Flop Odds Question

[IggyWH]

Probably best if I put this in the probability forum but I'll forget it there and I'm sure someone here can answer me.

Preflop AA vs KK

What is the probability that 2 Kings come on the flop?

I never really cared about learning flop odds but this one interests me since it happened to me last night.

[grouchie]

I laughed a good hearty chuckle last night when those two Kings hit the flop last night.

[grouchie]

oh, and two hands after you left the table, someone flopped quads on me.

Found that one amusing as well.

[IggyWH]

I guess I could have recognized your name... knew you had to be from here though when you made the B&M comment to that dude who thought his crap don't stink.

[TheNoodleMan]

http://twodimes.net/poker/

[IggyWH]

[ QUOTE ]
http://twodimes.net/poker/

[/ QUOTE ]

Thanks but I don't think that site will give me what I want. I don't want to know odds of AA vs KK, I just want to know given 1 person has AA dn one person has KK, what are the odds that 2 Kings will be flopped.

[mosdef]

I'll try this one.

there are 17,296 possible flops from the 48 cards left in the deck.

there are 46 possible flops containing both Ks.

Prob(2K on flop | AA, KK known hole cards) = 46/17,296 = 0.266%.

[IggyWH]

[ QUOTE ]
I'll try this one.

there are 17,296 possible flops from the 48 cards left in the deck.

there are 46 possible flops containing both Ks.

Prob(2K on flop | AA, KK known hole cards) = 46/17,296 = 0.266%.

[/ QUOTE ]

Not sure where you got the 17,296 from so maybe you can explain. I did it a different way :

A flop of :

k(1) k(2) x

Where x is any card other than the 2 aces and 4 kings, x = 46. There's then 6 ways you can arrange a flop given the 2 kings. They are :

k(1) k(2) x
k(2) k(1) x
x k(1) k(2)
x k(2) k(1)
k(1) x k(2)
k(2) x k(1)

Each one of those has 46 different ways of coming up so 46 * 6 = 276 possible different flops.

Given that I know 4 cards, there's 48 cards that can come out first, then 47 cards, and finally 46. 48*47*46 = 103776 total possible flops.

So I took the King flops (276) and divided it by the total possible flops (103776) and I get 0.00266 or 0.266%, the same answer you gave me.

So it seems as if the math is correct, I'm just not seeing how you got 17296 possible flops but it's a hot day and my mind isn't working too well today /images/graemlins/smile.gif

[BruceZ]

[ QUOTE ]
[ QUOTE ]
I'll try this one.

there are 17,296 possible flops from the 48 cards left in the deck.

there are 46 possible flops containing both Ks.

Prob(2K on flop | AA, KK known hole cards) = 46/17,296 = 0.266%.

[/ QUOTE ]

Not sure where you got the 17,296 from so maybe you can explain. I did it a different way :

A flop of :

k(1) k(2) x

Where x is any card other than the 2 aces and 4 kings, x = 46. There's then 6 ways you can arrange a flop given the 2 kings. They are :

k(1) k(2) x
k(2) k(1) x
x k(1) k(2)
x k(2) k(1)
k(1) x k(2)
k(2) x k(1)

Each one of those has 46 different ways of coming up so 46 * 6 = 276 possible different flops.

Given that I know 4 cards, there's 48 cards that can come out first, then 47 cards, and finally 46. 48*47*46 = 103776 total possible flops.

So I took the King flops (276) and divided it by the total possible flops (103776) and I get 0.00266 or 0.266%, the same answer you gave me.

So it seems as if the math is correct, I'm just not seeing how you got 17296 possible flops but it's a hot day and my mind isn't working too well today /images/graemlins/smile.gif

[/ QUOTE ]

Divide 103776 by 6 and you get 17296. He's counting each flop only once ignoring order, instead of 6 times, and this is the number of combinations = C(48,3) = 17296. You computed the number of permutations = P(48,3) = 103776.

[IggyWH]

Thanks for clearing that up... been too long since I had a stats class /images/graemlins/smile.gif