...this situation happens alot...you have a strong Ace...AK or AQ, flops comes A little little,
say you suspect your 1 opponent on the flop plays any Ace...
What are the odds he has paired up w/ his A AND kicker for 2 pair? (suppose you bet the pot, he calls, so you strongly suspect he also has an ace and you're deciding what to do on 4th st) ... (orrrr, you bet 1.5 the pot on the flop and he raises...you with your strong A and wondering does he have 2 pair w/ his weak A)
So the question is, what is the probability he has paired his weak Ace, for 2 pair?

(my gut feeling is pretty low...say only a 7-10% chance) anyone know?

If he is re-raising your more-than-pot-sized bet, the odds that he has hit two pair are pretty much 100%, it seems to me. Either that or he's a total fish. Decide which and act accordingly.

But, OK, the actual odds before the play happens. Assume: AK in your hand, Ax in his hand, flop comes Ayz. What are the odds that either x=y or x=z.

We know 4 cards for sure. 48 left.
Set x = 7. (just picked that randomly) Now 47 unknown cards left.
Odds that y = 7: 3 in 47
Odds that z = 7 (assuming y<>7): 3 in 43.

I say "3 in 43" because we're assuming that the two flop cards are not the same: y <> z. Say y is an 8. Then z cannot be any 8. Right. I hope that makes sense.

Anyway, I get a 12.9% chance that he has two pair.

But it's probably higher than that, because "A-little-little" implies that the flop did not have any As, Ks, Qs, or Js in it. If so and if you're sure he is not playing AJ or better, then his odds of hitting two pair go up.

Taking out all the As, Ks, Qs, and Js as possibilities for the flop, you're left with only 36 cards that can flop. 35 after putting a 7 in your opponent's hand. So 3 in 35 and then 3 in 31: the chance that he hit is now 17.4%.

All I know is I'm sick of getting beat by someone who called my preflop raise right after me with A6 unsuited getting the six on the river.