Blackjack; grayjack; snackjack; basic strategy; card counting; bet variation; strategy variation



Document Type

Original Research Article


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 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. More importantly, the simplicity of snackjack allows us to do computations that would be prohibitively time-consuming at blackjack. We can thereby enhance our understanding of blackjack by thoroughly exploring snackjack.

Funding Sources

The work of SNE was partially supported by a grant from the Simons Foundation (429675). The work of JL was supported by a 2019 Yeungnam University Research Grant. The granting agencies had no involvement in any aspect of this research.

Competing Interests

The authors have no competing interests.


We quoted several sources in the paper, and these short quotes fall under the fair use doctrine.

Included in

Probability Commons