Step­wise Vari­ables

Guide writ­ten by Playspout. Con­tri­bu­tions from the Amaz­ing Com­munity.

Feel free to use the gloss­ary as needed.

In­tro­duc­tion to step­wise vari­ables #

Step­wise vari­ables are vari­ables that don’t in­crease by the same per­cent­age with each level. For some vari­ables, such as q2 in T1, doubles its value each time it is bought. However, for some other vari­ables, such as q1 in T1, buy­ing a level will not al­ways in­crease its value by the same amount. Some­times its value in­creases by 10%, some­times by 5.5%. This guide will ex­plain these step­wise vari­ables, how to de­term­ine the per­cent­age in­crease from buy­ing these vari­ables, and how to use these in­form­a­tion to op­tim­ise strategies.

Step­wise vari­ables in ori­ginal the­or­ies #

All step­wise vari­ables in ori­ginal the­or­ies are based on mod­u­lus 10 (mod10). The gen­eral for­mula is:

\((10 + x mod 10)^{\floor(\frac{x}{10})} - 10 \)

For ori­ginal the­or­ies, all vari­ables writ­ten in sci­entific nota­tion are step­wise vari­ables.

A con­tro­ver­sial the­ory #

After reach­ing ee20k \(F(t)\) and com­plet­ing The­ory 9, you will un­lock cus­tom the­or­ies. Each cus­tom the­ory gives up to 150 tau. It usu­ally takes more than 3 months to reach this point. It takes ap­prox­im­ately 1 month of act­ive play for each cus­tom the­ory to reach 100 tau. There­fore it is not feas­ible for us to reach e150 tau on all cus­tom the­or­ies.

After the­ory 9 com­ple­tion, you might no­tice that the tau/​hour of a lot of the­or­ies are very quick. In fact, be­cause of 3R9, this tau/​hour is one of the highest in the whole game. Be­cause of this, it would be help­ful to have something to re­li­ably util­ise this tau/​hour peaks.

There ex­ists a cus­tom the­ory that can auto­mat­ic­ally buy vari­ables ac­cord­ing to pre-pro­grammed rules. It can also auto­mat­ic­ally pub­lish the the­ory at close to op­timal points. Fur­ther­more, it can switch between dif­fer­ent the­or­ies de­pend­ing on the ex­tra­pol­ated tau/​hour of each one. This cus­tom the­ory is quite con­tro­ver­sial amongst top play­ers, however it is valid to use. The cus­tom the­ory, made by rus, is called The­ory Auto­mator (TA) and it can be down­loaded here.

An al­tern­at­ive over­push ver­sion of the same the­ory can be down­loaded here.

2 TA ver­sions? Which one should I choose? #

The over­push ver­sion is for LONG term max­im­isa­tion of \(f(t)\) and tau. It is bet­ter if you wish to play the game for at least 1 year. It is also bet­ter if you wish to climb the lead­er­boards LONG term. If you want more in­stant grat­i­fic­a­tion, the ‘stand­ard’ TA is bet­ter. It is also faster to ee50k \(f(t)\). For a more de­tailed ex­plan­a­tion on over­push­ing and cash­ing in, please see my other blog post on over­push­ing.

How use­ful is TA for each the­ory? #

TA does act­ive strategies for you. It also auto­mat­ic­ally pub­lishes for you. With these 2 facts, we can es­tab­lish that TA is most use­ful for the­or­ies that have strong act­ive strategies as com­pared to idle strategies. It is also more use­ful for the­or­ies with short pub­lic­a­tion times.

There­fore, the most use­ful the­or­ies for TA are T1, 3, 5, 7, 8. TA in par­tic­u­lar is not really use­ful for T2 since it already has long pub­lic­a­tion times, AND there is­n’t a strong act­ive strategy for T2. In fact, I’d re­com­mend NOT us­ing TA to run T2.

How long to use The­ory Auto­mator (TA) #

Here we as­sume that your goal is to max­im­ise the \(f(t)\) gain. There are many factors to con­sider; the main one be­ing how of­ten do you check the game. The more of­ten you check the game, the earlier you should stop us­ing TA. We will go through a couple of ex­amples and give gen­eric ad­vice:

Su­per Idle Player (once per week) #

For this player, we will run TA un­til ee50k \(f(t)\). We will then start to manu­ally do T2 and pos­sibly T6. We will run TA on everything else. At ee60k, we will con­sider manu­ally do T4. Prac­tic­ally, we will never manu­ally do T1, 3, 5, 7, 8 ever again.

Stand­ard Idle Player (once per day) #

For this player, we will run TA un­til about ee40k \(f(t)\). We will then manu­ally do T2 and T6. We will con­tinue to run TA to about ee50k \(f(t)\). We will then manu­ally do T4 as well. We will con­tinue to use TA for T1, 3, 5, 7, 8 un­til ee60k \(f(t)\). Af­ter­wards, we will then aban­don TA and manu­ally do all the­or­ies.

Semi Act­ive Player (3 times per day) #

For this player, we will aban­don us­ing TA for T2 straight away. At about ee30k \(f(t)\), we will also aban­don us­ing TA for T6. At about ee40k \(f(t)\), we will aban­don TA on T4. Fi­nally, at about ee50k \(f(t)\), we will aban­don us­ing TA for everything else.

Hy­per Act­ive Player (10 times+ per day) #

For this player, we will aban­don us­ing TA for T2, 4, 6 straight away. At about ee40k \(f(t)\), we will aban­don TA for everything.