IBM Ponder This #094 · February 2006

Puzzle for February 2006.

This month's puzzle is about a simple 2 player poker like gambling game. The two players each ante 1 unit to a pot. Then each player receives a random number uniformly distributed between 0 and 1. Each player knows the value of his number but not the value of his opponent's number. The first player is then given an opportunity to bet one additional unit. If the first player doesn't bet there is a showdown and the player with the highest number collects the antes. If the first player bets the second player may call by matching the bet or drop out (giving the antes to the first player). If the second player calls there is again a showdown and the player with the highest number collects the pot (consisting of 4 units, the bets and the antes). If both players follow their optimal strategy what is the value of the game? In other words if they play (optimally) a large number of games how much is the first player expected to win (or lose if the value is negative) per game?

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The first 100 people who answer correctly will be listed. The answer will be posted a week after the 100th is received, or at the end of the month.

Solution

Best opened after a real attempt

To be added.