Continuous Blackjack is a variant of the classic poker game blackjack. Here are the rules:
- The game will run for many rounds, say, one billion.
- Each round every player's position is reshuffled randomly.
- From the first player, each player plays their turn in order, and other players can observe the previous players' actions.
- Each player can choose to hit or stay. If the player chooses to hit, a random number is generated from the standard uniform distribution and added to the player's total sum, should the player choose to stay, the current turn terminates.
- Players' scores are the total sums as long as they don't exceed 1, in which case the score will be 0. At the end of each round, the player with the highest score receives one point.
- In the rare scenario where two or more players get the same highest score, they will share the point equally among them.
The strategies here are based on my paper Continuous Blackjack: Equilibrium, Deviation and Adaptive Strategy