It seems that the second scenario is slightly better for player A. This problem can be solved through the
negative binomial distribution, which measures the probability of having n successes before k failures. In this case, we need to calculate how much is likely that A's opponent wins 0 through 54 games before A wins his 55th game. This can be achieved with a single line in R:
Code:
> pnbinom(54,55,.55)
[1] 0.8529248
For the second scenario, we evaluate the probability of A to win a set and then in the same fashion the probability of winning 11 sets:
Code:
> pWinSet<-pnbinom(4,5,.55)
[1] 0.6214209
> pnbinom(10,11,pWinSet)
[1] 0.8735609
A good 2% improvement for player A.