Online Poker Research Paper

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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.

But developing an AI system capable of defeating elite players in full-scale poker with multiple opponents at the table was widely recognized as the key remaining milestone.

Pluribus, a new AI bot we developed in collaboration with Carnegie Mellon University, has overcome this challenge and defeated elite human professional players in the most popular and widely played poker format in the world: six-player no-limit Texas Hold'em poker.

He’s very good at extracting value out of his good hands.” —Chris Ferguson, WSOP champion “It is an absolute monster bluffer.

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I would say it’s a much more efficient bluffer than most humans.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.(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 twist has made poker resistant to AI techniques that produced breakthroughs in these other games.In recent years, new AI methods have been able to beat top humans in poker if there is only one opponent.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.We are sharing details on Pluribus in this blog post, and more information is available in , the AI that beat human pros in two-player no-limit Hold’em in 2017, as well as other algorithms and code developed in Tuomas Sandholm’s Carnegie Mellon University research lab.In particular, Pluribus incorporates a new online search algorithm that can efficiently evaluate its options by searching just a few moves ahead rather than only to the end of the game.


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