User blog comment:OceanSushi/A Mini Research on the Optimal Maruyu Batch Size/@comment-26154973-20160224100353/@comment-26154973-20160225073322

About rates, this is what is claimed by both this wiki and Japanese wikiwiki (and other places like http://ch.nicovideo.jp/mimishibo/blomaga/ar863908, don't know if it's statistically verified somewhere though), see "Expected" and "Chance" columns in Modernization (divide expected value by Maruyu count) and http://wikiwiki.jp/kancolle/?%B6%E1%C2%E5%B2%BD%B2%FE%BD%A4#yf0a0918 (so even if you mix Kai and non-Kai, expected value should be a sum of 1.2 per non-Kai and 1.6 per Kai).

Let's say success gives +a luck with probablity p and failrure gives +b < a luck with probabilty q = 1 - p, then expected value is pa + qb (for 50% it's just 1.5, 1.75, 1.5, 1.625, 1.6 per Maruyuy Kai, so 2-sets would be better, for variable rates expected value defined to be 1.6 per Maruyuy Kai, hence the variable rates), you can then do normalization b -> 0, a -> 1 and realize that the distributions are binomial distributions, so by plotting unnormalized pmf's:

https://i.imgur.com/ghhOeM2.png

While for 50%:

https://i.imgur.com/Qsw4Cyu.png