SOLUTION: House Edge in Blackjack: In a large casino, thehouse wins on its blackjack tables with a probablility of 50.7%. All bets at blackjack are 1 to 1: If you win, you gain the amount yo

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Question 90905This question is from textbook Using and Understanding Mathematics A Quantitative Reasoning Approach
: House Edge in Blackjack: In a large casino, thehouse wins on its blackjack tables with a probablility of 50.7%. All bets at blackjack are 1 to 1: If you win, you gain the amount you bet; If you lose, you lose the amount you bet.
a: What is the expected value to you of a single game? What is the house edge? If I am able to understand part a I should be able to understand the the rest of the problem. 3 days to go until the quarter is over. Thanks very much for your help this past year. This question is from textbook Using and Understanding Mathematics A Quantitative Reasoning Approach

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Let "x" be the gain on a bet:
P(gain x) = 0.507
P(lose or -x) = 1-0.507 = 0.493
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Expected Value calculation:
Random variable is the gain:
(gain x-dollars) * (0.493) = +0.493x dollars
(lose x-dollars) * (0.507) = -0.507x dollars
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Take the sum to get the expected gain:
0.493x-0.507x = -0.014x or a loss of 1.4% on each bet
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I'm not sure I know what you mean by "house edge".
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Cheers,
Stan H.