The Situation You are playing Texas Hold’em against one other opponent. You and

Question

The Situation
You are playing Texas Hold’em against one other opponent.

You and your opponent have both already bet $24,000 into the pot each. Your opponent now adds $10,000 to the pot. You only have $10,000 left in total.

While you consider what to do, your opponent, in an effort to rattle you, reveals his down cards. They are 10 10.

The Problem
Should you call his bet by tossing the rest of your money into the pot, or should you fold and give up the pot to your opponent?

Remember your opponent has at least a pair of 10s. What cards could come up to make your hand better? What could come up to make your opponent’s hand better? Is there any way you could tie each other? Also look at the expected value of the game. If you fold, you are assured a loss of $24,000. Make sure this fact is used in your analysis.

Explanation / Answer

Cards that could make your hand better:

Right now, your opponent has a 3 of a kind. A flush or a straight beats a three of a kind:

Spades: 5, 8
Hearts: 5, 8
Diamonds: 2, 4, 5, 8, 9, J, Q, K, A
Clubs: 5, 8

Crossed out numbers will improve your opponent's hand more than yours.

Your opponent already has a three of a kind, he wants to get 4 of a kind, or a full house if he wants to beat a flush or a straight. He is already beating your high card.

Cards that could make his hand better:

Spades: 3, 9
Hearts: 3, 4, 10
Diamonds: 4, 9
Clubs: 3, 4, 9

Any other card leaves the condition of the game unchanged, namely you lose.

I cannot think of a way that the gane ends in a draw.

We have 44 cards left in the deck. 13 of those 44 will allow us to win, the expected value of the game if we continue is:

EV = (13/44) * (34,000) + (31/44)(-34000) = -$13,909

This is better than our Expected value of folding:

EV folding: -$24,000(1) = -$24,000

I would say, keep playing. You will probably lose money, but you have a chance of winning money if you stay in. If you fold, you are guaranteed to lose money.

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