[DiceyPlay]

Your question could be ambiguous. You asked about getting the same hand (any hand) 3 times in a row and then you qualified it with Ah9h.

For Ah9h it would be

[p(you get Ah or 9h as first card) * p(you get the other card as second card)]^3

or [2/52 * 1/51]^3 ~ .0000000004 = Extremely rare.

But being dealt any two cards 3 times in a row is [2/52 * 1/51]^2 ~ .0000006 = a little less extremely rare.

The difference is you don't care what you were dealt on the first hand. You just want to know how likely it is to come up 2 more times.

But what happened to you only happens 4 in 10 billion for Ah9h specifically! Or 6 times in 10 million for any two cards.