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Before a knockout tournament with 2^n players I pick two players. What is the probability that they have to play against each other at some point in the tournament?


If the score is 8-8 do I have more chance of winning if the winner is the first to reach 9 points or the first to reach 10 points?


A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

Snooker Frames

Age 16 to 18 Challenge Level:

The method for solving this problem is given in the solution to the problem Snooker.

You have to compare the probabilities of winning a match which is the best out of 11 frames with one that is the best out of 15 frames. In the first case the first player to win 6 frames wins the match and in the second case the first to win 8 frames wins the match.

Assume that each player has steady nerves and his chance of winning any frame (irrespective of who starts) is constant.

You can use the results in the problem Snooker for the probability that a player wins a match over 15 frames, given that his chance of winning any frame is $0.4$. All you have to do here is to use a similar method to work out the probability that this player wins a match over 11 frames. It is believed that the weaker players have a better chance of winning the matches over eleven frames than they do over fifteen frames. Do your results confirm this or not?