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 Tennis,anyone? (Posted on 2010-09-07)
As a condition for the acceptance to a tennis club a novice player N is set to meet two members of the club, G (good) and T (top, i.e. better than good) within a total of three games (i.e. at most three!).
In order to be accepted, N must win against both G and T in two successive games.
N is free to choose with whom to start: T or G.
Which one is preferable?

Attributed to the late Leo Moser (1921—1970)

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 re: Not so fast | Comment 4 of 7 |
(In reply to Not so fast by Steve Herman)

You are correct.  Please forgive my error.  Elimination of the second possibility (win, lose, win) results in the comparison of  -T versus -G:

2TG - TG² ~ 2TG - T²G.  Since T < G, this means -T > -G.  Thus Scenario 1 has the highest probability.  Player N should play Player T first.

When I first considered the problem, I reasoned that Game 2 must be won.  If Player G was played first, then Player T must be beaten in Game 2.  By playing Player T first, Player N gains two chances of beating T.  By playing Player G first, Player N only gets one chance to beat Player T.

 Posted by hoodat on 2010-09-07 13:05:14

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