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)

(In reply to

re: Not so fast by hoodat)

I looked up Moser's reasoning on google, but I am still not persuaded that playing T in the first game is the best ploy. This is not a coin toss. Unless N's tennis skills are fairly close to those of T, he will probably lose any games (one or two) against T and hence not gain membership. N is probably more likely to lose two games to T, than to G. Moser's solution seems to imply that N will always beat G, but no specs support that. Perhaps if N could be assured the service in the third game if played against T, this could tip the selection. Since G is weaker than T, it would be more likely that N could beat G either once or twice. Does Moser suggest that the probabilities always favor "T first" regardless of issues of relative skills? A provocative puzzle, but I am not sure that it comes under "probabilities" -- would you as a bystander be more or less likely to suggest starting with N vs T if you knew more?