What are the odds of pocket aces beating pocket aces?

[radradrad]

Jay, I don't think he is asking what you are answering. He is not asking to have the odds of one or two people getting pocket Aces. I THINK the question is what are the odds of either person winning (instead of tieing or being beat) WHEN two people have pocket Aces.
IF that is the question, the answer is 2.17% for each person to win flat out. That would include flushs or straight flush possibilities.

[DavidG1966]

You are all missing the 2 questions...

1) 1 in x hands 2 players will be dealt pocket aces during the same hand at a 10 player table... 1 in 10,000... 1 in 100,000... etc...

and

2) Given the same sinerio 1 in x hand will that play out with someone losing poket aces to pocket aces do to a flush.. 1 in 1,000,000 hands??????

Thats what he is asking... Does anyone know... I am curious also!

[DarkMagus]

My numbers agree with jay. So at a 10 handed table, approximately once in 6000 hands will two players get AA, and about 4% of the time either one will win by a flush. So in total the whole series of events occurs once in every 139,000 hands.

For a 6-handed table, two players get aces once in 18,000 hands, and one of them wins once in 416,000 hands.

[jay_shark]

n/50c2=n/1225 is the probability that if you hold aces , then one other player will hold aces, against n other opponents .

50c2 is the number of ways of selecting two objects from a collection of 50 objects .You may also find this button on most calculators so just look for n(c,r) or nCr .


For your second question , did you mean four flush on the flop ?

If that's the case, given that two players hold aces , it should be
2*12c3/48c3=2.54%

To radrad:

I already showed how one would get 2.17% .

2*[12c4*36 + 12c5]/48c5=2.173913%

[mykey1961]

Actually he asked 3 questions.

1) The title question.

It's not specific about who's AA wins or loses, so the answer is more like 4.34619%

2) How often will one opponent have AA if you have AA.
either 1/1225 or N/1225 depending on how you interpret "one opponent"

3) A combination of #2, and how often will the board show 4 of one suit given that both of you have AA.

if you assume "4 flush" means 4 on the board, and the A making a 5th.

(4*12*11*10*9*36*5)/(48*47*46*45*44*1225) = 0.003398%

or

(n*4*12*11*10*9*36*5)/(48*47*46*45*44*1225) = n*0.003398%

again depending on how you interpret "one opponent".

if you assume 4 flush to mean came up short of making a flush.

(12*11*10*36*35*20*4)/(48*47*46*45*44*1225) = 0.05286110%

or

(n*12*11*10*36*35*20*4)/(48*47*46*45*44*1225) = n*0.05286110%

again depending on how you interpret "one opponent".

#3 doesn't ask how often your AA will win or lose.

[sfetaz]

I am still a little confused however I will try to analyze the posts to make sense. I will clarify my questions though. 1 out of X number of hands will you be dealt pocket aces and an opponent will be dealt pocket aces is question one, what is X? Question 2 is 1 out of Y number of hands you will be dealt pocket aces and an opponent will be dealt pocket aces AND one of the two hands will lose because a 4 flush appears by the river, what is Y?

One other thing, why does the number of players at the table effect the answer? Wouldn't it logically be that you get pocket aces 1 out of every 221 hands because of 4/52 * 3/51, therefore the math would continue with 2/50 * 1/49 since you do not know anyone elses cards?

[Shroomy]

The number of players matter because if you have pocket aces against one player, only he could have pocket aces two, but if you had 9 other players any of them could have the aces, so its much more likely.

..that should help the previous posts make more sense.

[Buccaneer]

Strange question. Stranger Answers. I would think that the better question might be Given a ten player hand of hold'em what is the probability that player A will be dealt AA and another player is dealt AA and..........

Now the "and" has to include if other players with KK, 22, 78, etc fold or does everyone play to showdown, Do AA ever fold to a pair on the board, a straight, a possible flush, are any of the players behind on their house payment, is it raining in Spain, etc.

And of course everyone knows that AA never wins.