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Old 11-22-2002, 07:04 PM
Dynasty Dynasty is offline
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Join Date: Sep 2002
Location: Las Vegas
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Default Am I making this AK calculation correctly

bernie is telling me that I am incorrectly approaching/calculating a problem in a Beginners Questions thread. I'd like some feedback on whether I'm approaching the problem correctly.

Here's the problem: You've got AK in a pot being contested by yourself and 9 opponents. One Ace is in another opponent's hand. One King is in another opponent's hand. Have your chances of flopping a pair gone up or down?

My answer was that your chances of flopping a pair have gone up slightly and backed it up with these calculations.

First, without any extraordinary information, the chances of flopping a pair with AK is 28.96% or 2.45:1. These numbers are well known.

These are my calculation on how often you will flop a pair given the unusual information you have about one Ace and one King being in an opponent's hand.

Step 1: Calculate the the total # of possible flops given that only 32 cards remain in the deck- 32*31*30/6 = 4,960

Step 2: The number of A,x,y or K,x,y flops are 4 (number of Aces and Kings left in the deck)*28*27/2 = 1,512

1,512/4,960 = 30.48% or 2.28:1.

So, under normal circumstances when you don't make assumptions about what cards are in your opponents' hands, you will flop a pair 28.96% of the time. However, when you know exactly one Ace and one King are in your nine opponents' hands, the chances of flopping a pair slightly increase to 30.48%.

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