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The current most popular variant of poker, played in casinos and seen on television, is no-limit Texas hold'em. This game and a smaller variant, limit Texas hold'em, have been used as a testbed for artificial intelligence research since 1997. Since 2006, the Annual Computer Poker Competition has allowed researchers, programmers, and poker players to play their poker programs against each other, allowing us to find out which artificial intelligence techniques work best in practice. The competition has resulted in significant advances in fields such as computational game theory, and resulted in algorithms that can find optimal strategies for games six orders of magnitude larger than was possible using earlier techniques.
Self-play Monte Carlo Tree Search (MCTS) has been successful in many perfect-information two-player games. Although these methods have been extended to imperfect-information games, so far they have not achieved the same level of practical success or theoretical convergence guarantees as competing methods. In this paper we introduce Smooth UCT, a variant of the established Upper Confidence Bounds Applied to Trees (UCT) algorithm. Smooth UCT agents mix in their average policy during self-play and the resulting planning process resembles game-theoretic fictitious play. When applied to Kuhn and Leduc poker, Smooth UCT approached a Nash equilibrium, whereas UCT diverged. In addition, Smooth UCT outperformed UCT in Limit Texas Hold'em and won 3 silver medals in the 2014 Annual Computer Poker Competition.
The 32-year-old is the only person to have won four World Poker Tour titles and has earned more than $7 million at tournaments. Despite his expertise, he learned something new this spring from an artificial intelligence bot. Elias was helping test new soft ware from researchers at Carnegie Mellon University and Facebook. He and another pro, Chris "Jesus" Ferguson, each played 5,000 hands over the internet in six-way games against five copies of a bot called Pluribus. At the end, the bot was ahead by a good margin.
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Computing a good strategy in a large extensive form game often demands an extraordinary amount of computer memory, necessitating the use of abstraction to reduce the game size. Typically, strategies from abstract games perform better in the real game as the granularity of abstraction is increased. This paper investigates two techniques for stitching a base strategy in a coarse abstraction of the full game tree, to expert strategies in fine abstractions of smaller subtrees. We provide a general framework for creating static experts, an approach that generalizes some previous strategy stitching efforts. In addition, we show that static experts can create strong agents for both 2-player and 3-player Leduc and Limit Texas Hold'em poker, and that a specific class of static experts can be preferred among a number of alternatives.
In two-player zero-sum games a Nash equilibrium strategy is guaranteed to win (or tie) in expectation against any opposing strategy by the minimax theorem. In games with m ore than two players there can be multiple equilibria with different values to the players, and follow ing one has no performance guarantee; however, it was shown that a Nash equilibrium strategy defeated a variet y of agents submitted for a class project in a 3-player imperfect-information game, Kuhn poker . Thi s demonstrates that Nash equilibrium strategies can be successful in practice despite the fact that they do no t have a performance guarantee. While Nash equilibrium can be computed in polynomial time fo r two-player zero-sum games, it is PPAD-hard to compute for nonzero-sum and games with 3 or mor e agents and widely believed that no efficient algorithms exist [8, 9]. Counterfactual regret mi nimization (CFR) is an iterative self-play procedure that has been proven to converge to Nash equilibrium in two-p layer zero-sum .
In this tutorial, you will learn step-by-step how to implement a poker bot in Python. First, we need an engine in which we can simulate our poker bot. It also has a GUI available which can graphically display a game. Both the engine and the GUI have excellent tutorials on their GitHub pages in how to use them. The choice for the engine (and/or the GUI) is arbitrary and can be replaced by any engine (and/or GUI) you like.
Poker is considered a good challenge for AI, as it is seen as combination of mathematical/strategic play, and human intuition, especially about the strategies of others. I would consider the game a cross between the two extremes of technical vs. human skill: chess and rock-paper-scissors. In the game of chess, the technically superior player will almost always win, an amateur would lose literally 100% of their games to the top chess playing AI. In rock-paper-scissors, if the top AI plays the perfect strategy, of each option 1/3rd of the time, it will be unbeatable, but also by definition be incapable of beating anyone. To see why let's analyse how it plays against the Bart Simpson strategy: If your opponent always plays rock, you will play rock 1/3rd of the time, paper 1/3rd and scissors 1/3rd, meaning you will tie 1/3rd, win 1/3rd, and lose 1/3rd.
The AI, called Pluribus, defeated poker professional Darren Elias, who holds the record for most World Poker Tour titles, and Chris "Jesus" Ferguson, winner of six World Series of Poker events. Each pro separately played 5,000 hands of poker against five copies of Pluribus. In another experiment involving 13 pros, all of whom have won more than $1 million playing poker, Pluribus played five pros at a time for a total of 10,000 hands and again emerged victorious. "Pluribus achieved superhuman performance at multi-player poker, which is a recognized milestone in artificial intelligence and in game theory that has been open for decades," said Tuomas Sandholm, Angel Jordan Professor of Computer Science, who developed Pluribus with Noam Brown, who is finishing his Ph.D. in Carnegie Mellon's Computer Science Department as a research scientist at Facebook AI. "Thus far, superhuman AI milestones in strategic reasoning have been limited to two-party competition. The ability to beat five other players in such a complicated game opens up new opportunities to use AI to solve a wide variety of real-world problems."
You are right that the algorithms in Pluribus are totally different than reinforcement learning or MCTS. At a high level, that is because our settings are 1) games, that is, there is more than one player, and 2) of imperfect information, that is, when a player has to choose an action, the player does not know the entire state of the world. There is no good textbook on solving imperfect-information games. So, to read up on this literature, you will need to read research papers. Below in this post are selected papers from my research group that would be good to read given that you want to learn about this field.