DEVELOPMENT OF AN ACCURATE BASIC STRATEGY

Basic Strategy is the term applied to a system of play providing the highest betting yield without keeping track of the cards al-ready played. It was the search for such a strategy that led Messrs. Baldwin, Cantey, Maisel, and McDermott to spend three years pounding calculators. As covered in Chapter One, their work attracted the attention of Professor Thorp and was im-proved by him through the use of an MIT computer. Later Julian Braun of IBM assisted Dr. Thorp in refining his calculations for the second edition of Thorp's Beat the Dealer (Braun is also the developer of the Basic Strategy presented here)

These events show the two ways to determine Basic Strategy decisions: calculation and simulation. Baldwin et al. used a calcu-lation method that was extremely laborious. To determine a cor-rect strategy of play, you must consider every possible combina-tion of cards that can be dealt, calculate the probability, and determine whether the hand wins, loses, or pushes. I doubt whether the four original researchers calculated the probability of the dealer getting a hand of A, 2, A, 2, 7, A, A, 6 in that order. The chance of getting this hand is very remote, yet skipping this and other rare combinations reduces the accuracy of the results.

For this reason, Braun wrote a program to cycle through EVERY possible interactive combination of player and dealer hands. Although the program was complicated to devise, once developed it was a simple task to accurately determine the Basic Strategy by using the computer to do a complete combinatorial analysis. This was much faster than actually playing millions of Blackjack hands in an effort to determine the Basic Strategy.

Braun also wrote a simulation program to evaluate the per-formance of count systems. In a simulation, the computer actually "deals" hands to itself randomly and records the results. Perform-ing millions of calculations per second, an enormous number of hands can be "played" and recorded in a short amount of time. Every system developed or evaluated in this website has had at least one million hands simulated to determine the correct performance figures. (Details of Braun's computer programming technology can be found in the Appendix of his report, "The Development and Analysis of Winning Strategies for the Casino Game of Blackjack," available from the Gamblers website Club or Rouge et Noir. )

One of the first results of these studies was to confirm mathe-matically something many gamblers had guessed from experi-ence: The player's advantage depends upon the dealer up card. The table shows the probabilities that the dealer will bust with each possible up card and the corresponding player advantage with the correct Basic Strategy.

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