## May 28, 2019

#### Submission Title

Snackjack: A toy model of blackjack

#### Session Title

Session 1-3-D: Cards and Dice

Event

#### Start Date

28-5-2019 1:45 PM

#### End Date

28-5-2019 3:10 PM

Probability

#### Abstract

Snackjack is a highly simplified version of blackjack that was proposed in Ethier's The Doctrine of Chances (2010, p. 674) and given its name in Epstein's The Theory of Gambling and Statistical Logic (2013, p. 291). 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 there is no insurance. We analyze the game, both single and multiple deck, deriving basic strategy and one-parameter card-counting systems. Unlike in blackjack, these derivations can be done by hand, though it may nevertheless be easier and more reliable to use a computer. The main point is that the simplicity of snackjack allows us to do computations that would be prohibitively time-consuming at blackjack. The result is that we can enhance our understanding of blackjack by thoroughly exploring snackjack.

#### Keywords

toy model, blackjack, grayjack, snackjack, basic strategy, card counting

#### Author Bios

Stewart N. Ethier is Professor Emeritus of Mathematics, University of Utah. He received his Ph.D. in Mathematics in 1975 from the University of Wisconsin - Madison. His research focuses on applied probability, and he is the author of The Doctrine of Chances: Probabilistic Aspects of Gambling. He has presented papers at 11 of the past 12 ICGRTs.

Jiyeon Lee is Professor of Statistics, Yeungnam University, South Korea. She received her Ph.D. in Mathematics in 1995 from Pohang University of Science and Technology. Her research focuses on applied probability, and she presented a paper on video poker at the 16th ICGRT.

#### Funding Sources

S. N. Ethier is partially supported by a grant from the Simons Foundation (429675), which had no involvement in any aspects of this research.

#### Competing Interests

There are no competing interests.

#### Share

COinS

May 28th, 1:45 PM May 28th, 3:10 PM

Snackjack: A toy model of blackjack

Snackjack is a highly simplified version of blackjack that was proposed in Ethier's The Doctrine of Chances (2010, p. 674) and given its name in Epstein's The Theory of Gambling and Statistical Logic (2013, p. 291). 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 there is no insurance. We analyze the game, both single and multiple deck, deriving basic strategy and one-parameter card-counting systems. Unlike in blackjack, these derivations can be done by hand, though it may nevertheless be easier and more reliable to use a computer. The main point is that the simplicity of snackjack allows us to do computations that would be prohibitively time-consuming at blackjack. The result is that we can enhance our understanding of blackjack by thoroughly exploring snackjack.