Assume at step n, the male that without a partner has density fn(x) ( relative to the original density of 1), the females that does not have a partner has density gn(x) = fn(1-x) then at step n+1: f(n+1)(x) = fn(x)* (integration(0~1-x)[fn(x)])/(integration(0~1)[fn(x)]) the result guess would be 1-(1/(1*2) + 1/(3*4) +1/(5*6) +....) (unproved)