion
FI is a great theory to try. The difficulty of the math, which is can be intimidating is not as bad as it seems. Even still, with milestone unlocked
milestones, FI is probrably not the best first CT. However, it would do great as a 2nd, and is quite possibly the best theory to idle.
Complexity
FP is a very intimidating theory, however, it's strategy execution is not too bad, although it require knowledge of some more advanced concepts (4/5).
FP represents a sharp increase in mathematical difficulty, present in the 2 pages of math and long complex equations. This makes FP a nightmare to
solve, without simplification. Furthermore, it's strategies require understanding of stepwise variables, and is the first theory to make this
mandatory. For these reasons, FP is a very complex theory
Speed
FP takes 103 days to complete, making it the fastest now second fastest theory in the entire game. FP starts with a huge timewall before 1e95, but after passing that it
becomes, and stays, very strong. Rates drop to 0.07 during the 1e95 timewall, but then jump to 4. These rates start strong, jumping at every
milestone, up to 10-13 at strong milestones through until 1e950 where it first drops below 0.1. Rates fall back below 0.1 at the FP basin form
1e1350 - 1e1560 with the 1e1500 milestones bringing the rates back up. It reached up to 0.5 at 1e1660 and falls to 0.2 by theory endgame
FP takes 4 days to 1e100 (past the wall), 5 days (21h) to 1e700, 7 days (20h) to 1e950 (end of MS), 19 days to 1e1250,
69 days to 1e1550 (end of basin), and 103 days to complete fully.
Activity
FP is a generally active theory. It has a 1.15 ratio pre-ms, a ratio of 6 during MS, which may be the highest active/idle ratio ever seen, and
a ratio of 1.2 post-ms. This makes it an active theory, and idling during the MS period is heavily punished (1e700 - 1e950). Do not idle during MS.
FP is an active theory.
Conclusion
FP is a difficult theory. But that's understandable because it is the one of the fastest theories. You definitely have to play FP, but I would not recommend it to
beginners. However, it's MS is relatively easy, with only 1 milestone getting added and removed, and "winging it" is generally very possible,
ironically, making FPMS a decent way to learn some MS skills
Complexity
RZ is a decently simple theory (3/5). RZ plays around with the Riemann Zeta function, a famous mathematical function. This theory puts
\(\zeta(\frac{1}{2}, ti)\) on the denominator, meaning rho spikes when the function hit's zeroes. However, as there is no closed form
solution to the Riemann Zeta function, this behaviour is hard to predict. This is generally okay, with strategies mainly ignoring this behaviour
up until 1e600 rho. Past that, finding good zeroes is mostly trial and error. The strategies are generally quite easy to perform, with RZ being
a more idle theory with simple MS.
Speed
RZ takes 67 days to complete, making it by far the fastest theory to complete in the game. Rates stay very high, mostly about 10 before 1e150 rho,
They then begin to decay until 1e250 to 3 tau/hour (still unbelievably high) and spikes again to 10. It decays to 1.3 at 1e600 where it gets a boost
back to 2.7. From them decay is relatively constant with no new milestones. It falls below 1 at 1e750, and below 0.1 at. Post 1e950 it bounces
between 0.15 and 0.25 for a while, falling below 0.1 only at 1e1450. RZ is somehow a great earlygame theory and lategame theory, making it one of
the fastest theories in the game
Activity
RZ is a mostly idle theory past the MS stage. It has semi-optional MS before full milestones, but after is a mostly idle theory, with doubling strats
only giving a small boost to speed. RZMS is generally simple, with a QS (quick swap) strat being the only actual MS.
Conclusion
RZ is a very strong theory, and also a good idle theory. It is generally all round very powerful, so you should play it, ideally early on. Deriving
strategies, especially finding zeroes post 1e600 rho is a bit difficult, but the execution is simple. Wouldn't recommend as first theory, but
good to play after.
Complexity
MF is a more complex theory to play, but the math, whilst intimidating, is relatively easy to understand (3/5). MF in unique in the fact that is has
2 prestige layers, unlike every other theory and custom theory to date. This adds a new dimension to the theory and makes it a very different play
experience. The math however, whilst intimidating and long, consist only of finite combinations of basic operations, so is quite manageable.
Speed
MF takes 189d to complete, making it the 5th fastest / 4th slowest theory to complete. MS has a rho -> tau conversion of 1, meaning you only need to
reach 1e600 rho to complete it. Therefore, the theory will feel a lot slower then other CTs, but still be just as fast. MF drops below 1 tau/hour at
1e100 tau (equivalent 1e250), lingering at 0.1 - 0.2 between 1e160 and 1e300, before slowly decaying, bump back up to 0.1 - 0.2 at 1e500 just before
the end. This is a fairly normal decay rate, nothing special.
Activity
MF is an active theory... at the start of pubs, and an idle theory at the end. MF has 2 levels of prestige. This means early in the publication you
will need to r "v reset". However, as the publication continues, these "v resets" will take longer and longer. Between v resets, the theory is
idleable, as doubling chasing does not provide much of a boost
Conclusion
MF is not that much of a complex theory, but it still have some complexity. It is very different from all other theories in the game, and
thus is harder to find strategies for. (also it has a logistic function and I don't think anyone want's more T5, no offense Mathis we love you
for making a CT). Due to this I don't think it is a good theory to start with, or even be your second theory. But, once you've gotten used to
custom theories as an idea, MF is a great fun theory to play.
Complexity
BaP is a simple theory to play (2/5), but a complex one to master. BaP is very similar to T2, and, as long as you do a little research on the
Basil Problem, and/or read a guide (how about this one!) on it, the math should be relatively simple and the execution familiar. The Perma-level
unlocked milestones may seems confusing, but are easy to get used too
Speed
BaP takes 151d to complex making it the 4th fastest theory. It is very slow to start, and never really picking up, just grinding it out faster then
all the others, maintaining a solidly constant 0.1 - 1 tau/hour. Well, that is until...
Activity
BaP is a very idle theory with Autobuy All being the best strat for the majority of it, apart from its MS stage. It's MS is very similar to T2 MS but
with much longer swapping times, making it okay to idle even then. BaP get's overnightable pubs over 8h at [TBA]. Overall, BaP is a very idle
theory
Conclusion
BaP is a good beginner theory. The presence of Perma-level milestones and the initial slowness makes it very similar to EF in this regard, with a bit
more MS. My advice is the same as EF: You will have to play it at some point, and if you are looking for an early idle theory it can provide, but
I would hold off playing EF for a bit, and not play it first
Complexity
Just afk (0/5)
Speed
Lot's of timeloss. You never actually get you from it, so it takes infinity days to complete, making it the slowest CT
Activity
Just afk
Conclusion
Well...
You can't talk about which custom theory to play first without mentioning this one. TA has been the subject of many debates in the community whether it should be used, or even allowed. However it's use is allowed, and it can be a valuable tool in your arsenal. If you use it right
But first, I need to teach you about Efficiency: Efficiency refers, essentially, to how much timeloss you are causing by playing the game imperfectly. Time advantages and tau advantages, whilst similar are not the same thing. If I were to do my overpushing, and get lots and lots of T2, I will get a time advantage over someone playing greedy, even if i have a tau disadvantage, and less f(t). The time advantage means I have more Long-term potential (because of my faster actives, in this case)
Why is this important? Well, TA is very inefficient. The time gains you are getting by playing active theories when sleeping is negligable compared to the time loss of not playing CTs at all. Time wise, it is far, far better to run an idle CT and idle theory instead of TA. However, of course, post 20k, especially in the 20-30k zone, your main theories are fast. Like really fast. So fast that it may be tempting to use TA on them, to speed up progress. However, in most cases, this is incorrect, from the purely optimising point of view. (Technically Purely optimally, TA should be used by idle players in the early lategame, around 20-30k for T1 and T5 maybe, but also purely optimally you are not an idle player).
Personally, I recommend using TA for the first few minutes T5 recovery (because nobody likes that), and if you want, a bit between 20k and 30k (because who doesn't like the dopamine hit of big number go up, let's be honest). BUT, I must emphasise, play the CTs. For 3 reasons:
These 3 reasons are aimed at the possibly fictional person who tries TA and can't be bothered playing CTs, I'm not entirely sure if that person exists but hey I wrote it and this is my guide so I'm leaving it there