Since the introduction of ChatGPT and GPT-4, these models have been tested across a large number of tasks. Their adeptness across domains is evident, but their aptitude in playing games, and specifically their aptitude in the realm of poker has remained unexplored. Poker is a game that requires decision making under uncertainty and incomplete information. In this paper, we put ChatGPT and GPT-4 through the poker test and evaluate their poker skills. Our findings reveal that while both models display an advanced understanding of poker, encompassing concepts like the valuation of starting hands, playing positions and other intricacies of game theory optimal (GTO) poker, both ChatGPT and GPT-4 are NOT game theory optimal poker players. Profitable strategies in poker are evaluated in expectations over large samples. Through a series of experiments, we first discover the characteristics of optimal prompts and model parameters for playing poker with these models. Our observations then unveil the distinct playing personas of the two models. We first conclude that GPT-4 is a more advanced poker player than ChatGPT. This exploration then sheds light on the divergent poker tactics of the two models: ChatGPT's conservativeness juxtaposed against GPT-4's aggression. In poker vernacular, when tasked to play GTO poker, ChatGPT plays like a nit, which means that it has a propensity to only engage with premium hands and folds a majority of hands. When subjected to the same directive, GPT-4 plays like a maniac, showcasing a loose and aggressive style of play. Both strategies, although relatively advanced, are not game theory optimal.
Combinatorial game theory
Combinatorial game theory, also known as CGT is a distinct branch of mathematics and theoretical computer science that studies combinatorial games, and is distinct from "traditional" or "economic" game theory. CGT arose in relation to the theory of impartial games, the two-player game of Nim in particular, with an emphasis on "solving" certain types of combinatorial games. A game must meet several conditions to be a combinatorial game. These are:
- The game must have at least two players. - The game must be sequential (i.e. Players alternate turns.)
- The game must have perfect information (i.e. no information is hidden, as in Poker.)
- The game must be deterministic (i.e. non-chance). Luck is not a part of the game. - The game must have a defined number of possible moves. - The game must eventually end. - The game must end when one player can no longer move. Combinatorial Game Theory is largely confined to the study of a subset of combinatorial games which are two player, finite, and have a winner and loser (i.e.
Poker is a game of skill, much like chess or go, but distinct as an incomplete information game. Substantial work has been done to understand human play in poker, as well as the optimal strategies in poker. Evolutionary game theory provides another avenue to study poker by considering overarching strategies, namely rational and random play. In this work, a population of poker playing agents is instantiated to play the preflop portion of Texas Hold’em poker, with learning and strategy revision occurring over the course of the simulation. This paper aims to investigate the influence of learning dynamics on dominant strategies in poker, an area that has yet to be investigated. Our findings show that rational play emerges as the dominant strategy when loss aversion is included in the learning model, not when winning and magnitude of win are of the only considerations. The implications of our findings extend to the modeling of sub-optimal human poker play and the development of optimal poker agents.
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