26 Feb '08 20:50

Suppose you are playing a game that involves yourself, your opponent, and a referee. The rules of the game are as follows:

1. Each person picks a number between 1 and 100, and keeps it secret.

2. Once all 3 numbers have been picked, they are revealed.

3. The person who comes closest to the referee's secret number without going over wins. If both players go over, or if both players tie, the game is repeated until there is a winner.

By symmetry, each player has an equal chance of winning this game. However, assuming your opponent doesn't have time to work out a strategy of his/her own and picks at random, is there a number you can pick to maximize your chances of winning?

1. Each person picks a number between 1 and 100, and keeps it secret.

2. Once all 3 numbers have been picked, they are revealed.

3. The person who comes closest to the referee's secret number without going over wins. If both players go over, or if both players tie, the game is repeated until there is a winner.

By symmetry, each player has an equal chance of winning this game. However, assuming your opponent doesn't have time to work out a strategy of his/her own and picks at random, is there a number you can pick to maximize your chances of winning?