#1
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Help with formula: Likelihood of ovecards flopping
Specifically, I was trying to calculate the probability of overcards flopping to Pocket Pairs in Hold'em.
For example, % of time overcards would flop against someone holding pocket 3's. For the first card of the flop, I calculated the % of an overcard as such: 44/50 = 88% But how do I extend this for the following two cards to come with an total flop %? Independently, flop card one is 44/50, two is 44/49, three is 44/48? And then how would I arrive at the total %? Thanks. |
#2
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Re: Help with formula: Likelihood of ovecards flopping
I believe it is one of the appendices in SS1
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#3
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Re: Help with formula: Likelihood of ovecards flopping
[ QUOTE ]
I believe it is one of the appendices in SS1 [/ QUOTE ] I think %'s are listed for specific holdings, but I am curious about the math behind the probabilities rather than just final results. |
#4
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Re: Help with formula: Likelihood of ovecards flopping
Usually, the best way to solve these problems is to figure out the probability of the event NOT occuring and then subtract that from 1.
In your case, assuming you have a pair of 3s, odds of the first card being an undercard/equal card is 6/50, then 5/49, then 4/48. Multiply these together and get 120/117600 = .001 So there is a .001 chance that all 3 cards on the flop will be 3 or less, thus there is a .999 chance that the cards will be overs. |
#5
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Re: Help with formula: Likelihood of ovecards flopping
[ QUOTE ]
Usually, the best way to solve these problems is to figure out the probability of the event NOT occuring and then subtract that from 1. In your case, assuming you have a pair of 3s, odds of the first card being an undercard/equal card is 6/50, then 5/49, then 4/48. Multiply these together and get 120/117600 = .001 So there is a .001 chance that all 3 cards on the flop will be 3 or less, thus there is a .999 chance that the cards will be overs. [/ QUOTE ] So extending that formula, I came up with: 22 = 100% of at least 1 overcard 33 = 99% at least 1 overcard 44 = 99 55= 98 66=96 77= 92 88 = 86 99 = 79 tt = 69 jj = 56 qq = 41 kk = 22 % AA = 0% of at least 1 overcard Do these numbers look correct? thanks for the help |
#6
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Re: Help with formula: Likelihood of ovecards flopping
Looks rizzite. But I'd check with Dizzle in da S U P to the per sizzite.
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#7
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Re: Help with formula: Likelihood of ovecards flopping
I will give you an example of one pair of cards. You can easily due a hole spread sheet in excel.
You have 55 There is 9 ranks above 5 for a total of 36 cards There is two other fives There is 3 ranks below fives for a total of 12 cards There are a total of 50 cards which make a total of (50c3) 19600 unique flops. 0 overcards = (12c3) = 220 flops One overcard = 36*(12c2) = 2376 flops Two overcards = (36c2)*12 = 7560 flops Three overcards = (36c3) = 7140 flops Set or Full house = 2*(36c2) = 2256 flops Four of a kind = (2c2)*48 = 48 flops If you add them all up they equal 19600 flops. If you don't know what 12c3 is it is an expresion that is equal to the different three card combinations out of 12 cards. You can find it in excel = combin(12,3) or mathematically it is 12*11*10/1*2*3, another example is (12c2) = 12*11/1*2. Cobra |
#8
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Re: Help with formula: Likelihood of ovecards flopping
[ QUOTE ]
[ QUOTE ] I believe it is one of the appendices in SS1 [/ QUOTE ] I think %'s are listed for specific holdings, but I am curious about the math behind the probabilities rather than just final results. [/ QUOTE ] Buy "More Hold Em Excellence" by Lou Krieger $19.95 |
#9
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Re: Help with formula: Likelihood of ovecards flopping
[ QUOTE ]
I will give you an example of one pair of cards. You can easily due a hole spread sheet in excel. You have 55 There is 9 ranks above 5 for a total of 36 cards There is two other fives There is 3 ranks below fives for a total of 12 cards There are a total of 50 cards which make a total of (50c3) 19600 unique flops. 0 overcards = (12c3) = 220 flops One overcard = 36*(12c2) = 2376 flops Two overcards = (36c2)*12 = 7560 flops Three overcards = (36c3) = 7140 flops Set or Full house = 2*(36c2) = 2256 flops Four of a kind = (2c2)*48 = 48 flops If you add them all up they equal 19600 flops. If you don't know what 12c3 is it is an expresion that is equal to the different three card combinations out of 12 cards. You can find it in excel = combin(12,3) or mathematically it is 12*11*10/1*2*3, another example is (12c2) = 12*11/1*2. Cobra [/ QUOTE ] Very cool. I was trying to set up in Excel. Was not aware of the combin function, but its use seems invaluable for this sort of analysis. Thanks! |
#10
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Re: Help with formula: Likelihood of ovecards flopping
[ QUOTE ]
I believe it is one of the appendices in SS1 [/ QUOTE ] Hey I am new on 2+2, where do I find this appendices?? and what is SS1?? [img]/images/graemlins/confused.gif[/img] Thx |
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