A Pair of Aces Twice in a Row?

There’s been a discussion on 2+2 of the odds of getting dealt a pair of aces in Texas Hold’em twice in a row.

My immediate thinking was: the odds of getting dealt aces in (4*3) in (52*51) = 1 in 221. The odds of this twice in a row in 1 in (221 * 221) = 1 in 48841.

I was wrong. On further reflection I realised that there is no correct answer, because there is insufficient info. The question should be “what’s the odds of getting pocket aces twice in a row given….“

For example, what’s the odds of getting aces twice in a row in the next two hands is 1 in 48841.

But the odds of getting aces twice in a row given that you got aces in the first hand is only 1 in 221. Not so remarkable after all.

And the odds of getting dealt pocket aces twice in a row during a session of 100 hands? Pretty high I guess!