Odds of loosing AA vs AA

[easypete]

I was reading a post here about the KJ vs KJ with the turned straight. It made me think about this hand.

Seeing that I'm still re-learning how to use combinations, I have a couple questions.

I was in a hand, about 2 months ago, in a S&G at PS. It was the 5th hand in the tourney, I had already gotten AA (second hand). I got AA again UTG. I raised about 3x the pot and the BB goes all in. I call.

It's AA vs AA.

Now the odds of getting dealt AA is:

C(4,2)/C(52,2) = 1 in 221

This is pretty straight forward. Now how do you calculate the odds of two players being dealt AA on the same hand?

If I would hazard a guess I would say:

C(4,2)/C(52,2) * 1/C(50,2) = 1 in 270,725? Is this correct?

Now, with this being said, and assuming that I have a chance in being correct thus far.... I lost the hand to a board 4 flush.

The probability of that is:

C(12,4)/C(48,5) = 1 in 3459?

So the probability of this happening is 1 in 936,491,919? Is this correct?

If so, I guess I can stop worrying about this happening to me again.

[BigBiceps]

One of the hands will win 4.35% of the time with a flush. So the chance you will lose with AA vs AA is 2.175%

http://twodimes.net/h/?z=59100
pokenum -h ac as - ah ad
Holdem Hi: 1712304 enumerated boards
cards win %win lose %lose tie %tie EV
As Ac 37210 2.17 37210 2.17 1637884 95.65 0.500
Ad Ah 37210 2.17 37210 2.17 1637884 95.65 0.500

[steveyz]

Well, the odds that two people will be dealt AA at the same time is not that same thing as the odd that someone else is dealt AA at the same time that you are dealt AA.

If you are dealt AA, the chance that one particular opponent has the two other aces is 1/C(50,2). On a full table with 9 opponent, the chance that one of your opponents also has AA is 9/C(50,2) = 1 in 136 or so.

So the odds that you have AA and one of your opponents has AA is 1/221 * 1/136 = ~1/16469.

In odds that you lose is 2.17% as the other poster said, so the odds of it overall is 1 in 758961 or so. If you play 10k hands/month, it should happen every 6 years or so.

[easypete]

OK... I'm missing something.

I'm assuming that the only way you can loose AA vs AA is the flush. Anything else is a split pot, right?

How can the percentage of loosing be as much as 2.17%?

C(12,4). number of possible 4 card combinations of the 12 remaining suited cards. = 495 possible combinations.

C(48,5). Number of possible 5 card boards of the remaining 48 cards = 1,712,304.

495/1712304 = 0.000289 --> 0.0289%

Am I missing something?

[steveyz]

As long as there is either a 4-flush or flush on board, someone will win, either you or your opponent, both being equally likely.

Now let's see what are the odds of a 4-flush or flush being dealt.

Odds of a 4-flush (but not flush) on board, =
4 * 5 * (13/52 * 12/51 * 11/50 * 10/49 * 39/48) = 4.29%,

Odds of flush on board =
4 * (13/52 * 12/51 * 11/50 * 10/49 * 9/39) = 0.198%

Added together, one of the AAs will win 4.29% + 0.198% = 4.49%. Actually this figure is a bit too high, because there will be a few hands where there is a straight flush on board, which means the pot is once again chopped.

[Bozeman]

You are missing:

4 possible suits

44 other cards that can be with your 12c4 combination

(multiply counting 5 flushes)

(str8 flushes)

Craig

[Hirez]

i've had this happen to me twice, but still no royal flush, i feel ripped off! /images/graemlins/frown.gif