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)
The probabilities are the same either way.
Let T = probability of beating Player T
Let G = probability of beating Player G
There are three outcomes for each player:
Lose, Win, Win  Win, Lose, Win  Win, Win, 
For playing Player T first:
[(1T) * (T) * (G)] + [(T) * (1G) * (G)] + [(T) * (G)] = TG * (3  T  G)
For playing Player G first:
[(1G) * (G) * (T)] + [(G) * (1T) * (T)] + [(G) * (T)] = TG * (3  T 
G)
The probabilities are the same.

Posted by hoodat
on 20100907 12:12:55 