question archive In a large? casino, the house wins on its blackjack tables with a probability of 51
In a large? casino, the house wins on its blackjack tables with a probability of 51
Subject:StatisticsPrice:2.87 Bought7
In a large? casino, the house wins on its blackjack tables with a probability of 51.4?%. All bets at blackjack are 1 to? 1, which means that if you? win, you gain the amount you? bet, and if you?lose, you lose the amount you bet.
a. If you bet? $1 on each? hand, what is the expected value to you of a single? game? What is the house? edge?
b. If you played 300 games of blackjack in an? evening, betting?$1 on each? hand, how much should you expect to win or? lose?
c. If you played 300 games of blackjack in an? evening, betting?$5 on each? hand, how much should you expect to win or? lose?
d. If patrons bet ?$10,000,000 on blackjack in one? evening, how much should the casino expect to? earn?
Purchase A New Answer
Custom new solution created by our subject matter experts
GET A QUOTE
Answer Preview
Answer:
(a). Probability of player loosing = Pr(loosing) = 51.4% = 51.4 ÷ 100 = 0.514
Pr(winning) = 1 - 0.514 = 0.486
Expected value of single game, when we bet $1
E($1) = ( 1×0.486) - (1×0.514) = - $0.028
It means, we will loose $0.028
(b). When we play 300 games , we expect to loose
= 300 × ( -0.028) = -$8.40
(c). Expected value, when we bet $5 on each hand
E(5) = ( 5×0.486 ) - ( 5×0.514 ) = -$0.14
When we play 300 games, we expect to loose
= 300 × (-0.14) = -$42
(d). Probability of casino winning = 0.514
Probability of casino loosing = 0.486
When patron bet $10000000, casino expected to earn
= ( 10000000 × 0.514 ) - (10000000 × 0.486 ) = $280000
