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Second, I think the flop equity is so large that you're giving up too much. The hero has 12 outs, he's a 1.2:1 favorite to win by the river. By 3-betting the flop he's getting in an extra BB, of which the hero nets .833 given his odds of winning.

So, 3 betting the flop = +.83BB

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I'm pretty sure this is flawed.

You are giving hero 83% equity, which he doesn't have.

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Argh, yea, 1/1.2 = 83%, but it should be 1/2.2 = 45%.

Flop bet is still better EV depend on how you see the odds of a check through or 4-flush hurting you, but it's much closer.

I suck so I deleted my post.