You regularly play in a local poker game of Texas Holdem, but you feel something

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 two
aces in the last 1511 rounds. After counting all your double aces, you realized that you had 6 total double ace
hands in 1511 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

a. THe probability of getting 2 doulbe aces = 4C2/ 52C2 = 0.004525

so in n = 1511 rounds

total number of expected chances to get 2 double aces = 1511 * 0.004525 = 6.84

Standard deviation of expected chances of getting 2 double aces = sqrt [1511 * 0.004525 * 0.995475] = 2.61

(b) P - value = Pr (getting 2 aces < 6; 6.84; 2.61)

Z = (6 - 6.84)/ 2.61

Z = -0.32

p - value = (-0.32)

where is the standard probability distribution.

p - value = 0.3745 >>> 0.05

as p - value by binomial = 0.474

so we can say that p - value is good enough so we can say that Game is fair to me.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.