In a large casino, the house wins on its blackjack tables with a probability of

Question

In a large casino, the house wins on its blackjack tables with a probability of 50.8%. All bets at blackjack are 1 to 1if 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? b. If you played 400 games of blackjack in an evening, betting $6 on each hand, how much should you expect to win or lose? c. If patrons bet $5,000,000 on blackjack in one evening, how much should the casino expect to earn? evening, betinog 93 ch houild he caino expect to cama a. The expected value to you of a single game is S (Simplify your answer.) The house edge is S (Simplify your answer.) | b. You should expect to | Simplify your answer.) c. The casino should expect to earn S Simplity your answer.)

Explanation / Answer

For the house, probability of win, p=0.507; probability of loss, q=1-0.507=0.493

The reverse is true for the person playing the game.

(a) The expected gain for the person in a single game if he bets $1 = 1 x 0.493 - 1 x 0.507 = - $ 0.014

So the person's expected loss per game os $ 0.014

The house gains $ 0.014 per game. For a 10-game set, house edge = $ 0.14

(b) For a bet of $6 on each game, expected loss for the person playing the game = 6 x 0.014 = $ 0.084

For 400 games, expected loss = 600 x 0.084 = $ 50.4

(c) For a bet of $ 500,000, expected gain for the casino = 500000 x 0.014 = $ 7,000

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