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

A single game of snooker is called a frame. In the first round
of a snooker tournament, the matches are played over eleven frames
(so the first player to win six frames wins the match). In the
later rounds matches are played over 15 frames. Assume that each
player has steady nerves and his chance of winning any frame
(irrespective of who starts) is constant.

In the problem
Snooker you were asked to find the probability that a player
wins a match over fifteen frames, given that his chance of winning
any frame is $0.4$. You should now find the probability that this
player wins a match over eleven 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?

Does this surprise you, or not? Why?

Numerical
investigation: Is it generally the case that more frames
lead to a reduced chance of a weaker player winning? Devise a
spreadsheet which computes the chance of a weaker player winning a
match in which the first player to $1, 2, 3, 4, \dots, 17, 18$
frames wins. The world snooker championship final is taken over the
best of $35$ frames. In order to have at least a $10\%$ chance of
winning such a final, what probability of winning each frame would
you need to have? Plot $\log(n)$ against $P(win)$.