Toward Legalization of Poker: The Skill vs. Chance Debate

This paper sheds light on the age-old argument as to whether poker is a game in which skill predominates over chance or vice versa. Recent work addressing the issue of skill vs. chance is reviewed. This current study considers two different scenarios to address the issue: 1) a mathematical analysis supported by computer simulations of one random player and one skilled player in Texas Hold\u27Em, and 2) full-table simulation games of Texas Hold\u27Em and Seven Card Stud. Findings for scenario 1 showed the skilled player winning 97 percent of the hands. Findings for scenario 2 further reinforced that highly skilled players convincingly beat unskilled players. Following this study that shows poker as predominantly a skill game, various gaming jurisdictions might declare poker as such, thus legalizing and broadening the game for new venues, new markets, new demographics, and new media. Internet gaming in particular could be expanded and released from its current illegality in the U.S. with benefits accruing to casinos who wish to offer online poker

Catching Card Counters

The casino industry has been researched through a variety of disciplines including psychological gambling habits, technological advances, business strategies, and mathematical simulations. In the vast number of studies that have been conducted, there are few scholarly articles that focus on the specific aspect of card counting. The majority of games in the casino are designed to favor the “house”. This study focuses on the game of blackjack, in which players using a card counting strategy can tip the odds in their favor. A computer simulation was used to model the betting strategy of a card counter who would bet methodically. Conversely, the unpredictable betting strategy of a “normal” gambler was gathered through observations of over one thousands hands of blackjack. The comparison of the two led to deviations in behavior and betting habits. An understanding of these differences will provide a casino with additional information to catch card counters at the table

Learning to Reason: Leveraging Neural Networks for Approximate DNF Counting

Weighted model counting (WMC) has emerged as a prevalent approach for probabilistic inference. In its most general form, WMC is #P-hard. Weighted DNF counting (weighted #DNF) is a special case, where approximations with probabilistic guarantees are obtained in O(nm), where n denotes the number of variables, and m the number of clauses of the input DNF, but this is not scalable in practice. In this paper, we propose a neural model counting approach for weighted #DNF that combines approximate model counting with deep learning, and accurately approximates model counts in linear time when width is bounded. We conduct experiments to validate our method, and show that our model learns and generalizes very well to large-scale #DNF instances.Comment: To appear in Proceedings of the Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20). Code and data available at: https://github.com/ralphabb/NeuralDNF

Information and Attitudes to Risk at the Track

Abstract There have been many attempts, theoretical and empirical, to explain the persistence of a favorite-longshot bias in various horse betting markets. Most recently, Snowberg and Wolfers (2010) have shown that the data for the US markets support a misperceptions of probability approach in line with prospect theory over a neoclassical approach of the Quandt (1986) type. However, their paper suffers from two basic difficulties which beset much of this literature. First, the theoretical model used fails to allow for the existence of horse betting markets which either display no such bias (or a reverse bias) as in Hong Kong and at least one large Australian market (Busche and Hall, 1988, Schnytzer, Shilony and Thorne, 2003 and Luppi and Schnytzer, 2008). Second, econometric testing and theoretical modeling are facilitated by the highly unrealistic assumption that the betting population is homogeneous with respect to either information or attitude to risk or (usually) both. Our purpose is to show that allowing for heterogeneous betting populations (in terms of both attitude to risk and access to information) permits the explanation for the different biases (or their absence) observed in different markets within a strictly neoclassical framework of rational bettors. We conclude with empirical support for our model.