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# Texas Hold Em

Submitted By sashaw
Words 568
Pages 3
Texas Hold’em
In this scenario of the Texas Hold'em game, I have a six of diamonds and a seven of diamonds dealt as face-down cards. On the table, face up, the 3(three) of diamonds, the 4 (four) of clubs, 9( nine) of spades and the 10 (ten) of diamonds have been dealt. My opponent has revealed their two cards; they are the 10 of clubs and the 10 of spades. We both have bet \$24,000 and my opponent has just raised by \$10,000.
In deciding whether I should call the bet or fold, I will need to look at the likelihood of getting a better hand than my opponent. There are 52 cards in a deck and seven have already been dealt. My opponent currently has three of a kind. The simplest way for me to beat that hand is to get a straight. In order to achieve this, the one of the final two community cards needs to be an eight. No eight has been dealt. The odds of an eight being dealt are 4 in 45 and 4 in 44, respectively over the next two community cards. Overall, the odds of this occurring is 1 in 11.125, an 8.99% chance. This will allow me to beat my opponent’s three of a kind.
However, I have the potential for an even better hand. Currently, I have two diamond cards and there are two diamond cards within the community cards. One more diamond card and I would have a Flush, which is one hand better than a straight and two hands better than a three of a kind. There are a total of 13 diamond cards. Four have been dealt, leaving 9. The odds that they are dealt are 9 in 45 and 9 in 44. That is 9 in 44.5, or a 20.22% chance.
There is only a 2.25% chance of my opponent getting a four of a kind. However, my opponent could get a full house, which would beat a straight and a flush. My opponent will get a full house if a three or a four is thrown. There are six of these cards left in the deck. The odds of the community card giving the opponent a full house are 6 in 45, and 6 in 44. That is 6 in 44.5, or a 13.48% chance of getting a full house.
It must be taken into consideration that my opponent already has a good hand. While I have a 29.21% chance of getting a hand that is better than a three of a kind, my opponent has a 13.48% chance of getting an even better hand. In the end, I have an existing 70.79% chance of losing \$34,000 if he chooses to call the bet, even if my opponent’s hand gets no better. So his choices are an approximately 30% chance of winning \$34,000, a 70% chance of losing \$34,000, or a 100% chance of losing \$24,000 with a 100% chance of keeping \$10,000.
While I have a much better chance of improving my hand than my opponent does, my opponent has a significantly higher chance of winning. Not to mention that there are two more cards to be thrown. Mathematically, I should fold as my opponent has over a 70% chance of winning.

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