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

Click here to see ALL problems on Probability-and-statistics

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.
---------------------
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
-------------------------------
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.
------------------------
If the game is fair The expected value of the game is zero.
------------------------
Equation:
(64974/64975)*(-10) + (1/64975)(x-10) = 0
---
Multiply thru by 64975 to get:
64974*(-10) + x-10 = 0
x = 64975(10)
---
x = $640,970 (amt. the casino should pay if the customer gets a straight flush)
==================
Cheers,
Stan H.