Risk and Reward by N. Richard Werthamer

Author:N. Richard Werthamer
Language: eng
Format: epub, pdf
Publisher: Springer US, New York, NY

(7.2)

and then defining auxiliary functions

(7.3)

The Kronecker delta functions in (7.2) are defined as δ(i, j) ≡ 1 for i = j, and ≡ 0 for i≠j. It is important when interpreting these definitions to recognize that d(j) = 0 when j is outside the range 1 ≤ j ≤ 10. The expressions (7.1a)–(7.1c) can then be recast, respectively, in the nonrecursive form,

(7.4)

The conditional probabilities P determine the outcome of Player’s contest against Dealer. Whereas for Player the variable c represents the total value of his first two cards (except for split pairs, analyzed later), similar probability functions also apply to Dealer, where the variable instead represents the value of just her upcard; we will use the notation u instead of c when referencing Dealer. Also, while P(j|c) for Player depends implicitly on his stick/hit parameters s, s ′ , the corresponding Dealer’s function P(j|u) implicitly assumes her mandatory (or sometimes s ′ = 18).

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