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Articles 1 - 6 of 6
Full-Text Articles in Statistics and Probability
Snackjack: A Toy Model Of Blackjack, Stewart N. Ethier, Jiyeon Lee
Snackjack: A Toy Model Of Blackjack, Stewart N. Ethier, Jiyeon Lee
UNLV Gaming Research & Review Journal
Snackjack is a highly simplified version of blackjack that was proposed by Ethier (2010) and given its name by Epstein (2013). The eight-card deck comprises two aces, two deuces, and four treys, with aces having value either 1 or 4, and deuces and treys having values 2 and 3, respectively. The target total is 7 (vs. 21 in blackjack), and ace-trey is a natural. The dealer stands on 6 and 7, including soft totals, and otherwise hits. The player can stand, hit, double, or split, but split pairs receive only one card per paircard (like split aces in blackjack), and …
Teaching A University Course On The Mathematics Of Gambling, Stewart N. Ethier, Fred M. Hoppe
Teaching A University Course On The Mathematics Of Gambling, Stewart N. Ethier, Fred M. Hoppe
UNLV Gaming Research & Review Journal
Courses on the mathematics of gambling have been offered by a number of colleges and universities, and for a number of reasons. In the past 15 years, at least seven potential textbooks for such a course have been published. In this article we objectively compare these books for their probability content, their gambling content, and their mathematical level, to see which ones might be most suitable, depending on student interests and abilities. This is not a book review (e.g., none of the books is recommended over others) but rather an essay offering advice about which topics to include in a …
Pair-A-Dice Lost: Experiments In Dice Control, Robert H. Scott Iii, Donald R. Smith
Pair-A-Dice Lost: Experiments In Dice Control, Robert H. Scott Iii, Donald R. Smith
UNLV Gaming Research & Review Journal
This paper presents our findings from experiments designed to test whether we could use a custom-made dice throwing machine applying common dice control methods to produce dice rolls that differ from random. In earlier research we calculated the percentages of control a craps player needs to break even or beat the house (Smith and Scott, 2018). Using the most common practices of dice control in craps, we established how dice should be configured (i.e., set) and thrown to achieve certain outcomes such as not rolling a seven in the point cycle. We decided to run experiments to see if a …
Optimal Conditional Expectation At The Video Poker Game Jacks Or Better, Stewart N. Ethier, John J. Kim, Jiyeon Lee
Optimal Conditional Expectation At The Video Poker Game Jacks Or Better, Stewart N. Ethier, John J. Kim, Jiyeon Lee
UNLV Gaming Research & Review Journal
There are 134,459 distinct initial hands at the video poker game Jacks or Better, taking suit exchangeability into account. A computer program can determine the optimal strategy (i.e., which cards to hold) for each such hand, but a complete list of these strategies would require a book-length manuscript. Instead, a hand-rank table, which fits on a single page and reproduces the optimal strategy perfectly, was found for Jacks or Better as early as the mid 1990s. Is there a systematic way to derive such a hand-rank table? We show that there is indeed, and it involves finding the exact optimal …
Golden Arm: A Probabilistic Study Of Dice Control In Craps, Donald R. Smith, Robert Scott Iii
Golden Arm: A Probabilistic Study Of Dice Control In Craps, Donald R. Smith, Robert Scott Iii
UNLV Gaming Research & Review Journal
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 …
Mathematical Models Of Games Of Chance: Epistemological Taxonomy And Potential In Problem-Gambling Research, Catalin Barboianu
Mathematical Models Of Games Of Chance: Epistemological Taxonomy And Potential In Problem-Gambling Research, Catalin Barboianu
UNLV Gaming Research & Review Journal
Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of the knowledge attached to mathematical models of games of chance and the act of mathematical modeling, arguing that such …