Question:-
2 players, A and B, play a series of games where player A has a 60% chance of winning each time. The winner of the series is the first player to win 3 games in a row. What is the probability of player A winning the series? Further question: 2 players, A and B, play a series of games where player A has a 60% chance of winning each time. The winner of the series is the first player to win 2 more games than their opponent. What is the probability of player A winning the series?
MyApproach:-
I've tried so many ways to solve this problem but it does not seem to resemble any other "probability game" I've encountered. So here are my thoughts:
Suppose there are n games. The result of last 4 games is determined: BAAA (representing winner). Starting from there, we fill in A or B back without placing three in a row.
I am stuck here and tried solving the problem for when n=4,5,6..... But it does not seem to work out, where I find no pattern.
For the second part, I got: Suppose there are n games, so A wins n/2+1 and B wins n/2-1. Therefore the probability is 0.6^(n/2+1) x 0.4^(n/2-1).