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Where did you come up with 11:1?
I think you may be making this a little too complicated, and you may be making some leaps that I disagree with about this particular villain. He min-raised and called a 3-bet preflop - but he sees 47% of flops. He's an undeniable fish. On top of that this is button vs. blind, so if he has any positional awareness (and self-awareness of his own table image) whatsoever, there's more incentive for him to call. His range is huge up to that point. I really think going to the flop, he's not very far north of any two cards. Suited connectors, unsuited connectors, suited and unsuited gappers, all pocket pairs (prob. not AA-KK), any two high cards, maybe some high card + dangler hands, Ax. After that, given his general play style and high aggression level, you can't take it on faith that he will only play back at you with hands that have you beat. I wouldn't be exactly eager to get my money in, but with the way the hand was played and the pot size on the turn, I'm not getting away from it by that point. But I do expect to lose my share (2/3 of the time, or hopefully, a little less).
So put together a few ranges, run 'em through Pokerstove, and it will tell you what kind of equity you have. I don't have stove installed any more but I used to do this kind of exercise all the time just to get a feel for it. My feeling here is that there's a fair amount of bullshit in his range, and that gives us the equity we need to make a 2:1 call.
But if the previous betting had gone differently and the money behind was greater relative to the pot, I'd fold it.
(Say OP - when are you going to give us the outcome?)
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