>>940
１０００色までやってみた。
https://i.imgur.com/CSDDMr0.png
線形回帰で係数をもとめたら 1.609356


> # n種類のガチャからm種類を集めるまでの期待値
> collector <- function(n=100,m=80,print=TRUE){
+ library(gmp)
+ x=(n-m+1):n
+ x=as.bigq(x)
+ y=sum(n/x)
+ if(print) print(y)
+ return(asNumeric(y))
+ }
> collector(5,4)
Big Rational ('bigq') :
[1] 77/12
[1] 6.416666667
> collector(100,80)
Big Rational ('bigq') :
[1] 10075468010284923492783367185945796008025/63382159299738615604121644486647548688
[1] 158.963786
> n=1:1000
> r=0.8
> y=sapply(n,function(x)collector(x,round(r*x),print=F))
> plot(n,y,bty='l',col='gray')
> lm=lm(y~n) ; lm

Call:
lm(formula = y ~ n)

Coefficients:
(Intercept) n
-1.941193 1.609356