Odds question

[CaptureMan]

Hi, I was playing a LHE game with 4 players and myself (5 total) and I got dealt AA twice in a row (they held up both times) and was just wondering what are the odds of doing this at a 5 person table?

[BlibbityBlabbity]

I will take a pre coffee stab at getting dealt AA twince in a row....so it is probably wrong, but.

6 (possible AA combinations)/1326 (possible card combinations)=220:1 (to get AA once)
220:1 x 220:1 = 48840:1 to get AA twice in a row

As far as WINNING with the hands both times, that depends on the hands you were up against. But, take the % that is equal to the odds you had to win against the hand/hands you showed down with and multiply them together to get a ROUGH idea.

Edited to fix math (but still before coffee)...now off to get that coffee.

[JDMcNugent7]

Your math seems right, but i feel like ive seen get people get pocket aces twice in a row Way more than 1:48,840
dont you ?

[BrianSwa]

but are you really keeping accurate track of how many hands you have seen? bet if you take all your online hands ever I know mine are well over 100,000 hands then it would even out in long run.

[Akverno]

.000642% roughly. I once head an empirical stat on pocket aces holding up against nine randomly drawn hands, if it's accurate that's the odds of it happening. Got to love those statistics classes.

Edit: I entered the zeros wrong, already had excel knock em out, big mistake. I as well need coffee.

[Talking Poker]

You guys are looking at this wrong... forgetting one very important piece of information.

Yes, the odds of getting AA on exactly the NEXT two hands are indeed 220:1 * 220:1 = a shitload (48,400:1).

But that's not what happened. What you are really asking about here is what are the odds of getting dealt AA immediately AFTER getting dealt AA? And that is simply..... 220:1.

See the difference? If in the middle of your tourney, you had said, "I bet I get AA the next two hands in a row" and wanted to calculate the odds of it happening, you would indeed be talking about the big number. But if you didn't say it until AFTER you got the AA the first time, the odds of you getting them on the following hand were only 220:1 again.

The cards have no memory, so each hand dealt is an independent event. People like to look backwards in time to calculate odds, but you can't do that. You have to look forward.

Another much simpler example: Say we are flipping a coin. On our past 4 flips, the coin has landed heads each time. What are the odds of it landing heads on the next flip?

50%. It will be Heads or Tales with equal probability, and the coin doesn't care what happened on the last four flips.

Now.... if I ask you what the odds are of the coin landing Heads on the NEXT 5 flips, then the odds become: *.5*.5*.5*.5*.5 = 3.125%

Get it?

[Akverno]

I thought the question was what are the odds of getting dealt pocket aces twice in a a row and them holding up.

edit: the odds of pocket aces are actually a little less then 220:1, it's .4525%, 220:1 is .4545%. I had a stats teach that liked poker.