27. BlackJack BlackJack is a popular casino game in which a player is dealt two cards where the value of the card corresponds to the number on the card, face cards are worth ten, and aces are worth either one or eleven. The object is to get as close to 21 as possible without going over and have cards whose value exceeds that of the dealer. A blackjack is an ace and a ten in two cards. It pays 1.5 times the bet. The dealer plays last and must draw a card with sixteen and hold with seventeen or more. The following distribution shows the winnings and probability for a $20 bet. In cases where the dealer and player have the same value, there is a tie (called a "push"). Source: "Examining a Gambler's Claims: Probabilistic Fact-Checking and Don Johnson's Extraordinary Winning Streak" by W.J. Hurley, Jack Brimberg, and Richard Kohar. Chance Vol. 27.1, 2014. Winnings Probability 0 0.0982 $30 0.0483 $20 0.389275 -$20 0.464225
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To do this, we multiply each winning amount by its corresponding probability and then sum up the results. Expected Value = (0.0982 * $30) + (0.0483 * $20) + (0.389275 * -$20) + (0.464225 * $0) Expected Value = ($2.946) + ($0.966) + (-$7.7855) + ($0) Now, we sum Show more…
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Blackjack, or twenty-one as it is frequently called, is a popular gambling game played in Las Vegas casinos. A player is dealt two cards. Face cards (jacks, queens, and kings) and tens have a point value of $10 .$ Aces have a point value of 1 or $11 .$ A 52 -card deck contains 16 cards with a point value of 10 (jacks, queens, kings, and tens) and four aces. a. What is the probability that both cards dealt are aces or 10 -point cards? b. What is the probability that both of the cards are aces? c. What is the probability that both of the cards have a point value of $10 ?$ d. A blackjack is a 10 -point card and an ace for a value of $21 .$ Use your answers to parts (a), (b), and (c) to determine the probability that a player is dealt blackjack. (Hint: Part (d) is not a hypergeometric problem. Develop your own logical relationship as to how the hypergeometric probabilities from parts (a), (b), and (c) can be combined to answer this question.)
Jeff V.
Blackjack, or twenty-one as it is frequently called, is a popular gambling game played in Las Vegas casinos. A player is dealt two cards. Face cards, queens, and kings) and tens have a point value of $10 .$ Aces have a point value of 1 or $11 .$ A 52 -card deck contains 16 cards with a point value of 10 jacks, queens, kings, and tens) and four aces. a. What is the probability that both cards dealt are aces or 10 -point cards? b. What is the probability that both of the cards are aces? c. What is the probability that both of the cards have a point value of 10$?$ d. A blackjack is a 10 -point card and an ace for a value of $21 .$ Use your answers to parts $($ a), $(b),$ and $(c)$ to determine the probability that a player is dealt blackjack. (Hint: Part (d) is not a hypergeometric problem. Develop your own logical relationship as to how the hypergeometric probabilities from parts $(a),(b),$ and $(c)$ can be combined to answer this question.)
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