Quote:
Every time you play a hand differently from the way you would have played it if you could see all your opponents' cards, they gain; and every time you play your hand the same way you would have played it if you could see all their cards, they lose. Conversely, every time opponents play their hands differently from the way they would have if they could see all your cards, you gain; and every time they play their hands the same way they would have played if they could see all your cards, you lose.
For the sake of argument, let's assume that you will either check or fold perfectly if a flush card comes on the river denying him any implied odds that might prompt him to "trade" a small mistake in calling a bet or raise in the hopes of you making a big mistake on the next card if the flush comes in.
Case 1: According to FTOP, you have correctly assessed SB's call as a mistake. Had he known that you had AK, and if he also had reason to believe that he had no implied odds if he caught his flush, then he would have folded to your bet because he didn't have the right pot odds to call. Since he would have folded if he'd seen your cards but called anyway, then he made a mistake.
Case 2: You actually made a "mistake" with your min-raise because if you had known that he was on a draw, then you would have needed to raise more than the minimum to give him incorrect odds to call the raise. His call of the min-raise was "correct" because he'd have been +EV to call that min-raise even if you'd turned your cards face up.
Once money is in the pot, it is no longer any one player's money. So, for you to avoid giving him correct pot odds to chase a 5:1 shot, you would need to raise to at least $13 in order to give him 4.55:1 pot odds to call chasing his 5:1 flush draw. Since you didn't raise the right amount, you made a "mistake" in Case 2 allowing SB to correctly call and see if he makes his flush on the river.
EDIT: From a strategy perspective, if you bet the turn at all, then bet at least 1/2 the pot. Even if it is mathematically "incorrect" for him to call 1/3 of the pot, if he's willing to call 1/3, then he'll probably call 1/2 or even 3/4. You have position. You suspect he's drawing. So bet more if you bet at all. You can always fold to a big river bet if the flush comes. And you will also have the option to check behind on the river if you get some kind of non-flush scare card that might give him a straight or 2-pair and he checks. Finally, I know HoH talks about a 1/3 pot bet in a situation like this, but that is for tournament play where survival is paramount because you can't "rebuy" if you bet more only to have villain catch his flush on the next street.