Fundamental Theorem of Poker

[bradha]

I am trying to figure out whether this theorem would say I have gained in the following case:

I am the big blind in holdem (limit), and have Qx. There is one limper, and the small blind folds. Flop is A-K-K.
I decide to bet out, folding to a raise, and checking/folding the rest of the hand if I am called. The limper folds.

Suppose the limper had a hand that is even worse than my Q. FTOP says that I gain if I forced my opponent to play differently than they would have if they could see my cards.
1. If my opponent can see that he/she is behind my hand, and doesn't have pot odds to catch up, folding makes sense and FTOP would indicate that I have lost by not having them call or raise me.
2. On the other hand, if my opponent could see how weak I am, they might realize that I could be bluffed out, so then FTOP indicates that they have lost my not raising me.
3. If I could see my opponents hand, I certainly wouldn't want to give a free card, and I would keep betting as long as I was ahead.

For most poker hands there are many different lines depending on knowledge assumptions.
1. The way play would go if all hands were face up - we each know the others hand, and know that the opponent knows our hand.
2. The way play would go if each knew the others cards, but didn't think that our cards were known.
3. The way play would go if I know my opponents cards, they don't know mine, but they know that I know their hand.
4. The way play would go if I don't know my opponents hand, but know that they know mine.
5. I know my opponents cards, but they don't know mine or realize that I know theirs.
6. Opponent knows my cards, but I don't know it, and don't know their cards.
7. Noone knows the others cards.

It seems to me that FTOP talks about two of the cases, but I am a little unclear on whether it is 5 and 6 or 3 and 4. Then again it might be referring to 1 or 2 in comparison with 7. I just got through this chapter in Theory of Poker, and I am still unclear on which knowledge assumptions FTOP is referring to.