This paper advances a line of work exploring how to approximate the Nash equilibrium of a game that's too large to compute directly. The idea is to create a smaller abstraction of the game by combining information sets, solve for equilibrium in the smaller game, then map the solution back to the original game. The topic relates to NIPS since this is a state-of-the-art method to program game-playing AI agents like poker bots. The authors prove new bounds on the error of the approximation that are very general. The authors provide the first general proof that an e'-Nash equilibrium in an abstraction leads to an e-Nash equilibrium in the original game.

A fundamental challenge in imperfect-information games is that states do not have well-defined values. As a result, depth-limited search algorithms used in singleagent settings and perfect-information games do not apply. This paper introduces a principled way to conduct depth-limited solving in imperfect-information games by allowing the opponent to choose among a number of strategies for the remainder of the game at the depth limit.

Neural Information Processing Systems http://nips.cc/

In the context of multi-player, general-sum games, there is a growing interest in solution concepts involving some form of communication among players, since they can lead to socially better outcomes with respect to Nash equilibria and may be reached through learning dynamics in a decentralized fashion. In this paper, we focus on coarse correlated equilibria (CCEs) in sequential games. First, we complete the picture on the complexity of finding social-welfare-maximizing CCEs by proving that the problem is not in Poly-APX, unless P = NP, in games with three or more players (including chance). Then, we provide simple arguments showing that CFR--working with behavioral strategies--may not converge to a CCE in multi-player, general-sum sequential games. In order to amend this issue, we devise two variants of CFR that provably converge to a CCE. The first one (CFR-S) is a simple stochastic adaptation of CFR which employs sampling to build a correlated strategy, whereas the second variant (called CFR-Jr) enhances CFR with a more involved reconstruction procedure to recover correlated strategies from behavioral ones. Experiments on a rich testbed of multi-player, general-sum sequential games show that both CFR-S and CFR-Jr are dramatically faster than the state-of-the-art algorithms to compute CCEs, with CFR-Jr being also a good heuristic to find socially-optimal CCEs.

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. Furthermore, we describe a poker agent that used static experts and won the 3-player events of the 2010 Annual Computer Poker Competition.

Counterfactual Regret Minimization (CFR) is a popular, iterative algorithm for computing strategies in extensive-form games. The Monte Carlo CFR (MCCFR) variants reduce the per iteration time cost of CFR by traversing a smaller, sampled portion of the tree. The previous most effective instances of MCCFR can still be very slow in games with many player actions since they sample every action for a given player. In this paper, we present a new MCCFR algorithm, Average Strategy Sampling (AS), that samples a subset of the player's actions according to the player's average strategy. Our new algorithm is inspired by a new, tighter bound on the number of iterations required by CFR to converge to a given solution quality. In addition, we prove a similar, tighter bound for AS and other popular MCCFR variants.

This paper introduces the Poker Hand History (PHH) file format, designed to standardize the recording of poker hands across different game variants. Despite poker's widespread popularity in the mainstream culture as a mind sport and its prominence in the field of artificial intelligence (AI) research as a benchmark for imperfect information AI agents, it lacks a consistent format that humans can use to document poker hands across different variants that can also easily be parsed by machines. To address this gap in the literature, we propose the PHH format which provides a concise human-readable machine-friendly representation of hand history that comprehensively captures various details of the hand, ranging from initial game parameters and actions to contextual parameters including but not limited to the venue, players, and time control information. In the supplementary, we provide over 10,000 hands covering 11 different variants in the PHH format. Building on our previous work on PokerKit, a premier poker hand simulation tool, we demonstrate the usages of our open-source Python implementation of the PHH parser. The source code of the parser is available on GitHub: https://github.com/uoftcprg/pokerkit

Poker is in the family of imperfect information games unlike other games such as chess, connect four, etc which are perfect information game instead. While many perfect information games have been solved, no non-trivial imperfect information game has been solved to date. This makes poker a great test bed for Artificial Intelligence research. In this paper we firstly compare Game theory optimal poker to Exploitative poker. Secondly, we discuss the intricacies of abstraction techniques, betting models, and specific strategies employed by successful poker bots like Tartanian[1] and Pluribus[6]. Thirdly, we also explore 2-player vs multi-player games and the limitations that come when playing with more players. Finally, this paper discusses the role of machine learning and theoretical approaches in developing winning strategies and suggests future directions for this rapidly evolving field.