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Old 07-28-2007, 11:12 PM
jay_shark jay_shark is offline
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Join Date: Sep 2006
Posts: 2,277
Default Re: Probability so. holding a better hand preflop

First off you can use pokerstove to figure out what hands fair better than your pre-assigned range . Once you've established this range , you can use simple combinatorics to establish how many hand combos there are .

ie you hold A10 utg and your range normally consists of 88+ A9s+ k10s+ QTs+AJo+KQo . This means your opponent should re-raise or at least call with hands like AQ+ 10+ . Lets calculate the number of hands that your opponent would at least call with .

aq: 12 hands since there are 3 aces multiplied by 4 kings
ak: 12 "
10+: 3+6+6+6+3 = 24

So in total there are 12+12+24= 48 hands that are good .
Here is a very good approximation :

Label the players 1,2,3,4,5 . The probability player 1 (or any for that matter ) doesn't hold any of the 48 hands is (50c2-48)/50c2 .Take this number to the power 5 and then take the complement .

1- [(50c2-48)/50c2]^5 = 18.1%

Let me know if you need more clarity .
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