By Peter Griffin
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Additional resources for The Theory of Blackjack: The Complete Card Counter's Guide to the Casino
Example text
For example, failure to double down 11 v 3 would cost the player 29% with a full deck, while hitting a total of 13 against the same card would carry only a 4% penalty. Hence, the latter change in strategy can be expected to arise much more quickly than the former, sometimes as soon as the second round of play. Volatility Some plays are quite unfavorable for a full deck, but nevertheless possess a great "volatility" which will overcome the 28 previous factor. Consider the effects of removal on, and full deck gain from, hitting 14 against a four and also against a nine: Full Deck Gain by Hitting Effects of Removal for Hitting 14 v.
Their average value for any subset is our "best linear estimate" of how much (in %) would be gained or lost by hitting. Similarly, any of the several hundred playing decisions can be approximated by assigning appropriate single card payoffs to the distinct denominations of the blackjack deck. The distribution of favorability for changing (violating) basic strategy can be studied further by using the well known normal distribution of traditional statistics to determine how often the situations arise and how much can be gained when they do.
We can liken the full deck loss from violating basic strategy to the distance that has to be traveled before the threshold of strategy change is reached. The effects of removal (or more precisely their squares, as we shall learn) are the forces which can produce the necessary motion. The following table breaks down strategy variation into each separate component and was prepared by the normal approximation methods. The averaging assumes a penetration of the deck such that variations in strategy are equally likely to be contemplated from n = 10 to n = 49 cards remaining.