SOLUTION: If casino five card stud were fair, how much should it pay to a player who bets $10 and gets a straight flush versus a dealer who gets two pair? The odds against getting a straight

Question 249076: If casino five card stud were fair, how much should it pay to a player who bets $10 and gets a straight flush versus a dealer who gets two pair? The odds against getting a straight flush in five card stud are about 64974 to 1. Thank you!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If casino five card stud were fair, how much should it pay to a player who bets $10 and gets a straight flush versus a dealer who gets two pair? The odds against getting a straight flush in five card stud are about 64974 to 1.
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With those odds against the probability of not getting a straight flush
is 64974/64975
The probability of getting a straight flush is 1/64975
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Let x be the random variable tracking player earnings:
x values are : -10 and x-10 where x is the amount paid the player if he
gets a straight flush.
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If the game is fair The expected value of the game is zero.
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Equation:
(64974/64975)*(-10) + (1/64975)(x-10) = 0
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Multiply thru by 64975 to get:
64974*(-10) + x-10 = 0
x = 64975(10)
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x = $640,970 (amt. the casino should pay if the customer gets a straight flush)
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Cheers,
Stan H.

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