# Poker Hands - three matching cards of a kind • full house...

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STAT 230: Introduction to Probability and Random Variables Summer 2009 Problem set: Introduction to Poker Poker is a game played with a standard 52 playing card deck. There are 4 suits: spades, clubs, diamonds and hearts. Each suit has the same 13 cards. There are 9 numbered cards: 2 through 10, and 4 face cards: jack, queen, king and ace. Each player is dealt 5 cards from the deck. The object is to get a 5- card combination (known as a hand) that is more valuable than everyone else's. The harder it is to get a particular hand, the more valuable it is. A kind is defined either as a number (example 3, 10, etc.) or as a face (example ace, jack, etc.). Here are the hands in order from least importance to most: pair : two matching cards of a kind. two pairs : two matching cards of a kind, and two matching cards of another kind. three of a kind

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Unformatted text preview: : three matching cards of a kind. • full house : three matching cards of a kind and two matching cards of another kind. • four of a kind : four matching cards of a kind. 1. In how many ways we can get each of these hands? The calculations should be based on a five-card draw. Remark: In a game like Texas holdem poker, where you have two hole cards and there are five community cards on the board, the probability of catching a specific hand increases. It is not the case here, just consider a five-card draw. Other Poker hands: • Straight : 5 cards in a row. The suits don't matter. • Flush : 5 cards from the same suit. The cards don't matter. • Straight flush : 5 cards in a row from the same suit. • Royal flush : The 10, jack, queen, king and ace from the same suit. 2. In how many ways we can get each of these hands?...
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Poker Hands - three matching cards of a kind • full house...

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