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A SIMULATION STUDY OF TEXAS HOLD ’EM POKER: WHAT TAYLOR SWIFT UNDERSTANDS AND JAMES BOND DOESN’T

Part of: Game theory

Published online by Cambridge University Press:  08 August 2018

J. FALLETTA Open the ORCID record for J. FALLETTA [Opens in a new window]  and
S. WOODCOCK Open the ORCID record for S. WOODCOCK [Opens in a new window]
J. FALLETTA
Affiliation:
School of Mathematical and Physical Sciences, University of Technology Sydney, Sydney, Australia email jay.falletta@uts.edu.au, stephen.woodcock@uts.edu.au
S. WOODCOCK*
Affiliation:
School of Mathematical and Physical Sciences, University of Technology Sydney, Sydney, Australia email jay.falletta@uts.edu.au, stephen.woodcock@uts.edu.au
*
✉stephen.woodcock@uts.edu.au
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Abstract

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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.

Keywords

pokersimulationprobability

MSC classification

Primary: 91A60: Probabilistic games; gambling
Type
Research Article
Information
The ANZIAM Journal , Volume 60 , Issue 1 , July 2018 , pp. 55 - 64
Copyright
© 2018 Australian Mathematical Society 

References

Alspach, B., “7-card poker hands”, 2000; http://people.math.sfu.ca/alspach/comp20/.Google Scholar
Bowling, M., Burch, N., Johanson, M. and Tammelin, O., “Heads-up limit hold’em poker is solved”, Science 347 (2015) 145–149; doi:10.1126/science.1259433.Google Scholar
Caballero, J., Ownby, R. L., Rey, J. A. and Clauson, K. A., “Cognitive and performance enhancing medication use to improve performance in poker”, J. Gambl. Stud. 32 (2016) 835–845; doi:10.1007/s10899-015-9576-4.Google Scholar
Gilpin, A., Sandholm, T. and Sørensen, T. B., “A heads-up no-limit Texas hold’em poker player: Discretized betting models and automatically generated equilibrium-finding programs”, in: Proc. 7th Int. Conf. Autonomous Agents and Multiagent Systems, AAMAS 2008 (Estoril, Portugal). Volume 2 (eds Padgham, L., Parkes, D. C., Müller, J. P. and Parsons, S.), (International Foundation for Autonomous Agents and Multiagent Systems, Richland, SC, 2008) 911–918; http://repository.cmu.edu/compsci/1447/.Google Scholar
Hopley, A. A. B., Dempsey, K. and Nicki, R., “Texas Hold’em online poker: A further examination”, Int. J. Ment. Health Addiction 10 (2012) 563–572; doi:10.1007/s11469-011-9353-2.Google Scholar
Javarone, M. A., “Is poker a skill game? New insights from statistical physics”, Europhys. Lett. 110 (2015) 58003; doi:10.1209/0295-5075/110/58003.Google Scholar
Javarone, M. A., “Modeling poker challenges by evolutionary game theory”, Games 7 (2016)Article ID 39; doi:10.3390/g7040039.Google Scholar
Li, R., Li, W., Shang, L., Gao, Y. and Zhang, M., “Opponent’s style modeling based on situations for Bayesian poker”, in: Proc. Conf., Sydney, Australia, 4–7 December 2012 (eds Thielscher, M. and Zhang, D.), (Springer, Berlin, Heidelberg, 2012) 385–396; doi: 10.1007/978-3-642-35101-3_33.Google Scholar
Lockett, A. J. and Miikkulainen, R., “Evolving opponent models for Texas Hold ’em”, in: Proc. IEEE Conf. Computational Intelligence in Games (Perth, Australia) (2008) 31–38; http://nn.cs.utexas.edu/?lockett:cig08.Google Scholar
Meinz, E. J., Hambrick, D. Z., Hawkins, C. B., Gillings, A. K., Meyer, B. E. and Schneider, J. L., “Roles of domain knowledge and working memory capacity in components of skill in Texas Hold’Em poker”, J. Appl. Res. Mem. Cogn. 1 (2012) 34–40; doi:10.1016/j.jarmac.2011.11.001.Google Scholar
Schoonmaker, A. N., The psychology of poker (Two Plus Two Publishing, Henderson, NV, 2000).Google Scholar
Sklansky, D., The theory of poker: A professional poker player teaches you how to think like one, 4th edn (Two Plus Two Publishing, Las Vegas, NV, 1999).Google Scholar
Tammelin, O., Burch, N., Johanson, M. and Bowling, M., “Solving heads-up limit Texas Hold’em”, in: Proc. Twenty-Fourth Int. Joint Conf. Artificial Intelligence, IJCAI, 2015 (eds Yang, Q. and Wooldridge, M.), (AAAI Press/International Joint Conferences on Artificial Intelligence, Palo Alto, CA, 2015) 645–652; https://www.ijcai.org/Proceedings/15/Papers/097.pdf.Google Scholar
van der Kleij, A. A. J., “Monte Carlo tree search and opponent modeling through player clustering in no-limit Texas Hold’em Poker”, Master’s Thesis, University of Groningen, The Netherlands, 2010; http://www.ai.rug.nl/mwiering/Tom_van_der_Kleij_Thesis.pdf.Google Scholar
Wilensky, U., NetLogo (Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL, 1999); http://ccl.northwestern.edu/netlogo/.Google Scholar