Odds of an A or K hitting flop

[Lloyd]

Yes I searched but couldn't find the answer using the logical term that came to mind. What are the odds of an A or K hitting the flop when you have AK. Assume a 10-handed hold em game. I presume you have to factor in the odds of somebody else having an A or K, which I presume is pretty likely in a full game.

And what about someone with a pair flopping a set. Would you factor in the likelihood of someone having one of their cards or just assume both cards are in the deck.

I'm trying to figure out the odds of AK (suited and off suit) being ahead of a pocket pair on the flop.

Thanks.

[David04]

Well I'm not sure what the odds of an ace or king flopping is, but AK is a slight dog to any PP, and a huge dog to AA or KK. I don't know if this helps though. [img]/images/graemlins/blush.gif[/img] [img]/images/graemlins/blush.gif[/img]

[Drunken Monkey]

If you have looked at your cards (AK)
50 cards left in the deck:

Odds you are against a PP. (One or more.)
13*(4/50)*(3/50)*9=~.573

Against AA or KK:
(3/50)*(2/49)*2=~.0049

Now the odds of hitting a pair or better:
(6/50)+(6/49)+(6/48)+(6/47)+(6/46)=~.6255

Only a pair:
(6/50)*(43/49)*(42/48)*(41/47)*(40/46)=~.0699

Note: I don't think this takes away flushes or straights.

He hit his set:
(Assuming you are only against on PP)

(2/50)+(2/49)+(2/48)+(2/47)+(2/46)=~.2085

Those are the numbers (I think I did the math right. If not I am sorry). He is the real world working knowledge.

The probibility of holding any specific pocket pair is:
(You have AK)
(4/50)*(3/49)=~.0049

So if the flop comes say 2 5 7
Your opponent would have to have either 22, 55, or 77.

Chances of those are (Prop. of Specific PP) * (number of sets posible)

In this case 3.

If the flop came K 2 5 there even a smaller chance he has a set since you hold one of the kings and you are looking at two.

Hope this helps.

[Cobra]

Some of the Odds of improving AK on the flop are as follows:

1. Odds of four of a kind

2*(3c3)/(50c3)=.01%

2. Odds of a Full house

2*(3c2)*3/(50c3)=.09%

3. Straight

4*Power(4,3)/(50c3)=1.31%

4. Trips A or K (no boat)

2*(3c2)*44/(50c3)=1.35%

5. Two pair A and K

3*3*44/(50c3)=2.02%

6. Pair of A or K some of the boards have a second pair

6*(44c2)/(50c3)=29%

So the total of a pair of A,K or better would be 33.78%

Cobra

[Stork]

In SSH, Miller states that you will hit an ace or king on the flop 32.4 unseen cards that could flop.

[Cobra]

I don't know if I did something wrong but if you subtract out the straight possibilities you get the chance of hitting at least and AK as 32.4%. I think this is the percentage you are talking about.

Cobra

[gaming_mouse]

[ QUOTE ]
Yes I searched but couldn't find the answer using the logical term that came to mind. What are the odds of an A or K hitting the flop when you have AK. Assume a 10-handed hold em game. I presume you have to factor in the odds of somebody else having an A or K, which I presume is pretty likely in a full game.

[/ QUOTE ]

For some reason, it doesn't seem anyone has answered you question, which is "What is the chance you pair up on the flop"?

First of all, the number of players does not matter. We are interested in the unseen cards only -- this automatically factors in the chance that opponents might hold one of your cards. There've been two threads in the last week with a further explanation of why this is true.

In any case, the calculation you need is:

1 - ((44 choose 3)/(50 choose)) = .3248

This makes you about a 2:1 dog to hit your pair on the flop.

gm

[Cobra]

I figured the straight wrong it should be.

Power(4,3)/(50c3)=.33%

Cobra

[Lloyd]

thanks