Why the Player Never Wins in the Long Run at LA Blackjack
First published in the Journal for Undergraduate Mathematics and Its Applications, vol. 20, no. 2 (Summer 1999), by the Consortium for Mathematics and Its Applications.
To get around an old California law that prohibits the game of "21," California card casinos introduced a variation of standard Blackjack, called LA Blackjack, in which the objective is to get as close as possible to 22 without going over.
The standard game of Blackjack, or "21", pits the player against the dealer ("the house"). Money lost by the player represents an equivalent gain by the house, and vice versa. In contrast, LA Blackjack pits the player against other players. Each player gets a turn to be the "banker" and collect money from the other players at the table, while the house collects a percentage of the total money bet. Mathematicians developed optimal plays for standard Blackjack many years ago, while the optimal plays for LA Blackjack are largely unexplored.
We analyze this game, develop a basic strategy for the player, explore the possibility of employing bet variance to raise the player's expected return, and conclude that a player cannot develop a profitable strategy.