4 Binomial Test: Question You regularly play in a local poker game of Texas Hold

Question

4 Binomial Test: Question You regularly play in a local poker game of Texas Holdem, but you feel something is off with that game. In particular, you feel that you never see enough aces before the flop. Every round, the players get 2 cards each before the flop (so you may end up with two aces if lucky). You decided to count the total number of times you got double aces in the last 1610 rounds. After counting all your double aces, you realized that you had 10 total double ace hands in 1610 rounds. Use binomial test to check whether the game was fair to you. a. How much aces would you expect? b. What is your p-value for the one-sided test? (probability of getting even more extreme deviation from the expected value)

Explanation / Answer

Getting 2 aces before the flop, probability, p = 4C2/52C2 = 0.0045

n = 1610

expected number of aces, mean = np = 7.285

(a) Hence expected number of aces are 7.285 or 7

std. dev. = sqrt(n*p*(1-p)) = 2.693

x = 10

P(X>10) = P(z > (10 - 7.285)/2.693) = 0.1567

Hence p-value = 0.1567

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