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The process begins with the formation of all possible player totals of 21, such as (T,T,A), (T,9,2), (T,9,A,A), . . . (2,2,2,A.... A). For each of these player hands, the dealer's exact probabilities are figured for the up card being considered and from this the player's standing expectation is computed, stored, and indexed for retrieval. (The indexing and retrieval mechanism for all possible hands is one of the more difficult aspects of the computer program.)
In this manner the computer cycles downward through the player's totals until finally the exactly correct strategy and expectation is available for any possible player hand. The procedure is not, of course, restricted to four deck analysis; applied to any prespecified set of cards it will yield the absolutely correct composition dependent strategy and associated expectation, without any preliminary guesswork as to what totals the player should stand with.
The cascading process can also be harnessed together with the pair splitting algorithm in the early part of this chapter to answer, once and for all, questions about what is the best strategy and consequent expectation for any number of decks and any set of rules. A summary of strategies, including two card "composition" dependent exceptions