Journal Article
15 December 2025
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- Journal Article15 December 2025
How Casino Match Play Promotions Can Hook Gamblers (and Non-Gamblers)
Casino operators frequently use promotional gambling vouchers, free play and match play. In the case of free play, customers are offered gambling credits that function much like real money and patrons are able to quickly turn their promotional play into cash without risking their own money. Match play, however, can only be employed at table games and their use necessitates gamblers to wager their own funds. We conduct a thorough analysis of how match play can affect gamblers’ individual behavior. First, we assess the value of match play promotions, which we argue is ambiguous. Then, using behavioral economics concepts, we consider how match play promotions affect the risk appetite of casino patrons. While our analyses suggest that profit seeking casino operators are wise to prioritize match play promotions, we provide evidence that match play offers could be used to target and exploit individuals suffering from a gambling-related disorder. As such, their usage as marketing tools may not align with responsible gambling initiatives.
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Journal Article4 February 2026
Cash or Crash: Return to Player Percentages and Expected Value of Crash Games
Crash games are a new type of casino game offered on some online gambling sites. The first crash game was created by the online cryptocurrency casino Bustabit. Other cryptocurrency casinos started offering their own versions of crash games. Now mainstream online casinos have developed their own crash games—notably Rocket by DraftKings. Crash games are easy to learn and play. They offer the opportunity to increase your bet by many hundreds of multiples—though, as we show when deriving expected values, these outcomes are rare. In this paper, we study the history of crash games and calculate theoretical values of crash game bets. We then use data from two popular online crash games to study the behaviors of players and return to player (RTP) percentages.Journal Article12 February 2026
A Mechanistic Model of the Wash Shuffle and Monte Carlo Exploration of its Impact on Card Shuffling in Texas Hold’em
In casino games using a standard deck of cards, a wash shuffle is sometimes performed prior to the rest of the card shuffling procedure. Unlike other methods of shuffling, the wash shuffle has not yet been well studied. To this end, we first develop a mechanistic model of the wash shuffle based on our observation of how cards tend to move when a wash shuffle is being performed. Then, we use this model to simulate the card shuffling procedure used in casino poker rooms, and explore the resulting impact on where the cards are dealt in the context of Texas Hold’em poker. We find that while the addition of the wash shuffle does produce probabilities in line with what would be expected from a perfect shuffle in terms of where individual cards will end after the shuffling is performed, it still shows deficiencies in terms of breaking up clumps of cards that have started next to each other, which has significant implications in games like Texas Hold’em in which several cards are dealt face up.Journal Article23 March 2026
Can a slot machine’s allocation of pay table variance affect a gambler’s time on device?
Modified pay tables from a licensed reel slot machine were altered to examine whether two games with equal variance and par could produce meaningful differences in the duration of play, at the level of the individual gambler. To the best of our knowledge, this was the first study to examine this possibility. Industry executives consider time on device (TOD) to be a critical measure of gaming value, especially for losing players. Additionally, TOD experiences are theorized to produce knock-on effects related to loyalty behaviors. The results of 18 simulations featuring six different player engagement protocols supported the ability of differences in the allocation of pay table variance to significantly impact the spins per losing player. These outcomes indicated that games with the same par and total variance should not be assumed to produce the same expected TOD. For operators, the findings suggest that more meaningful/precise pay table descriptors could help them populate slot floors with games that are more likely to produce their desired TOD outcomes. For game makers, the results present opportunities to supply games that improve the outcome targeting of individual player experiences. For decades, par has been the primary focus of pay table metrics and gaming value. But par is a long-term measure of central tendency, with multiple studies indicating that differences in pars do not generate significantly different session-level results. This study, along with several others, indicates the considerable ability of variance to impact the player’s visit-level outcome.Most Popular Articles
Journal Article
3 November 2012
The Probability Distribution of the Sum of Several Dice: Slot Applications
The probability distribution of the sum of two fair dice is used to calculate the house advantage of various bets in craps, and is readily available in probability and statistics books and gaming literature. The probability distribution of the sum of A: dice (for k >= 3) is derived in this paper using the method of moment generating function. A recursion formula for deriving the probability distribution of the sum of k dice (for k >= 3) from the probability distribution of the stun of k-1 dice is also given. There are no gaming books or journal articles that demonstrate how a multi-reel slot game is developed. As an application of the probability distribution of the sum of k dice derived in this article, a slot game based on the sum of five dice is presented.Journal Article
17 December 2012
Journal Article
17 December 2012
Casino Technology: Player Tracking and Slot Accounting Systems
The objective of this research is to provide the casino industry with an unbiased, independent study on the available technologies in its business. Both the software manufacturers and the casinos recognize that tracking systems are far from being anything close to perfect. Thus, gaming companies are continually trying to improve the systems that they have on the market. In this paper the authors analyze player tracking and slot accounting systems based on their costs, functions, sizes, hardware requirements, and software requirements respectively, which may help casino executives better understand the technologies available to them and make more prudent and cost-effective decisions on purchasing gaming hardware and software.Journal Article
17 December 2012
Developing the Casino Marketing Plan
This article stresses the need to develop and implement structured marketing plans. He discusses the benefits of formal planning and the challenges of developing a researched, realistic plan. An outline or framework for a casino marketing plan appears at the end.Journal Article
3 May 2018
Golden Arm: A Probabilistic Study of Dice Control in Craps
This paper calculates how much control a craps shooter must possess on dice outcomes to eliminate the house advantage. A golden arm is someone who has dice control (or a rhythm roller or dice influencer). There are various strategies for dice control in craps. We discuss several possibilities of dice control that would result in several different mathematical models of control. We do not assert whether dice control is possible or not (there is a lack of published evidence). However, after studying casino-legal methods described by dice-control advocates, we can see only one realistic mathematical model that describes the resulting possible dice control, that in which the four faces on a rotating (horizontal) axis are favored. This is the model that we analyze in this paper.Journal Article
17 December 2012