When a bet cannot protect your hand - Convince me!

[Toonces]

I'm having a hard time buying the philosophy that you should forego a flop bet to make a bigger bet on the turn if your opponent is not making a mistake to call. I will give a scenario, and if it's wrong, please tell me where I went wrong.

MP call with 9 [img]/images/graemlins/spade.gif[/img] 8 [img]/images/graemlins/spade.gif[/img] Hero raises on the button with A [img]/images/graemlins/club.gif[/img] A [img]/images/graemlins/diamond.gif[/img]. Blinds fold and MP calls.

Flop is 3 [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/spade.gif[/img] K [img]/images/graemlins/heart.gif[/img] (5.5 small bets).

Assume that you are a superb cardreader and know that he is on a flush draw. Also assume that your opponent can read your cards and knows that he needs his flush to win (even though he is still prone to make a pot odds mistake). Also, for simplicity, I will assume that the flush has a 20% chance of hitting on the turn and a 20% chance of hitting on the river (ignoring redraws to AA and running 2 pair or a set for 98s).

I believe that if I were to read SSH properly, Ed would argue that since your opponent has proper odds to call both a flop bet (6.5:1) and a subsequent turn bet (4.75:1), that you should forego the flop bet so that he would be making a mistake to call a double bet on the turn (3.75:1) if a spade doesn't come.

Scenario 1A: Ed Miller checks the flop against smart villian
80% - No spade comes. Ed bets, villian folds properly. EV = +2.75(big bets)
20% - Spade comes. Villian bets, Ed folds. EV = 0
Overall EV = 2.2

Scenario 1B: Ed Miller checks the flop against dumb villian
64% - No spade comes on turn. Ed bets, villian calls. No Spade on river. Ed bets, villian folds. EV = +3.75
16% - No spade comes on turn. Ed bets, villian calls. Spade on river. Villian bets, Ed folds. EV = -1
20% - Spade comes on turn. Villian bets, Ed folds. EV=0
Overall EV = 2.24

Scenario 2A: Toonces bets the flop against smart villian. Villian calls.
64% - No spade comes on turn. Toonces bets, villian calls. No Spade on river. Toonces bets, villian folds. EV = +4.25
16% - No spade comes on turn. Toonces bets, villian calls. Spade on river. Villian bets, Toonces folds. EV = -1.5
20% - Spade comes on turn. Villian bets, Toonces folds. EV = -.5
Overall EV = 2.38

Scenario 2B: Toonces bets the flop against very dumb villian. Villian folds.
Overall EV = 2.75

Scenario 2C: Toonces bets the flop against slightly dumb villian
80% - No spade comes. Toonces bets, villian folds. EV = +3.25
20% - Spade comes. Villian bets, Toonces folds. EV = -.5
Overall EV = 2.5

Against both the smart and dumb villian, betting the flop wins, even though the villian has proper odds to call both times. Am I missing something about this concept? Would the math fail in another example? It seems to me that foregoing flop equity is usually too expensive to forego an extra flop bet.

If I had to guess, I would guess that the reason this example shows the opposite of Miller is that the flop equity is very large. Is there a mathematical example of a small flop edge that contradicts this?