# numbers: the anaesthetist

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The Independent Online
Anyone for tennis? It's a fascinating game, numerically speaking. Because of its scoring system, which clumps the points together into games, and the games into sets, the winner need not be the person who wins most points.

And when you take into account the advantage of the serve, it all comes down to tossing a biased coin in a curiously irregular series of experiments.

To take a simple example: suppose we have reached a score of deuce and the server has a two-to-one chance of winning each point (which is about the average level in men's tennis). Then the server will have a four-in- nine probability of winning the game in the next two points, compared with a one-in-nine chance of losing it and a four-in-nine chance of being back to deuce.

Pursuing that line of argument, we may calculate that the server has an 80 per cent overall chance of winning the game from deuce, compared with a 20 per cent chance of losing.

Going back to the start of the game, the sums become more complicated, but work out at just about a 1 in 7 chance of breaking serve. Which is about one game in each set.

So the whole match is decided on precisely when, in a long series of bent-coin tosses, the unlikely tails come up.

When Pete Sampras is serving, however, he wins five points to every two of his opponents'. And that works out at colossal 92.7 per cent chance of holding serve.

Competition: Time for a spot of mixed doubles, I think.

Mishap in Chopin's nest. Mind below!

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