BRUTAL- What are the odds?

[sickofants]

My gut tells me that these ARE gonna be pretty long odds.

Player 1: Pr(Pocket pair)=13*(4C2/52C2)=1/17
Player 2: Pr(Different pocket pair)=12*(4C2/50C2)=72/1225

So odds of both starting with a pocket pair are 72/20825

Now we need both players to hit their set and for the final flop card to be a blank, that is:

(2/48)*(2/47)*(44/46)=11/6468

Multiplying these probabilities together gives: 6/1020425 or about 1:170072 (which is somewhere close to 256*64)

You can be rest assured that if you have QQ in the hole against one opponent, the probability that opponent has AA or KK are:

2*(4C2/50C2)=12/1225

so the odds are about 1:104