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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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 Whose serve? | Comment 5 of 7 |

I composed a reply and tried to post it a couple hours ago, but it seems to have been lost, so I'll try again.

This is only remotely a "probability" problem since we have no information on the strength of N.  We are told that T is a stronger player than G, so presumably N other things being equal will have better chances against G.  N will face a different opponent in game two than in game one, and must face the first opponent again in game three if it goes that far.  We have no information on whether or how service is determined (for the first, or any, game), though generally a player has a better chance on serve than otherwise.

Since N must win two consecutive games, these would have to be once against G and once against T.  We must be able to assume that N is warmed up for whichever order he follows .

Playing G first would allow N more warmup before facing T, and he would play T only once (the second game), so this seems the obvious choice (unless he is trying to psych out T who may just be a local "top").  We can only guess why a tennis club would hope to attract members with such procedure, or why N would want to join.  Since service is such an advantage, no club would decide on anything less than winning a set, and more likely a match.

 Posted by ed bottemiller on 2010-09-07 16:40:22

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