Optimal Blackjack Strategy with 'Lucky Bucks'

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 lucky-buck conditions, giving the player an expected gain of 26# or 55# per dollar bet.