David wrote:I didn't read your whole post

Well, I don't think I did.
I think I read it that ...
- On the 3rd hand, your odds are .45% - Correct.
- On the third hand, your odds are .45%, if you hit the same hand for the previous two hands. - Which I don't agree with
At least I don't think so
I'm tired

basically, its a logical AND of the probabilities.
whenever you read aloud and say AND, it means you have to multiply probabilities.
so if you are talking about getting AA in isolation on the first hand, or the third hand, the probablility is the same, because they are independent events.
but if you are talking about getting AA on the first hand
AND the third hand, then you multiply the probabilities together
= 0.45% * 0.45% = 0.002%
what i did then was say that twice in 3 hands meant you could have AA on the first 2 hands of the 3, or the last 2 hands, and these still count as twice in 3 hands, so i multiplied by 3.
but if you wanna talk about getting AA on hand 1 and then AA on hand 3 then its 1 in 49000, so thats what i probably should have quoted.
by extension, if you wanna talk about getting pocket rockets 3 times in a row, then you have to cube the percentage of getting pocket rockets once, which equates to about 1 in 10million