Old Jimmy and young Pete are both tennis champions. They have played each other many times, each winning exactly half of the matches. When both are fresh Jimmy is much the better player, but he tires rapidly so his probability of winning the kth set is p
k, where p is the probability that he wins the first set.
If they always play best-of-five matches, what is the value of p?
I was looking for a check - the agreement of Charlie's and my results
provide this.
For the sake of completeness, the correct closed form (made from adding the probabilities of the 10 cases listed by myself and by
Charlie) is:
p^6 + p^7 + 2p^8 + 2p^9 - p^10 - 2p^11 - 2p^12 - 3p^13
- 3p^14 +6p^15 = 0.5
closed form
