Blackjack Table A standard deck of playing cards contains 52 cards...
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Blackjack Table A standard deck of playing cards contains 52 cards divided equally into four suits: Spades, Hearts, Diamonds, and Clubs. Each suit contains thirteen cards: 2, 3, 4, 5, 6, 7, 8, 9, 10, J(ack), Q(ueen), K(ing), A(ce). You walk up to the blackjack table at your local casino and ask to be dealt in. You are dealt two cards, the 5 of hearts and the 7 of spades. You see that the dealer also has two cards. One is face down, and the other is the 6 of clubs. You decide to let it ride and hope the dealer busts.

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1 Blackjack Table
A standard deck of playing cards contains 52 cards divided equally into four suits: Spades,
Hearts, Diamonds, and Clubs. Each suit contains thirteen cards: 2, 3, 4, 5, 6, 7, 8, 9, 10, J(ack),
Q(ueen), K(ing), A(ce).
You walk up to the blackjack table at your local casino and ask to be dealt in. You are dealt
two cards, the 5 of hearts and the 7 of spades. You see that the dealer also has two cards. One is
face down, and the other is the 6 of clubs. You decide to let it ride and hope the dealer busts. The
dealer's hidden card is revealed to be the 8 of clubs, making the dealer's hand worth 14 points.
What is the probability that the dealer busts? You may assume that the dealer is
usign only 1 deck, and that you have not observed the values of any other cards.
Inblackjack,theworthofthedealer'shandisdeterminedbysummingthevaluesofhisindividual
cards. Numbered cards are worth their face value. Jacks, Queens, and Kings are worth 10 points,
and Aces are worth either 11 or 1 point (in this question, Aces will always be worth 1 point). The
dealer starts with 2 cards and repeats the following strategy:
If the dealer's hand is worth 16 or fewer points he draws another card. The value of the dealer's
hand is now the value of his two starting cards, and all the cards that he has subsequently drawn.
When the dealer stops drawing, the value of his hand will be 17 or higher. If it is higher than
21, the dealer is said to have "bust" meaning that his hand is worthless. If it is between 17 and 21
(inclusive) then the dealer's hand is worth its value.
2 Sadistic Tendencies*
You are captured by a Russian spy and tortured for information. Every time you fail to answer
his question adequately, he plays the following game:
First, he draws a number randomly between 1 and 4. This becomes the comparison value.
He then draws a number from between 0 and 4. If it is greater than or equal to the comparison
value, you get a lash with a wet noodle, and he draws again. He...

A1) The dealer would bust when his score crosses 21. With 14 in hand and a draw lined up, if the card shows up 8 or more then the dealer goes bust. The probability of that is 23/48. Although it may happen that dealer draws an Ace and then in the next draw draw , draws 7 or more...

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A1) The dealer would bust when his score crosses 21. With 14 in hand and a draw lined up, if the card shows up 8 or more then the dealer goes bust. The probability of that is 23/48. Although it may happen that dealer draws an Ace and then in the next draw draw , draws 7 or more...