#1
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odds of flopping quads
What is the proper formula for figuring the odds
on flopping quads when I have a pocket pair in HE? Any help would be appreciated. I keep getting different answers. Thanks. |
#2
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Re: odds of flopping quads
You have 2 cards in your hand, leaving 50 unseen cards. There are (50 choose 3)=19600 different flops that can come up. (2 choose 2) * (48 choose 1)=48 of these give you quads. Probability of flopping quads is 48/19600.
Would you believe that once I flopped quads with a pocket pair 4 straight times? Well, you shouldn't. |
#3
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Re: odds of flopping quads
Thanks for reply. However, I figure the possible flops to be (50*49*48)=117600. I agree on the 48. So, I get 48/117600. Am I miscounting the total number of flop combos?
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#4
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Re: odds of flopping quads
50*49*48 gives you every possible combination, but it makes it order dependent. Dividing by 6 takes out the order dependency, and gives you the correct total of 19600 combinations.
TT |
#5
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Re: odds of flopping quads
That's the issue! Thanks to both for the help. Got it now. Much appreciated.
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#6
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Re: odds of flopping quads
I tried this. Here is my results using Aces.
50*49*48=117600 total possible flops. AAx = happens 48 times AxA = happens 48 times xAA = happens 48 times 144 ways two Aces can come up in 117600 flops. 144/117600 I get 3/2450. [img]/forums/images/icons/confused.gif[/img] Where does my logic fail? And what does (50 choose 3) and (2 choose 2) and (48 choose 1) mean? |
#7
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Re: odds of flopping quads
(N Choose K) is equal to the number of ways that one can choose K differentiable objects from N total differentiable objects (without repetition).
The formula is: (N Choose K) = N! / [ (N-K)! K! ] N! = 1 * 2 * 3 * ... * N Hope that helps! RMJ |
#8
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Re: odds of flopping quads
So (48 choose 47) = (48 choose 1) = 48?
but (48 choose 46) = 1028? I knew I should have studied math. |
#9
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Re: odds of flopping quads
"AAx = happens 48 times"
"Where does my logic fail? And what does (50 choose 3) and (2 choose 2) and (48 choose 1) mean? " Your logic fails because there are two ways to get each outcome. Say you have AcAs, then board could come AhAdx or AdAhx. So you get 288/117600=3/1225=48/19600 as given earlier. Craig |
#10
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Re: odds of flopping quads
Yes, that is precisely correct.
(48 choose 47) = (48 choose 1) = 48 This is a combinatorial identity, that is, (N choose K) = (N choose (N-K)). Do you see why this must be true? Say you've got 48 balls, numbered from 1 to 48. If you choose 47 of them to take away, you can see what you did from a different perspective... that you chose 1 from 48 to leave. It follows then that if you have N differentiable objects, and you choose K of them, it's the same as if you "chose" (N-K) of them to not be chosen. If you still don't see why this is true, please ask again, and I will try to provide a different example. RMJ |
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