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Raising the flop just has too much value not to in this situation.

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Can you quantify it? <scenarios snipped>

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It's a matter if pot equity. Do you get more equity on a flop raise or the turn raise?

The flop raise is strictly for value, you have little fold equity. The turn raise is definately value -EV, so the question becomes: does this turn raise have enough fold equity to overcome the flop equity you gave up by not raising the flop?

Fold equity is tough to quantify, but we can quantify our equity by value. We have 12 outs ~ 45% pot equity at the flop.

Scenario: flop raise
Flop raise = +3SB *.45 - 1SB(your cost to raise) = +.17BB
Turn = +1BB * .25 = .25BB (25% shot we made our hand and bet the turn for value, costs 0BB to take the free card)
River = +1BB * .45 = .45BB (we had a 45% of making the hand by the river)
Total = +.87BB

Scenario: Raise the turn as a semi-bluff on a miss.
Flop call = +0BB
Turn raise = (2BB * .45) - (2BB * .55) = -.1BB (we get .45*2BB if we hit or make it on the river, we lose 2*.55BB if we miss because we could still hit the river.)
River = +1BB * .45
Total = +.35BB

So, waiting until the turn to raise is a net -.52BB over raising the flop. The question is, does the added fold equity gain back more than .52BB? Adjust for the fact that the BB might come along and foil the fold equity, that we might make our hand on the turn and lose it on the river, and that we had fold equity in our flop raise line if we followed up on the turn.

And perhaps most important, if we do fold them out on the turn with a semi-bluff we lose our .45BB equity we'd get on the river on a made hand, which really means we're giving up .97BB (I think, the percentages on each permutation are starting to lose me...). And how do we know they won't fold to a raise when the flush hits if they'll fold when it doesn't hit?

I don't really know, seems like giving up the .52BB with all the caveats would require a lot of fold equity on the turn.

Do the numbers look ok? Seems like I always screw up something.