Online Poker Research Paper

(This is also true for two-player general-sum games.) Moreover, in a game with more than two players, it is possible to lose even when playing an exact Nash equilibrium strategy.One such example is the , in which each player simultaneously picks a point on a ring and wants to be as far away as possible from any other player.

(This is also true for two-player general-sum games.) Moreover, in a game with more than two players, it is possible to lose even when playing an exact Nash equilibrium strategy.One such example is the , in which each player simultaneously picks a point on a ring and wants to be as far away as possible from any other player.

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In two-player and two-team zero-sum games, playing an exact Nash equilibrium makes it impossible to lose no matter what the opponent does.

(For example, the Nash equilibrium strategy for rock-paper-scissors is to randomly pick rock, paper, or scissors with equal probability.) Although a Nash equilibrium is guaranteed to exist in any finite game, it is not generally possible to efficiently compute a Nash equilibrium in a game with three or more players.

It did a very good job of putting me to tough decisions when I didn’t have a strong hand and getting value when it had the best hand.

It was a fun challenge and I’d enjoy the opportunity to compete with it again.” —Trevor Savage, professional poker player “Pluribus is a very hard opponent to play against.

As humans I think we tend to oversimplify the game for ourselves, making strategies easier to adopt and remember.

The bot doesn't take any of these shortcuts and has an immensely complicated/balanced game tree for every decision.” —Jimmy Chou, professional poker player “It was incredibly fascinating getting to play against the poker bot and seeing some of the strategies it chose.

And that’s what makes it so difficult to play against.

You're always in a situation with a ton of pressure that the AI is putting on you and you know it’s very likely it could be bluffing here.” —Jason Les, professional poker player "Whenever playing the bot, I feel like I pick up something new to incorporate into my game.

The Nash equilibrium is for all players to be spaced equally far apart along the ring, but there are infinitely many ways this can be accomplished.

If each player independently computes one of those equilibria, the joint strategy is unlikely to result in all players being spaced equally far apart along the ring.