Quote:
Originally Posted by johnny_on_the_spot
Once saw a guy get AA 3x in a row
0.000009% chance of that happening
I actually got JJ three times in a row just last week which prompted me to think about the probabilities associated this sort of thing.
Your numbers are right, there's a 1/10793861 of it happening, but that's only if you ask "what is the probability that I get AA on the NEXT three hands" (or any other specific three hands).
In reality you don't count from there - everyone gets dealt AA sometimes so a more reasonable question is "given that I've just been dealt AA, what is the probability that I'll get AA again in both of the next two hands". This is *only* 1/48841 (~0.002%)
In reality, if you play a lot of hands in your life then there's a reasonable chance it'll happen. For example, if you play a million hands (which, of course, will take a live player many years) then you have about 1/11 (~9%) chance of seeing AA three times in a row. You'd need to play approximately 7.5 million hands to have a better than even chance of seeing it.
Of course, players 'see' a lot more hands than they play themselves - so the chances of seeing someone else do it will be better than the numbers for just you.