09 Sep '08 17:462 edits

Saw this one on a website, but I won't tell you which one until later (so it'll take a bit longer to find the answer!).

Three people are playing a game with the following rules:

1. Each player picks a natural number (i.e. 1, 2, ...) in secret.

2. After all players choose a number, the numbers are revealed.

3. The player with the lowest

4. If all three players pick the same number, each player wins $1.

To clarify the above, if the players pick (2,4,4) or (2,3,5) or (1,1,2) the lowest

If you are playing this game, what number-picking strategy will give you the highest expected value? You may assume that each of the other players is a "perfect" logician, and will try to maximize their own expected value.

HINT: The optimal strategy must be optimal no matter what strategy the other players use, so all three players will end up using the same one...

Three people are playing a game with the following rules:

1. Each player picks a natural number (i.e. 1, 2, ...) in secret.

2. After all players choose a number, the numbers are revealed.

3. The player with the lowest

*unique*number wins $3.4. If all three players pick the same number, each player wins $1.

To clarify the above, if the players pick (2,4,4) or (2,3,5) or (1,1,2) the lowest

*unique*number in each case is 2 and the player who picked it gets $3 (the other two players get $0). If the players pick (1,1,1) then there is no lowest unique number and all three players get $1.If you are playing this game, what number-picking strategy will give you the highest expected value? You may assume that each of the other players is a "perfect" logician, and will try to maximize their own expected value.

HINT: The optimal strategy must be optimal no matter what strategy the other players use, so all three players will end up using the same one...