Help with formula: Likelihood of ovecards flopping

[jonny quest]

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.

[DWarrior]

I believe it is one of the appendices in SS1

[jonny quest]

[ 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.

[efiusa]

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.

[jonny quest]

[ 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

[DWarrior]

Looks rizzite. But I'd check with Dizzle in da S U P to the per sizzite.

[Cobra]

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

[UtzChips]

[ 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

[jonny quest]

[ 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!

[lucas211]

[ 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