5. THE ADVANTAGEOUS SITUATIONS
Let n be the number of cards in the shoe that thus far have not been used in play. Let t denote the number of these n cards with the value nine. Assume that the n — t other cards have been selected at random from the 384 non-nines which were originally in the complete eight decks. Let two cards di and d2 be drawn from the n cards. By considering cases, we find the probability that The Banker’s first two dealt cards total nine. The side bet has positive expectation if and only if this probability exceeds 0.1.