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Wes, Hero has a 9TJQK straight already - he's only losing to AJ or a flush coming on the river if Villain has 2 hearts. I'd cap the turn and lead the river, I think although I'd always imagine the monster will get shown down to me from a tight player.

If raised, I call because the only hand that makes sense is AJ although it could always be another J9 which we chop.

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This opponent is a very tight player who is also not that aggressive. Becuz of this he can therefore be put on a very limited range here. AJo,KQo,J9s,TT is his range IMO. Since the hero is an underdog against this range, he should not put any more money in this pot then he has to. Capping the turn or betting the river is wrong IMO against this opponent.