CASE STUDY

Texas Hold'em

Texas hold'em or, more simply, hold'em, is now considered the most popular poker game. The Texas State Legislature officially recognizes Robstown, Texas, as the

Following are the details of Texas hold'em.

- Each player is dealt two cards face down, called "hole cards," and then there is a betting round.

- Next, three cards are dealt face up in the center of the table. These three cards are termed "the flop" and are community cards, meaning that they can be used by all the players; again there is a betting round.

- Next, an additional community card is dealt face up, called "the turn," and once again there is a betting round.

- Finally, a fifth community card is dealt face up, called "the river," and then there is a final betting round.

A player can use any five cards from the seven cards consisting of his two game's birthplace and dates the game back to the early 1900 s.

Three reasons for the current popularity of Texas hold'em can be attributed to (1) the emergence of Internet poker sites, (2) the hole cam (a camera that allows people watching television to see the hole cards of the players), and (3) Tennessee accountant and then-amateur poker-player Chris Moneymaker's first-place win of $\$ 2.5$ million in the 2003 World Series of Poker after winning his seat to the tournament through a $\$ 39$ PokerStars satellite tournament.

hole cards and the five community cards to constitute his or her hand. The player with the best hand (using the same hand-ranking as in fivecard draw) wins the pot, that is, all the money that has been bet on the hand.

There is one other way that a player can win the pot. Namely, if during any one of the four betting rounds all players but one have folded (i.e., thrown their hole cards face down in the center of the table), then the remaining player is awarded the pot. The best possible starting hand (hole cards) is two aces. What are the chances of being dealt those hole cards? After studying probability, you will be able to answer that question and similar ones. You will be asked to do so when you revisit Texas hold'em at the end of this chapter.

Recall that, to begin, each player is dealt 2 cards face down, called "hole cards," from an ordinary deck of 52 playing cards. The best possible starting hand is two aces, referred to as "pocket aces."

1. What is the probability that you are dealt pocket aces? (If you are struggling, think about the conditional probability examples from Deltamath).
2. What is the probability that you are dealt "pocket kings."
3. Using the result from part (a) and your analysis in part (b), find the probability that you are dealt a "pocket pair," that is, two cards of the same denomination (two 2s, two 3s, two 4s, etc.)
4. This week, we learned about basic principles of probability. Are there any applications from this week’s content to your major, your profession, or your interests? Please explain.

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