The­ory 9 to En­dgame

The World of Grind­ing, R9 Boost, and Cus­tom The­or­ies

Guide writ­ten by LE★Baldy and Snaeky. Con­tri­bu­tions from the Amaz­ing Com­munity.

This guide is cur­rently un­der­go­ing change. Keep in mind, strategies may change.

Feel free to use the gloss­ary as needed.

DO T9 BE­FORE EE50k

The­ory 9 #

There is no the­ory 9 guide and this is a guide for what to do after the­ory 9. Have fun fig­ur­ing out T9 for your­self and re­move stu­dents when fin­ished and put back into R9 and phi.

Gradu­ation rout­ing #

Rout­ing is based on your cur­rent Tau (\(\tau\)) and Phi (\(\varphi\)) num­bers.

Make sure to use the cal­cu­lat­ors and sim­u­lat­ors for op­timal gradu­ation, stu­dent, star, and the­ory op­tions.

Push F(t) with 3R9 swap­ping #

Mem­or­ize your stu­dent dis­tri­bu­tions with and without 30 R9 stu­dents. Use the stu­dent cal­cu­lator if needed. You will com­monly see people refer to this as R9 seap­ing as a long held name of the strategy.

1. Wait till \(F(t)\) stops grow­ing with stu­dents in R9 push­ing \(\tau\).
2. Start ac­cel (prefer­ably keep it between prestiges).
3. Po­ten­tially sit here to stack t for big­ger \(\varphi_2\) when you have stu­dents in \(\varphi_2\). Only do this when you are near a gradu­ation mark.
4. Re­spec all 30 stu­dents from R9.
5. Wait for the auto­prestige to prestige and swap back stu­dents to R9.
6. Re­peat.

Also see t stack­ing

R9 auto­prestige ex­pres­sion #

You can find the auto­prestige used for R9 Seap­ing here: Equa­tion. If you don’t have this ex­pres­sion, then you will have to manu­ally prestige each time (turn it off be­fore seap­ing).

Ref­er­ence R9 Swap­ping Auto­prestige Ex­plan­a­tion

How to prop­erly use the Gradu­ation Cal­cu­lator #

The gradu­ation cal­cu­lator is a great tool to be able to get the best \(F(t)\) to gradu­ate at given your \(\varphi\), \(\tau\), and stu­dents. It also has ad­di­tional fea­tures such as dif­fer­ence in R9 boost upon gradu­ation. The cal­cu­lator is for the \(\varphi\) you are us­ing to push. This means use the \(\varphi\) without any levels in R9. The cal­cu­lator also already takes into ac­count su­prem­acy up­grades and skipped stu­dents so no ex­tra work needs to be done. In­struc­tions on how to run are found in In­tro­duc­tion to Gradu­ation.

Three Steps To Get­ting The Best Res­ult #

1. After your pro­gress has slowed after re­cov­er­ing from a gradu­ation and near­ing the next gradu­ation, get res­ults from the cal­cu­lator. Only the \(F(t)\) out­put here is use­ful.
2. Upon ar­riv­ing to the most re­cent out­put, get a new set of res­ults from the cal­cu­lator.
3. Re­peat Step 2 un­til out­put is the same \(F(t)\) you are cur­rently at. This is when you should gradu­ate.

Note: You may run into a Tau is higher than Phi res­ult, or sim­ilar to this, but this is due to data run­ning that por­tion of the cal­cu­lator be­ing old and be­fore Cus­tom The­or­ies were in­tro­duced which shif­ted the re­l­at­ive amounts. This will be fixed in the fu­ture with more data (sub­mit here after any gradu­ation).

The­ory rout­ing and strategies #

For best the­ory rout­ing and push­ing, use the The­ory Sim and the The­ory Sim Guide to give the best strategy and mul­ti­plier for the next pub­lic­a­tions. Hu­man T5 is be­low:

T5 rout­ing #

Run­ning the act­ive strats will make this the num­ber one the­ory for a while and even­tual num­ber two after T6 takes over (e750-770+). A step-by-step on how to pro­gress the the­ory is be­low.

Steps Cre­ated by: Snaeky, Marks, Baldy, and Nerdy

1. x10 buy \(c_2\) manu­ally and auto­buy the rest un­til within ~\(e10\) of your pre­vi­ous pub­lic­a­tion.
2. Around your last pub mark within ~\(e10\), start auto­buy­ing \(c_2\) and stop auto­buy­ing \(c_1\) and \(q_1\). At this point:
   1. buy \(q_1\) up to \(15%\) of the cost of the next doub­ling pur­chase (\(2^x\) pur­chase),
   2. and buy \(c_1\) after you pur­chase \(c_2\) up to \(e1\) lower than \(q\). This limit will in­crease as you get higher \(\tau\) and fur­ther into a pub­lic­a­tion.
3. Once you reach the de­sired pub­lic­a­tion point, pub­lish.
4. Re­peat this for stonks.

Com­ment­ary

No com­ment­ary

T5 will al­ways give its best res­ults from act­ive play. However, after step 3, you can still get good res­ults while auto­buy­ing \(q_1\) and manu­ally pur­chas­ing \(c_1\) every 10-15min. This makes the the­ory slightly less act­ive and easier to deal with.

Ad­di­tional In­form­a­tion

Pur­chase \(c_2\) when \(1.5q > c_2*c_3^{1.1}\).

\(q\) be­gins to slow down when you reach \(2q > c_2*c_3^{1.1}\).

Strategy con­struc­ted by: Snaeky, Marks, Baldy, and Nerdy

t stack­ing #

A use­ful strategy in the later stages of a gradu­ation is \(t\) stack­ing. It refers to swap­ping mul­tiple times dur­ing a single prestige, the quant­ity will in­crease as you gain more \(F(t)\). At about 50k, you should start to do this at least once per prestige near the end of a gradu­ation to re­cover faster. Past 55k, you might need to do this more than once. The more of­ten the bet­ter, as the main goal is to in­crease \(F(t)\) with the swap, thus giv­ing us more \(dt\), al­low­ing for more \(t\), then just let­ting \(t\) build up over time. This can be re­peated mul­tiple times and res­ults in faster pro­gress for \(t\), es­pe­cially as each swap in­between profits from more \(\varphi\) due to ad­di­tional \(dt\) and \(t\). Over­all this speeds up the time a prestige needs to reach a high enough value for \(t\) to do a fi­nal swap com­pared to let­ting the game run fully idle.

Skipped stu­dents rout­ing #

Once you have enough stu­dents to al­ways have R4 to R7 maxed out (about 30k), you will want to look for “Big­mas”, stu­dents that will yields a lar­ger than nor­mal amount of \(\varphi\), and “Skip­mas”, stu­dents that will yield 0 ex­tra \(\varphi\), as they can­not be used for op­timal stu­dent dis­tri­bu­tion. These stu­dents may change if you do not use ac­cel, or your star val­ues are drastic­ally dif­fer­ent from the norm. So, to check if you have a Skipma or a Bigma, you will need check the cal­cu­lator at the \(F(t)\) that you just gradu­ated at for the stu­dents that you have not, and the next stu­dent that you will get, if the dis­tri­bu­tion has an ex­tra stu­dent, then it is a Skipma, if it has a lar­ger than nor­mal change in \(\varphi\) (nor­mally 1e9 dif­fer­ence), then it is a Bigma. You want to gradu­ate on a Bigma, and skip Skip­mas.

Due to fluc­tu­ations with stars, ac­cel, \(t\), and more, Skipma and Bigma can be situ­ation de­pend­ant. Be­low is a chart with nor­mal ac­cel and stars, but the stu­dents to skip due to Bigma and Skipma based on vary­ing levels of de­vi­ation from nor­mal t for that \(F(t)\). This does change based on CT’s as they shift data, but it is not the largest dif­fer­ence.

Note: The best way to de­cide a bigma skipma is to either cal­cu­late phi dis­tri­bu­tion your­self or use the gradu­ation cal­cu­lator which will auto­mat­ic­ally ask for in­form­a­tion for this cal­cu­la­tion if you are on 1dσ. In­struc­tions to run are found in In­tro­duc­tion to Gradu­ation.

Ex­plan­a­tion by: Snaeky and AfuroZamurai

Cal­cu­la­tions by: LE★Baldy

Su­prem­acy Equa­tion Past 48k #

When you get to ee48k, you will have all of the \(\psi\) up­grades and you can get rid of the old Auto­su­prem­acy Equa­tion. The old Auto­su­prem Equa­tion is very in­ef­fi­cient, but its the best that we have right now due to how Su­prem­acy up­grades are spaced be­fore the fi­nal \(\psi\) up­grade. It is not worth push­ing past an up­grade as there is no bo­nus to \(\varphi\) from \(\psi\), only \(d\psi\). When you hit about \(f(t)\) ee50k you can skip buy­ing most \(\psi\) up­grades and be able to re­cover fairly quickly. The Su­prem­acy Equa­tions for the \(F(t)\) that we know are as fol­lows:

Su­prem Equa­tion past ee48k:

(cos­tUpS(1)<e52&&psi+dpsi>e52)
||(cos­tUpS(3)<e411&&psi+dpsi>e411)
||(cos­tUpS(3)<e511&&psi+dpsi>e511)
||(cos­tUpS(3)<e531&&psi+dpsi>e531)
||(cos­tUpS(3)<e551&&psi+dpsi>e551)
||(cos­tUpS(3)<e571&&psi+dpsi>e571)

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Su­prem Equa­tion past ee52k:

(cos­tUpS(1)<e52&&psi+dpsi>e52)
||(cos­tUpS(3)<e511&&psi+dpsi>e511)
||(cos­tUpS(3)<e571&&psi+dpsi>e571)

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Su­prem Equa­tion past ee58-60k:

(cos­tUpS(1)<e52&&psi+dpsi>e52)
||(cos­tUpS(3)<e571&&psi+dpsi>e571)

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How to re­spec #

See the in­tro­duc­tion guide for re­spe­cing stu­dents and mile­stones.

Lemma #

All Lemma sec­tions already have the - but­tons un­locked. This gives back the full price paid into the up­grade. This al­lows for up­grade swap­ping or drop­ping up­grades at the very end to hit the lemma limit early. The amount re­speced is based on the x1, x10, x25, x100, xMax in the top right. On the right side, you can see the total levels bought. There is also a free re­set top right if a mis­take is made.