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.
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% :/