which street mister x?

A minraise will tempt the guy to do some funky stuff, including shoving in a little light, which we don't want.

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min raise his 1.25 flop bet.

I'd rather minraise with a better hand cos he may be more likely to come back over the top with a hand that may fold to a normal sized raise. If you minraise the flop you should probably be prepared to 4bet shove it too, and I'm not sure this is a good spot to do it.

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I recommend Cardrunners for superb poker coaching. It was honestly the single biggest improvement in my game signing up there! Sign-up fee might seem steep, but it pays itself back within weeks.

you should never ever minraise a flop this drawy with any part of your range

I play HU professionally and you can't apply standard HU 3 betting ranges to BvB battles, because in HU the SB is in position postflop where as here your in position postflop. That said I still prefer a call.

You have 15 outs vs most of his range so you have like 30% equity. Shoving here isn't all that bad, but unless you have some fold equity which I don't think you do, just call and suck out or c/f river.