A simulation study of Texas hold 'em poker: what Taylor Swift understands and James Bond doesn't

Recent years have seen a large increase in the popularity of Texas hold ’em poker. It is now the most commonly played variant of the game, both in casinos and through online platforms. In this paper, we present a simulation study for games of Texas hold ’em with between two and 23 players. From these simulations, we estimate the probabilities of each player having been dealt the winning hand. These probabilities are calculated conditional on both partial information (that is, the player only having knowledge of his/her cards) and also on fuller information (that is, the true probabilities of each player winning given knowledge of the cards dealt to each player). Where possible, our estimates are compared to exact analytic results and are shown to have converged to three significant figures. With these results, we assess the poker strategies described in two recent pieces of popular culture. In comparing the ideas expressed in Taylor Swift’s song, New Romantics, and the betting patterns employed by James Bond in the 2006 film, Casino Royale, we conclude that Ms Swift demonstrates a greater understanding of the true probabilities of winning a game of Texas hold ’em poker. doi:10.1017/S144618111800015

Bayesian opponent modeling in adversarial game environments.

This thesis investigates the use of Bayesian analysis upon an opponent¿s behaviour in order to determine the desired goals or strategy used by a given adversary. A terrain analysis approach utilising the A* algorithm is investigated, where a probability distribution between discrete behaviours of an opponent relative to a set of possible goals is generated. The Bayesian analysis of agent behaviour accurately determines the intended goal of an opponent agent, even when the opponent¿s actions are altered randomly. The environment of Poker is introduced and abstracted for ease of analysis. Bayes¿ theorem is used to generate an effective opponent model, categorizing behaviour according to its similarity with known styles of opponent. The accuracy of Bayes¿ rule yields a notable improvement in the performance of an agent once an opponent¿s style is understood. A hybrid of the Bayesian style predictor and a neuroevolutionary approach is shown to lead to effective dynamic play, in comparison to agents that do not use an opponent model. The use of recurrence in evolved networks is also shown to improve the performance and generalizability of an agent in a multiplayer environment. These strategies are then employed in the full-scale environment of Texas Hold¿em, where a betting round-based approach proves useful in determining and counteracting an opponent¿s play. It is shown that the use of opponent models, with the adaptive benefits of neuroevolution aid the performance of an agent, even when the behaviour of an opponent does not necessarily fit within the strict definitions of opponent ¿style¿.Engineering and Physical Sciences Research Council (EPSRC

Agent-Based Models and Human Subject Experiments

This paper considers the relationship between agent-based modeling and economic decision-making experiments with human subjects. Both approaches exploit controlled ``laboratory'' conditions as a means of isolating the sources of aggregate phenomena. Research findings from laboratory studies of human subject behavior have inspired studies using artificial agents in ``computational laboratories'' and vice versa. In certain cases, both methods have been used to examine the same phenomenon. The focus of this paper is on the empirical validity of agent-based modeling approaches in terms of explaining data from human subject experiments. We also point out synergies between the two methodologies that have been exploited as well as promising new possibilities.agent-based models, human subject experiments, zero- intelligence agents, learning, evolutionary algorithms

A simple axiomatics of dynamic play in repeated games

This paper proposes an axiomatic approach to study two-player infinitely repeated games. A solution is a correspondence that maps the set of stage games into the set of infinite sequences of action profiles. We suggest that a solution should satisfy two simple axioms: individual rationality and collective intelligence. The paper has three main results. First, we provide a classification of all repeated games into families, based on the strength of the requirement imposed by the axiom of collective intelligence. Second, we characterize our solution as well as the solution payoffs in all repeated games. We illustrate our characterizations on several games for which we compare our solution payoffs to the equilibrium payoff set of Abreu and Rubinstein (1988). At last, we develop two models of players' behavior that satisfy our axioms. The first model is a refinement of subgame-perfection, known as renegotiation proofness, and the second is an aspiration-based learning model.Axiomatic approach, repeated games, classification of games, learning, renegotiation

Machine learning applied to the context of Poker

A combinação de princípios da teoria de jogo e metodologias de machine learning aplicados ao contexto de formular estratégias ótimas para jogos está a angariar interesse por parte de uma porção crescentemente significativa da comunidade científica, tornando-se o jogo do Poker num candidato de estudo popular devido à sua natureza de informação imperfeita. Avanços nesta área possuem vastas aplicações em cenários do mundo real, e a área de investigação de inteligência artificial demonstra que o interesse relativo a este objeto de estudo está longe de desaparecer, com investigadores do Facebook e Carnegie Mellon a apresentar, em 2019, o primeiro agente de jogo autónomo de Poker provado como ganhador num cenário com múltiplos jogadores, uma conquista relativamente à anterior especificação do estado da arte, que fora desenvolvida para jogos de apenas 2 jogadores. Este estudo pretende explorar as características de jogos estocásticos de informação imperfeita, recolhendo informação acerca dos avanços nas metodologias disponibilizados por parte de investigadores de forma a desenvolver um agente autónomo de jogo que se pretende inserir na classificação de "utility-maximizing decision-maker".The combination of game theory principles and machine learning methodologies applied to encountering optimal strategies for games is garnering interest from an increasing large portion of the scientific community, with the game of Poker being a popular study subject due to its imperfect information nature. Advancements in this area have a wide array of applications in real-world scenarios, and the field of artificial intelligent studies show that the interest regarding this object of study is yet to fade, with researchers from Facebook and Carnegie Mellon presenting, in 2019, the world’s first autonomous Poker playing agent that is proven to be profitable while confronting multiple players at a time, an achievement in relation to the previous state of the art specification, which was developed for two player games only. This study intends to explore the characteristics of stochastic games of imperfect information, gathering information regarding the advancements in methodologies made available by researchers in order to ultimately develop an autonomous agent intended to adhere to the classification of a utility-maximizing decision-maker

Neuroevolution in Games: State of the Art and Open Challenges

This paper surveys research on applying neuroevolution (NE) to games. In neuroevolution, artificial neural networks are trained through evolutionary algorithms, taking inspiration from the way biological brains evolved. We analyse the application of NE in games along five different axes, which are the role NE is chosen to play in a game, the different types of neural networks used, the way these networks are evolved, how the fitness is determined and what type of input the network receives. The article also highlights important open research challenges in the field.Comment: - Added more references - Corrected typos - Added an overview table (Table 1

When Civil Rights Go Wrong: Agenda and Process in Civil Rights Reform

The aging of the persons leading the civil rights movement is only a metaphor for a more serious aging process that afflicts the movement. It is a sclerotic condition that has kept an old agenda and once-prodding - but now increasingly intolerant - ideas in place, a fixed way of thinking that has become more strident and resistant to change as it has become more complacent with itself. Once the opponent of conformity, some parts of the civil rights community now preach conformity within their communities. I see these not as indices of the venality of the civil rights movement, but as human responses that can be reformed by the contributions of a new generation. This change has already begun to occur, and my goal is to have a new generation build an immunity to sclerosis into the movement ..

A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work