IBM Ponder This #106 · February 2007

Puzzle for February 2007.

Consider the following two person game. Each player receives a random number uniformly distributed between 0 and 1. Each player can choose to discard his number and receive a new random number between 0 and 1. This choice is made without knowing the other players number or whether the other player chose to replace his number. What strategy should a player follow to ensure he will win at least 50% of the time?

REVISED, 2/5/07 -- After each player has had an opportunity to replace his number the numbers are compared and the player with the higher number wins.

Solution

Best opened after a real attempt

To be added.