Random Number Poker Answer

Rules

1. Two contestants are each assigned a number selected randomly from a uniform range between 0 and 1.
2. Player 1 has the option to retain his number or exchange it for a new randomly assigned number.
3. Knowing Player 1's choice, Player 2 can decide to either change his number or keep the original.
4. The player with the higher final number is declared the winner.

Questions

1. What would be the best approach for both players in this scenario?
2. If both contestants adopt the best strategies available, what chance does each have of winning?

Answers

• Player 1 should choose to switch if his number is below 0.567364; otherwise, he should hold onto it.
• If Player 1 opts to switch, Player 2 should choose to switch if his number is below 0.5; otherwise, he should remain with his original.
• In the case that Player 1 retains his number, Player 2 should switch if his number is lower than 0.660951; otherwise, he should keep what he has.
• Probability player 1 wins = 0.494333.
• Probability player 2 wins = 0.505667.
• If each contestant bets one number, Player 1's expected value is calculated to be -0.011333.