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Date: 17 Dec 2006 09:00:32
From:
Subject: How to calculate the odds of this draw?
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If I am holding K 7, how do I compute the chance (or odds) of flopping
3 Ks or 3 7s? That is, what is the mathematical formula?
(The K 7 are suited. But I do not believe that matters for this
computation.)
One Holdem program computes 1.3477% or 73.2 to 1. If that is correct,
how was it computed?
I compute 1.4388% or 68.5 to 1 as follows:
2 * 47 * (3 choose 2) / (50 choose 3)
My rationale.... There are "3 choose 2" ways of flopping a pair of Ks
(making 3 Ks when combined with my pocket cards) and 47 ways of
flopping a non-K. There are "50 choose 3" ways of flopping 3 cards.
Multiply that ratio by 2 for Ks __or__ 7s.
It is unclear to me if the phrase "chance of flopping" means simply at
the flop, or if it includes the turn and the river as well. But if is
the latter, my chances go up, not down.
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Date: 17 Dec 2006 19:59:45
From:
Subject: Re: How to calculate the odds of this draw?
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Steve Brecher wrote:
> If the result is to be limited to flopping only trips, then 47 becomes 44
> and the chance 1.3469%.
Right. Thanks for pointing out my mistake, which I see clearly now.
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Date: 18 Dec 2006 03:31:18
From: Chuck24seven
Subject: Re: How to calculate the odds of this draw?
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the odds of flopping your trip K is as follows:
you need to inclued the quads which is just flopping trips with that
other pesky king on the board too
there are 3 cards in the deckdeck of 50 (2 are in your hand and known)
that you ned 2 of
so you need KKK KKx KxK or xKK
figure the odds of each of those seperatly and then add them together
KKK = 3/50*2/49*1/48 = .00005102040816327
KKx = 3/50*2/49*47/48 = .00239795918367347
KxK and xKK give the same result of .00239795918367347
add all four together and you get .00724489795918367
divide 1 by this number to get your answer of 1 in 138 flops
now do the same for the 7's = same answer 1 in 138 flops trip 7s
but to get the accurate answer for flopping either you simply add all 8
equations together for an answer of .0144897959183673 or 1 in 69
69.0140845 if you are some type of math freak (lol)
now that is the dead on balls accurate answer and how it is figured
out. anyone who says otherwise is making a mistake somewhere
I did the problem in excel, and manually typed the numbers over in the
dark, hopefully I didn't mess up the numbers, but the answer IS
correct.
Chuck
--
Chuck24seven
- http://www.pokerhelper.com RGP Access News Forums -
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Date: 17 Dec 2006 18:03:40
From: Steve Brecher
Subject: Re: How to calculate the odds of this draw?
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nomail1983@hotmail.com <nomail1983@hotmail.com > wrote:
> If I am holding K 7, how do I compute the chance (or odds) of flopping
> 3 Ks or 3 7s? That is, what is the mathematical formula?
>
> (The K 7 are suited. But I do not believe that matters for this
> computation.)
>
> One Holdem program computes 1.3477% or 73.2 to 1. If that is correct,
> how was it computed?
>
> I compute 1.4388% or 68.5 to 1 as follows:
>
> 2 * 47 * (3 choose 2) / (50 choose 3)
>
> My rationale.... There are "3 choose 2" ways of flopping a pair of Ks
> (making 3 Ks when combined with my pocket cards) and 47 ways of
> flopping a non-K. There are "50 choose 3" ways of flopping 3 cards.
> Multiply that ratio by 2 for Ks __or__ 7s.
Your answer is correct if you include flopping Ks full of 7s or vice-versa.
If the result is to be limited to flopping only trips, then 47 becomes 44
and the chance 1.3469%.
--
For mail, please use my surname where indicated:
steve@surname.reno.nv.us (Steve Brecher)
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