A Mathematical Approach to Blackjack

Blackjack is a game that uses one or more 52-card decks. Players get two cards each and try to win by getting a hand that totals closer to 21 than the dealer’s without going over. Blackjack is a game of skill, and some people practice to improve their chances of winning. The game is also popular with gamblers who seek to beat the house edge.

Mathematics might be fearsome in school, but it can be a friendly companion at the table of blackjack. It’s an approach to the game that’s been around for over 60 years, ever since a group of U.S. Army mathematicians published a paper in 1956 that outlined for the first time a mathematically correct set of rules for blackjack, known as basic strategy.

To play, each player places a bet in front of them and the dealer deals them two cards, face up. Players then decide how to play their hands: stand (keep the same cards), hit (ask for another card), split (dealt two cards to each player), or double (bet twice the amount of their initial bet and only receive one additional card). If the player has a blackjack, they win the round by collecting all of the money in their wager pile.

The dealer then checks their hole card, and if they have a ten underneath, then the dealer has a blackjack and wins all of the players’ original wagers. They will also pay out any insurance wagers at 2 to 1. Otherwise, the game continues as usual.

If the dealer and the player both have a score of 17, then the round ends in a tie. However, if the dealer has a higher hand than the player’s (either 17 or 21), then the dealer sweeps the player’s bet and pays out one times their wager. The dealer’s blackjack also pays out 3 to 2.

We used an experimental design to examine psychological and behavioral effects of unjustified confidence in blackjack knowledge. In both studies, higher levels of unjustified confidence in blackjack knowledge were associated with greater outcome expectations and lower anxiety, but with less information search and consideration. Moreover, high confidence in blackjack knowledge was associated with greater risk taking in the game. However, these associations were stronger in study 1 than in study 2, suggesting that the results might have depended on how participants were recruited to the experiments. The raw data supporting the conclusions of this article will be made available by the authors without undue reservation. Wake Forest University’s Institutional Review Board approved the studies and all participants provided written informed consent before participating. The authors thank the participants and Dr. Robert Rosenfeld for their help and support with this research. The study was partially funded by a grant from the National Institutes of Health. The authors declare no other conflicts of interest. ES and AP contributed to the study design, data analysis, and writing of the manuscript.