Could someone please help on just b, c, and d? (PART 3) GAME 1: BLACKJACK In thi

Question

Could someone please help on just b, c, and d? (PART 3) GAME 1: BLACKJACK In this version you are dealt two cards from a standard deck of 52 cards. The object of the game is to total closer to 21 than the dealer without going over. Face cards are worth 10 pts, and aces are worth 1 or 11. All other cards are worth whatever their number is. All ties favor the dealer. If you beat the dealer, you double the money you have bet. Hand A: The dealer dealt himself a 10 of hearts. Ebert's cards dealt were an Ace of clubs and a 7 of hearts. a.) How much do you want to bet? Why did you choose this amount? b.) What is the probability that Ebert beats the dealer once the dealer's second card is dealt? c.) Is the probability from part "b" good news or bad news for Ebert? Explain why d.) Based on your chosen bet amount, what is your expected value? Explain what this represents. e.) Explain why the probability can never be greater than 1. f.) What would be Ebert's odds against winning?

Explanation / Answer

b)

Ebert's cards are Ace of clubs and a 7 of hearts. So Ebert's points close to 21 would be 11 + 7 = 18

Dealer has 10 of hearts. Maximum points can be achieved by the dealer now is 21 (get an ace). So, Dealer wins if he/she achieves the points between 18 to 21. That is dealer gets any cards between 8 to Ace (get points between 8 and 11). There are 4 cards for each card numbered 8, 9, 10, J, Q, K and A. So there are 4*7 = 28 cards. But 2 cards 10 of hearts and an Ace of clubs are already dealt. So the reamaining cards 28 - 2 = 26 cards make the dealer win.

So, the probability that the dealer win = 26/52 = 1/2

And the probability that Ebert beats the dealer = 1 - (1/2) = 1/2

c)

As, the probability is 1/2, both dealer and Ebert are equally likely to win the bet. So, it is both not a good or bad news for Ebert.

d)

When you win, the amount will be doubled. That is the amount will be 2 * $83 = $166

When you lose, you'll lose all the amount and your return will be $0

So, the expected value = Probability of win * Win amount + Probability of lose * Lose amount

= (1/2) * $166 + (1/2) * $0 = $83

This represents that in the long run of bets, your return will be the expected amount of $83.

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