221 * 221 * 221 = 10,793,861.
Wow. Didn't realize numbers increased that fast.

odds of hitting AA 3 times in a row are :

221 :1 first time
221 : 1 2nd time
221 : 1 3rd time

don't be tempted to think otherwise

ok I think there will be some blood because a lot of people are really confused by that.

hitting AA 3 times in a row has the same probability as hitting AA !

yes, this is random, all games are independant, so there's is absolutly NO reason (at least no mathematical reason) to have the probability of hitting AA just after AA has been dealt to be lower than 221:1, the probability remains the SAME !!!

people are confused by that because it seems extraordinary to have AA 3 times, in fact it's pure random.

if you make the inverse reasonning, do you really think you have more probability to hit AA after you've been dealt 10 garbage hands, 20 garbage, 1000 garbage ???
There's no change at all !

Nobody is amused by the fact that I got KK 4 times in a row and lost a buy in and a half?

ok I apologize I didn't understood !

so I'll give you the exact answer of hitting AA 3 times in a row.

As I'm kind I'll give you for i times in a row.

The probability of someone being dealt aces during a session of i+1 holdem hands is given by substracting 1 from the value of C(i) divided by 1326^(i+1)

ok and
C(i) =
(663+669 x racine(770)) / 28) x (660 +24 x racine (770) ) ^(i) +
(663-669 x racine(770)) / 28) x (660 -24 x racine (770) ) ^(i)

So for AA being dealt 3 times in a row the probability is 0.0041% that is 24475 : 1

source : http://www.math.sfu.ca/~alspach/comp45.pdf

edit : these numbers seems to be quite high compared to what you calculate, I'll ask Mulder and Skully to see if the truth is elsewhere..////