[etgryphon]

[ QUOTE ]
So I've had pocket Aces 1000 times since I started playing poker. The odds of getting A-A preflop is 1/221. Granted, I've played hundreds of thousands of hands...but that's irrelevant?

Sweet, I hit a 1-in-2.4675938837065992401101191361579e+2344 longshot! I'm not following.

[/ QUOTE ]

No. Sorry to disappoint you.

You have played many more hands than the 1000 hands that you got AA. I'm just saying your odds are based off of the sample size and consecutivity(sp?) without a time element.

So in your case, if you sat down at a table and play exactly one hand of holdem and got AA (Event A). Got up from the table and left for a week while people played poker with the same deck, changed the deck, played 1000s of hands. Then you came back and sat down played exactly one hand and got AA (Event B).

For you, the odds of that happening would be:

((# of ordered events) * Odds of Event A) * ((# of ordered events) * (Odds of Event B)) = ((1) * (1:216)) * ((1) * 1:216) = 1:46656

Now lets take the case of where you sit down and play 10 hands each time and one of those hands you get AA.

So now you have events 1 - 10 in the first session
and events 11 - 20 in the second session.

Session #1:
9 events where you DID NOT get AA: odds = 215:216
1 events where you DID get AA: odds = 1:216

Odds of Session #1:
(10) * ( (1/216) * (215/216)^9 ) = 1:~21.5

Session #2:
9 events where you DID NOT get AA: odds = 215:216
1 events where you DID get AA: odds = 1:216

Odds of Session #2:
(10) * ( (1/216) * (215/216)^9 ) = 1:~21.5

So odds of Session #1 and Session #2 happening:

1 * (1:21.5)^2 = 1:463.16

Hope this is clear. Mistakes?

-Gryph