Random Number Poker Answer

Rules

1. Two players are each given a random number drawn from a uniform distribution from 0 to 1.
2. Player 1 may keep his number or switch it for a new random number.
3. Player 2, knowing player 1's decision, may also switch or stick with his original number.
4. The higher final number at the end wins.

 

Questions

1. What is the optimal strategy for each player?
2. Assuming both players follow optimal strategy, what the probability of winning for each player?

 

Answers

• Player 1 should switch with less than 0.567364, otherwise stand.
• If Player 1 switches, then player 2 should switch with less than 0.5, otherwise stand.
• If Player 1 stands, then player 2 should switch with less than 0.660951, otherwise stand.
• Probability player 1 wins = 0.494333.
• Probability player 2 wins = 0.505667.
• Assuming each player wagers one number, then the expected value of player 1 = -0.011333.