Abstract

This article discusses the card game blackjack as played in the casinos of Las Vegas. The basic rules for the game are described in detail. The player's strategic problems are analyzed with the objective of finding the strategy maximizing his mathematical expectation.

A mathematical expression is derived giving a general solution to the player's problem of standing pat with a given hand versus drawing additional cards. No general solutions are possible for the other major strategic problems, however, and a detailed examination of individual situations is required. The formulas and methods for the case analysis are stated, but computational details are omitted. Similarly, the formula for the player's mathematical expectation is stated, but its numerical evaluation is not described. Detailed discussion is given to the problems arising in the combinatorial type of computations required by blackjack.

The “optimum strategy” determined by the above analysis differs substantially from the published strategies of card experts and the usual style of play in the casinos.