With AK, what are the chances someone has KK or AA

Originally Posted by The Bean Counter

Worth looking at articles on combinatorics. Think there's a couple on here.

Haven't looked at Ong's workings and I won't give you a perfect answer, but let's say we hold AhKh. Villains can only hold:

AdAc, AdAs, AcAs = 3 combos
KdKc, KdKs, KcKs = 3 combos
All combos of QQ = 6 combos

There are 1326 starting combinations of hole cards in poker, equal to (52*51)/2. There are 12 combos above, so the chance any one player holding QQ-AA is close to 1% i.e. 12/1326. Chance if there are 9 players left behind us to act is approx. 9%.

This isn't perfect because the 1326 includes combos we block with our AK, ignores that if the first player folds he likely doesn't have QQ+, etc, but you get the idea.

Was there a mistake somewhere. 9%?
I have played for many years and very often see AK heads up vs JJ, AQ, or worse hands.
I used to play 20 hours every week and I think I have only seen AK vs QQ or better like 50 times.