Random Number Poker Answer
- Two players are each given a random number drawn from a uniform distribution from 0 to 1.
- Player 1 may keep his number or switch it for a new random number.
- Player 2, knowing player 1's decision, may also switch or stick with his original number.
- The higher final number at the end wins.
- What is the optimal strategy for each player?
- Assuming both players follow optimal strategy, what the probability of winning for each player?
- 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.