Ex­po­nen­tial Idle Guides

What The­ory Should I Push

Guide writ­ten by Playspout. Con­tri­bu­tions from the Amaz­ing Com­munity.

Feel free to use the gloss­ary as needed.

It de­pends :)

All jokes aside, this seem­ingly simple ques­tion can have more in-depth an­swers than you might real­ize. Se­lect­ing a the­ory to push dur­ing the day de­pends on many factors; some are:

  1. How of­ten can you check your phones.
  2. Each the­ory’s pub­lic­a­tion length.
  3. Each the­ory’s act­ive/​idle ra­tio.
  4. Each the­ory’s \(\dot{τ}\).
  5. Over­push­ing im­plic­a­tions.

How of­ten can you check your phone(s) #

If you can only check your phone once every 8 hours or less of­ten, this is ba­sic­ally the same as overnight. In this case, you would prefer the­or­ies that do well while id­ling (low act­ive/​idle ra­tios). This makes sense be­cause if a the­ory has a really strong act­ive strategy, you would­n’t want to waste that po­ten­tial by id­ling for 8 hours+. Ex­amples of suit­able the­or­ies are T2, T4, T6, SL. No other the­or­ies have low act­ive/​idle ra­tios.

Each the­ory’s pub­lic­a­tion length #

This relates to the first reason. Let’s say you can check your phones once every 8 hours. However, the the­ory’s op­timal pub­lic­a­tion length is only 4 hours, then you start to auto­mat­ic­ally lose ef­fi­ciency by go­ing over the op­timal pub­lic­a­tion length. The ef­fi­ciency lost de­pends on the the­ory.

For ex­ample, T2 has the low­est in­tra-pub­lic­a­tion de­cay, so it re­tains its ef­fi­ciency quite well even if you go over the op­timal pub­lic­a­tion length. In con­trast, a the­ory like T3 has bad in­tra-pub­lic­a­tion de­cay. If the the­ory sim­u­lator says to pub­lish T3 after 3 hours and you let it idle for 8 hours, you will lose a lot of ef­fi­ciency. This in­tra-pub­lic­a­tion de­cay is dir­ectly re­lated to the concept of over­push­ing ef­fi­ciency ex­plained here.

From the ex­plan­a­tions above, if you’re forced to go over a the­ory’s op­timal pub­lic­a­tion length, you should at least do it on a the­ory that has low in­tra-pub­lic­a­tion de­cay. Once again, the suit­able the­or­ies are T2, T6, T4 (in this or­der). T2 is by far the best, with T6 second best. Per­son­ally I’d only do this for T2 and T6 only (not T4). For cus­tom the­or­ies, the 2 most suit­able the­or­ies are SL and EF, with pref­er­ence for SL.

Each the­ory’s act­ive/​idle ra­tio #

If you have act­ive time, you’d prefer to do the­or­ies that have high act­ive/​idle ra­tio (everything else be­ing equal). This is be­cause you can idle when you have time to do act­ive, but you can’t act­ive when you can only idle. So we may as well make the most of the avail­able act­ive time. The­or­ies with high act­ive/​idle ra­tio are T1/​T5/​T3/​T8, WSP. T7, CSR2, EF have mod­er­ate act­ive/​idle ra­tio.

However, do con­sider all the other factors as well. It is pos­sible (and even likely) that it is best to just push a more idle the­ory even when you have act­ive time.

Each the­ory’s taudot #

The faster a the­ory’s \(\dot{τ}\), the more we should do it. This is be­cause we can gain faster tau, which means more stu­dents, which means more \(\dot{τ}\). Once again, do con­sider other factors in con­junc­tion.

Over­push­ing im­plic­a­tions #

The bet­ter a the­ory is for over­push­ing, the more we should push it first. In gen­eral, this means T2, T6, T4 in that or­der should be pushed first. Cus­tom the­or­ies are not af­fected by over­push­ing.

Con­clu­sions #

Most of the factors lis­ted above are weighed to­ward do­ing more idle the­or­ies with long pub­lic­a­tion lengths and low act­ive/​idle ra­tios. By chance these the­or­ies are T2, T4, T6. The re­com­mend­a­tion is to push these the­or­ies first. Once these the­or­ies’ rates are sig­ni­fic­antly lower than oth­ers, push other the­or­ies act­ive only when you have act­ive time. If your T2, T4, T6 rates are MUCH slower than oth­ers however, you might de­cide to push other less idle friendly the­or­ies any­way even if you sac­ri­fice the act­ive strategy po­ten­tials. Ul­ti­mately, if you don’t care about lead­er­board rank­ings, you can just push whatever the­or­ies you en­joy.