Student Co-author

HMC Undergraduate

Document Type



Mathematics (HMC)

Publication Date



In the casino game blackjack or "21," mathematically determined best plays have been calculated by various mathematicians and gambling experts. These optimal playing strategies all assume that the casino pays even money on bets (excluding when the player has a "blackjack"). However, many casinos offer the player "lucky bucks" that pay the player either 3-to-2 or 2-to-1. In the usual game, the player's expected loss is under 1¢ per dollar bet. in this paper, we derive optimal strategies under luck-buck conditions, giving the player an expected gain of 26¢ or 55¢ per dollar bet.


First published in the Journal of Undergraduate Mathematics and Its Applications, vol. 14, no. 4 (Winter 1993), pg. 309-314, by the Consortium for Mathematics and Its Applications.

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© 1993 Consortium for Mathematics and Its Applications (COMAP, Inc.)

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