Aaron Foote’s research while affiliated with Wesleyan University and other places

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Figure 1. Flowchart illustrating how agents determine their actions. The decision involves their believed hand strength (associated with agent attribute), the minimum stake required to stay in the pot, and the current pot size. The agents bet in a manner that maximizes their expected winnings given their limited reasoning capabilities (Equation (2)).
Figure 3. All curves are the average of one hundred iterations of the simulation. (a) Sum of population marble count for each strategy over the epochs across one hundred iterations of the simulation for Unweighted learning. (b) The proportion of rational marbles in the population for unweighted learning. For each epoch, the total number of rational marbles is divided by the total number of marbles in the population, plotted for all epochs above for one hundred iterations of the simulation.
Figure 4. All curves are the average of one hundred iterations of the simulation. (a) Sum of population marble count for each strategy over the epochs across one hundred iterations of the simulation for Win-Oriented learning. (b) The proportion of rational marbles in the population for Win-oriented learning. For each epoch, the total number of rational marbles is divided by the total number of marbles in the population, plotted for all epochs above across one hundred iterations of the simulation.
Figure 5. Difference in Average Winnings of Rational and Random Strategies for every possible hand. The different regions are ranges of hands for which the rational agent plays differently, leading to different average winnings on those hands. The data is created by one hundred million hands played between a rational and random agent.
Figure A1. All curves are the average of one hundred iterations of the simulation. The plot shows the proportion of population marbles that are rational, for different values of φ. The legend on the right indicates the value of φ that each color corresponds to. The simulation involved ten thousand epochs of play between two hundred agents.
Factors in Learning Dynamics Influencing Relative Strengths of Strategies in Poker Simulation
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November 2023

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1 Citation

Aaron Foote

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Maryam Gooyabadi

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Nikhil Addleman

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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