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Old 11-21-2007, 06:18 AM
Cloodie Cloodie is offline
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Default Equity Question

I'm trying to incorporate range and equity calculations into my game but I've got a question about a fairly basic calculation I was trying to work out in my head.

If you call a raise preflop with KK (forget about 3 betting for now) and you know the original raiser is only playing the top 3% of hands (JJ+, AK) and the flop is..

A 9 4 rainbow

When trying to work out a quick calculation in my head I cam up with the following - You are ahead of JJ and QQ and as there are 6 possible ways to be dealt each of these hands you are ahead of 12 of his possible holdings. However, you are behind AK and AA of which there are 22 combinations. Therefore, you are ahead of 12 hands and behind to 22 so you're almost a 2-1 dog.

I ran the calculation in pokerstove to see if I was correct and it has me with 53.4% equity. Where have I gone wrong in my calculation?
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Old 11-21-2007, 06:33 AM
pzhon pzhon is offline
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Default Re: Equity Question

[ QUOTE ]

A 9 4 rainbow

... You are ahead of JJ and QQ and as there are 6 possible ways to be dealt each of these hands you are ahead of 12 of his possible holdings. However, you are behind AK and AA of which there are 22 combinations. Therefore, you are ahead of 12 hands and behind to 22 so you're almost a 2-1 dog.

I ran the calculation in pokerstove to see if I was correct and it has me with 53.4% equity. Where have I gone wrong in my calculation?

[/ QUOTE ]
When you see one ace on the board, there are only 3 AA combinations, and since you see two kings in your hand, there are only 6 AK combinations.

A[img]/images/graemlins/spade.gif[/img] on the board
K[img]/images/graemlins/spade.gif[/img] K[img]/images/graemlins/club.gif[/img] in hand

AA combinations: A[img]/images/graemlins/club.gif[/img] A[img]/images/graemlins/heart.gif[/img], A[img]/images/graemlins/club.gif[/img] A[img]/images/graemlins/diamond.gif[/img], A[img]/images/graemlins/heart.gif[/img] A[img]/images/graemlins/diamond.gif[/img]

AK combinations: A[img]/images/graemlins/club.gif[/img] K[img]/images/graemlins/heart.gif[/img], A[img]/images/graemlins/club.gif[/img] K[img]/images/graemlins/diamond.gif[/img], A[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/heart.gif[/img], A[img]/images/graemlins/heart.gif[/img] K[img]/images/graemlins/diamond.gif[/img] A[img]/images/graemlins/diamond.gif[/img] K[img]/images/graemlins/heart.gif[/img], A[img]/images/graemlins/diamond.gif[/img] K[img]/images/graemlins/diamond.gif[/img]

You may want to discount the hands by how likely they are to have taken the other actions you have seen. If you think someone with JJ will take that line only 1/3 of the time, then you should count that as 6*1/3 =2 combinations.

Anyway, 12/21 ~57%, not the 53% reported by Pokerstove. The difference is that JJ and QQ have 2 outs against you, while you have 0 outs against AA and 1 out against AK.
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Old 11-21-2007, 07:30 AM
Cloodie Cloodie is offline
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Default Re: Equity Question

Doh! Double Counting [img]/images/graemlins/blush.gif[/img]

Thanks for that
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