Statistics and Probability Commons^™

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

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

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

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

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

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 …

Racial Disparities In Cancer Screening Among Women With Chronic Joint Pain, Edith M. Williams, Laurene Tumiel-Berhalter, Christopher Purdy, Adrianne Ransom, Judith Anderson

Journal of Health Disparities Research and Practice

Chronic pain related disorders and breast and cervical cancer are more prevalent among African-American women compared with non-Hispanic White women. However, few studies address how racial differences in the context of comorbidity may compound these disparities. This study used secondary analysis of the National Health Interview Survey (NHIS) to assess racial differences in breast and cervical cancer screening and patient education among adult women with chronic joint pain conditions. Statistical analyses included chi-square and independent samples t-tests. African-American women compared with non-Hispanic White women were less likely to receive a pap smear or mammogram within the last two years and …

Not Always Black And White: Racial Bias For Birth Disparities From Excluding Hispanic Identification, Barbara L. Wilson, Cristi Coursen, Matthew Butler

Journal of Health Disparities Research and Practice

Despite gains in prenatal care (PNC) usage and birth outcomes for minority women during the past few decades, observed disparities between non-Hispanic Whites, Blacks, and Hispanics persist. Using the National Center for Health Statistics’ (NCHS) natality files from 1981 through 1998, Alexander, Kogan, & Nabukera (2002) examined live births of U.S. residents by trimester in which PNC was initiated and the appropriateness of that care based on the Adequacy of Prenatal Care Utilization Index (APNCU) (Kotelchuck, 1994). They found racial disparities between White and Black women in both the trimester of PNC initiation and the number of PNC visits made. …

Breast Cancer Screening Practices Among American Indians And Alaska Natives In The Midwest, Christine M. Daley, Melissa Filippi, Aimee S. James, Sarah Brokenleg, Stacy Braiuca, K. A. Greiner, Won S. Choi

Journal of Health Disparities Research and Practice

American Indian and Alaska Native (AI/AN) women currently have some of the highest mortality rates from breast cancer for any racial/ethnic group in the United States and some of the lowest screening rates. However, current data are not available for regional differences in screening, which can result in dramatically different stage at diagnosis and mortality. We conducted surveys with 120 focus group participants in a needs assessment of mammography among AI/AN in the greater Kansas City metropolitan area and parts of Northeast Kansas. We found that among women under age 40, for whom recommended screenings include only annual clinical breast …

Race And Hepatitis C Management Within The Veterans Administration, Joahd Toure, Joshua Metlay, Sandford Schwartz, Knashawn Morales, David Kaplan, Peter Groeneveld

Journal of Health Disparities Research and Practice

Objective: To examine black-white differences in hepatitis C treatment within the Veterans Administration (VA) and determine whether racial variation in specialty consultation explains differences in hepatitis C treatment between blacks and whites.

Methods: We performed a retrospective cohort study of 1040 veterans meeting VA eligibility criteria for hepatitis C treatment. We used multiple imputation to handle missing race data. Specialty consultation was determined from the VA outpatient medical dataset and hepatitis C treatment was determined from the VA decision support system. Conditional logistic regression was used to examine the association between race and hepatitis C treatment as well as race …

Poverty And Mortality Disparities In Central Appalachia: Mountaintop Mining And Environmental Justice, Michael Hendryx

Journal of Health Disparities Research and Practice

Objectives. This study investigated the associations between poverty rates, Appalachian mountaintop coal mining, and age-adjusted total mortality rates to determine if persons exposed to this form of mining experience greater poverty and higher death rates compared to other types of mining or other areas of Appalachia.

Methods. Mortality rates, poverty rates, Appalachian designation and mining activity were examined for counties in Kentucky, Tennessee, Virginia and West Virginia (N=403). Linear least squares models tested for annual group differences from 2000-2007 in total and child poverty, and total mortality, based on mining type and Appalachian location. Nested linear models accounting for state-level …