A greedy way to push a the­ory dis­tri­bu­tion is to push all 8 ori­ginal the­or­ies un­til they have sim­ilar /hour gains. However, this is not ne­ces­sar­ily op­timal for long term gains. Dis­tri­bu­tion over­push­ing is when you push cer­tain the­or­ies such that their /hours are less than oth­ers. This seems to con­tra­dict op­timal play, as gen­er­ally you’d gain more stu­dents quicker if you push all the­or­ies to equal rates. However, some the­or­ies do not be­ne­fit as much from the 3rd level of the 9th Re­search in the Stu­dents tab (3R9). There­fore it makes more sense to push the­or­ies that don’t be­ne­fit much from ad­di­tional stu­dents first. This al­lows us to use the ad­di­tional stu­dents to ac­cel­er­ate the rates of the­or­ies that do be­ne­fit sig­ni­fic­antly from 3R9.

We will com­pare the ef­fect of stu­dents on , vs the ef­fect of time on for each the­ory. For the equa­tions be­low, ‘K’ and ‘A’ are just con­stants, ‘S’ is the mul­ti­plier gained from hav­ing stu­dents (3R9 mul­ti­plier).

▶︎ The­ory 1 Permalink: the­ory-1#

▶︎ The­ory 2 Permalink: the­ory-2#

▶︎ The­ory 3 Permalink: the­ory-3#

▶︎ The­ory 4 Permalink: the­ory-4#

▶︎ The­ory 5 Permalink: the­ory-5#

▶︎ The­ory 6 Permalink: the­ory-6#

▶︎ The­ory 7 Permalink: the­ory-7#

▶︎ The­ory 8 Permalink: the­ory-8#

From pre­vi­ous work­ings, the over­push­ing coef­fi­cients are:

This means that for ‘per­fect’ over­push, we should push the max­imum of {, , , , , , , }. This will max­im­ize long term gain, as­sum­ing everything else is equal.