View Full Version : AK hits AA

12-28-2004, 01:19 AM
Probably an easy one for all the odds wizes out there..

I just got knocked out of a SnG tourney when I went all in with AK and got called by AA. The odds of both being dealt in the same hand must be astronomical...?

12-28-2004, 02:07 AM
it happens every once in awhile. The odds are low. (1/220)*(2/50)*(4/49). This calculation is a little off because it is assuming the order in which the cards are delt.

12-28-2004, 02:16 AM
So roughly .001484230055658627% of the time.

I knew the poker gods hated me. /images/graemlins/blush.gif

12-28-2004, 02:43 AM
There are three combinations of taking 2 aces out of the three remaining and there are 50*49/2 combinations of hole cards. So the odds of running into AA with AK are .24% or about once every 416 times. The odds of running into AA are dependent on how many hands there were at the beginning of the hand. For instance if there were 9 opponents active when you went all in the odds of running into AA go up to about 2.2%.

12-28-2004, 06:57 AM
Don't mean to hijack, but I always end up paying these off on Axx flops. I'm a sucker for at least 8 BB when I have AK vs. AA with an A on the flop.

12-28-2004, 10:31 AM
There are two different events (different information to count) you might want to have their odds:
1) At least one opponent to be dealt AA, while you hold AK
2) You to be dealt AK and at least one opponent to be dealt AA.
1) The probability is 3*n/1225
2) The probability is (16/1326)*(3*n/1225), where n is the number of your opponents.
These are preflop odds. If some cards were flopped, the information is different and so the odds.

12-28-2004, 03:12 PM
Another thing to note is that here, you're calculating the probability for just this one hand. In other words, before the tournament, the odds that you get knocked out on hand #54 with AK verse AA (which is really the question that you're asking) is the ~.001484% number listed above.

A more appropriate way of looking at it, is saying in any random stretch of 50 hands, what are the odds of losing in this situation. In that case, it is (1 - ((1 - .00001484)^50)), or 0.0742%.

If we stretch this out to say (this is assuming your average SnG is 50 hands), 20 SnG's (maybe a week's worth?), we make a very similar calculation... (1 - ((1 - .000742)^20)))... or 1.4736%.

I find this "Coincidence Theory" stuff to be very interesting... the "streelight effect" aspect of questions like this is absolutely necessary to consider in this case, as the relavant calculation, to me at least, doesn't seem to be "What are the odds of getting knocked out with these cards on THIS hand?", but instead "What are the odds of me getting knocked out with these cards?", which is what I've calculated for a ~week-long time-span.

12-30-2004, 02:05 AM
In two years, I've been involved in that situation four times. Twice I was the one with AA, won one unimproved, lost one when KK flopped. Twice I was the one with AK, once offsuit (lost) once sooted in clubs and I won with a flopped draw/river'd flush. Moral of the story? Only push your AK against AA when you know you're going to trip up the K or get a flush.

12-30-2004, 02:09 PM
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it happens every once in awhile. The odds are low. (1/220)*(2/50)*(4/49). This calculation is a little off because it is assuming the order in which the cards are delt.

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solution incorrect

01-03-2005, 04:33 PM
No the poker gods hate you when you have the aa and the flop comes 10 j q when your all in pf

01-04-2005, 12:40 AM
Actually, I just thought of something. If you have A/K the odds of someone else having AA are way lower. My origional calculation was what are the odds on a given hand that you are randomaly delt AK and someone else AA. Big diffrence in odds.