Introduction to Probability with Texas Hold’em Examples #5

Question

1. You are playing a hand of poker against one individual. Your hole cards are 8♦, 2♦ and your opponent’s hole cards are K♣, Q♣. The four cards on the table after the flop and the turn are J♦, 9♦, T♠, 5♥. Your opponent goes all in after the turn and you are left with the decision of folding or calling. The current pot size is c = $900,000 so that, if you call and win, your current chip stack will increase by $900,000. You would need to put in an additional b = $150,000 to call so that, if you call and lose, your current chip stack will decrease by $150,000.

a) If you call, what is the probability that you will win the hand? Note: Your opponent has a straight and, if you call, you can only win the hand with a flush. Thus, there is one more card coming out (the river card) and you need it to be a diamond to win.

b) You currently have $200,000 chips. If you call, what is the expected number of chips that you will have at the end of the hand?

c) If your goal is to maximize your expected number of chips, should you fold or should you call? Be sure to explain why you reached this conclusion.

Answer 1

a) about 18% using the rule of 2 and 4

b) 1.1M * 0.18 (result * probability) +

50K * 0.82 (result * probability) = 239K

c) you should call, your expected result is 39K more chips than you have now, so making this call would be +EV.

You can also solve this by looking at pot odds, your opponent is laying you 6:1 by going all in for 150k. this means you need a ~14.3% chance of winning or better to have a +EV call