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## 'Snooker Frames' printed from http://nrich.maths.org/

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?