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 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