[housenuts]

Correct me if my math is wrong,

Say buddy has a gutshot on the flop. Ignoring implied odds he needs 10.5:1 to call.
16.4 sb + bet + raise = 19.4 sb. Add in the original bettor who calls and it's 20.4 sb.

This means the gutshot will be getting just slightly less than 10.5:1 but the implied odds more than cover for it. He also has another chance to correctly call on the turn assuming there is no raise.

This post has been enlightening for me. I think by default I would have folded QJ, QT, or JT here just because it didn't seem right to call a raise with a gutshot. I never bothered to do the math. Note however that because of the 2 spades, the gutshot may in fact only have 3 outs.
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As for the hand I like to simply raise the flop. As sweetjazz says
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PS - Many bad players (i guess this includes me)who would actually ditch their gutshots at any point before the river will fold when you raise the flop. They learned a general rule ("don't draw to inside straights") and you profit off of their mistake in this particular hand.

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It also may get 3-bet which adds much more value, than making people incorrectly call on the turn would.