SOLUTION: If North American casino roulette were fair, how much should it pay to a player who bets $100 on black and a black number comes up? The odds against winning a bet on a black in ro
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Question 301291: If North American casino roulette were fair, how much should it pay to a player who bets $100 on black and a black number comes up? The odds against winning a bet on a black in roulette are 1.01 to 1. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! If North American casino roulette were fair, how much should it pay to a player who bets $100 on black and a black number comes up? The odds against winning a bet on a black in roulette are 1.01 to 1.
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P(no black) = 1.01/2.01
P(black) = 1/2.01
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Let the casino payoff be "x" dollars:
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Random values of casino gain: 100-x ; 100
Corresponding Probabilities: 1.01/2.01 ; 1/2.01
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Note: If game is "fair" E(x) = 0
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[1.01/2.01](100-x) + [1/2.01]100 = 0
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Multiply thru by 2.01 to get:
101-1.01x + 100 = 0
1.01x = 201
x =$199.01 (amt. casino should offer to pay if player wins on "black")
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Cheers,
Stan H.
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