[AaronBrown]

You have to be careful about your conditioning (not physical shape, logical conditioning).

If both players play the same set of hands, their equity has to be equal. However, suppose the other player plays only AA, KK and AKs, and she opens before I look at my cards. Out of the 1,326 possible combinations of pocket cards, she plays only 16.

I also play only 16 combinations of pocket cards, but since she opened I know that 7 of them are unavailable to me. So out of the 1,225 remaining sets of cards, I will play 9.

Still not looking at my cards, I know if she has AA she wins 80% of the time if I call with the same hand range, KK wins 36% and AKs 35% (counting ties as half wins). Since there are 6 AA's, 6 KK's and 4AKs's, her chance of winning is (6*80% + 6*36% + 4*35%)/16 = 52.2%. Since I call the same fraction of the time when she holds any of these three hands, the computation should be good. I think you are doing something like this to find that I have a slight disadvantage.

We know that logic must be incorrect, because it would say I have the advantage if I look at my cards first. That obviously cannot matter.

The explanation is a bit complicated. She doesn't have the 80% edge every time she holds AA, 1 time in 9 it's 50% (I also have AA), 6 times it's 81% (I have KK) and 2 times it's 88% (I have AKs). If you consider all the possibilities:

1 time out of 6 we have the same cards, 50%
3 time it's AA versus KK, 81%
1 time it's AA versus AKs, 88%
1 time it's AK versus AKs, 66%

each of the last three cases are equally likely to happen with either one of us having the advantage.