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Old 11-11-2005, 11:49 PM
yellowjack yellowjack is offline
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Join Date: Nov 2004
Location: Vancouver, Canada
Posts: 263
Default Re: adjusting hand range to flop

Initially there are 16 different ways that a player can have to make AK. When there is an ace on the flop, there are only 12.

Changing the percentages to fractions, the 1/4 * (12/16) = 3/16. All other hands are still 1/4.
P(AK) = (3/16) / ((3/16) + 3*(1/4)) = 1/5
P(QJ) = P(T9) = P(87) = 4/15
The probability of AK is reduced by 1/4 - 1/5 = 0.05 = 5%

For AA6, only 8 ways to make AK.
(1/4)*(1/2) = 1/8
P(AK) = (1/8) / ((1/8) + 3*(1/4)) = 1/7
P(QJ) = P(T9) = P(87) = 2/7
The probability of AK is reduced by 1/4 - 1/7 = 3/28 = 10.7%
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