Set over set?

If both of two players start with a pocket pair, a set over set flop will happen 1% of the time. Since you don't only see flops with pairs, it is less, but if there are many multiway pots and players who will see every flop with a pocket pair, it will happen more often.

There was a thread about this not too long ago. Long story short, the answer is that this will happen about once every 98 times two players with unequal pocket pairs see the flop.

Long story slightly longer: Suppose player A has KK and player B has AA (for example). What's the probability that the flop comes AKx (where x is neither A nor K)?

As we're assuming we know 4 cards' locations, the flop is randomly selected from the 48 remaining cards. So, there are C(48,3)=48*47*46/(3*2*1)=17296 equally likely flops. Of these, 2 * 2 * 44 = 176 are of the form AKx. (This is because there are 2 aces, 2 kings, and 44 'other' cards remaining in the deck.)

Therefore, the probability of flopping set over set is 176/17296; this is approximately 1.02%, or about once every 98.3 hands.

Of course, this probability applies to *any* two players with unequal pocket pairs; the result is independent of choosing AA vs KK in our