Poorly, I apparently missed the first term of X^0 $100 = expected cost of matches $20 = cost on this side per match X = probability of rejection (which leads

expected cost = cost of first match times probablity it is needed plus cost of second match times probability it is needed... plus cost of nth match times probability it is needed.

100 = 20x^0 + 20x + 20x^2...20x^n 5 = x^0 + x^1 ... x^n

The actual number is more like 72% :/