For the game Caribbean Stud Poker compute the expected value

For the game Caribbean Stud Poker, compute the expected value of the call option for the following cases. (a) (A, K, A , 8, 3) vs. dealer?s exposed Q. (b) A, K, A , 8, 3) vs. dealer?s exposed 8. (c) A, K, A , 8, 3) vs. dealer?s exposed 3. Please step by step to understand

Solution

a. The player will lose if the player has AKJ-high and dealer will have at least an AKQ-high or better. Now we calculate the probability that the dealer doesn\'t qualify. This is possible in three scenarios:

thus we have a total of 73826 ways dealer do not qualify. There are (464)=163185 possible dealer hands given what cards are currently face-up. Thus, the probability that the dealer doesn\'t qualify is approximately 0.4524. The probability that the player wins is zero, and the probability that the dealer wins is then approximately 0.5476.

Depending on the card table player play at, if dealer doesn\'t qualify player get back his money for a net winnings of 0, if dealer wins player loses his money for a net loss of 1, and if player wins he gets double his money for a net gain of 1.

Therefore, expected value for the call option for part (a) is (1)0.5476+(0)0.4524+(1)0.0=0.5476