Under a proposed new federal law, poker in US casinos would henceforth be played with a 65 card deck called a Trump deck. It is the same as an ordinary deck of 52 cards except for a fifth suit, called Trumps, that outranks the others, so if no player has a scoring hand, the best card to hold is the ace of Trumps. This creates one new hand, 5 of a kind, and changes the probabilities of all the hands. Generally speaking, hands like 3 and 4 of a kind become more common, and flushes become less common. The order of frequency is now royal flush, five of a kind, straight flush, four of a kind, flush, full house, straight, three of a kind, two pairs, one pair. (Definitions of the types of hands are easy to find online. The slides for Monday, November 21 may also be helpful.) Count the total number of possible poker hands with a Trump deck, and the number of hands of each of the above kinds. Be careful not to count a hand twice for example, if a hand is a straight flush, then it doesn't count as a flush, or as a straight; a full house doesn't count as 3 of a kind, or as 2 pairs.

Under a proposed new federal law, poker in US casinos would henceforth be played with a 65 card deck called a Trump deck. It is the same as an ordinary deck of 52 cards except for a fifth suit, called Trumps, that outranks the others, so if no player has a scoring hand, the best card to hold is the ace of Trumps. This creates one new hand, 5 of a kind, and changes the probabilities of all the hands. Generally speaking, hands like 3 and 4 of a kind become more common, and flushes become less common. The order of frequency is now royal flush, five of a kind, straight flush, four of a kind, flush, full house, straight, three of a kind, two pairs, one pair. (Definitions of the types of hands are easy to find online. The slides for Monday, November 21 may also be helpful.) Count the total number of possible poker hands with a Trump deck, and the number of hands of each of the above kinds. Be careful not to count a hand twice for example, if a hand is a straight flush, then it doesn't count as a flush, or as a straight; a full house doesn't count as 3 of a kind, or as 2 pairs.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...

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