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 rou

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Question 268054: 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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With those odds P(losing) = 1.01/2.01
and P(winning) = 1/2.01
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Let "x" be payback to a player.
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Note E(x) = zero if the game is "fair".
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E(x) = (winnings)(prob of win) + (loss)(prob of loss)
E(x) = (x-100)(1/2.01) - 100(1.01/2.01) = 0
Multiply thru by 2.01 to get:
x-100 - 1.01*100 = 0
x - 100 - 101 = 0
x = $201
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Cheers,
Stan H.