Re: Your action?
What exactly does betting do for us?
It protects us against non-pair hands that we are ahead of.
But does it really? All of these hands have at best 4 outs against us, and most if not all with a heart will be seeing the river anyway. The pot isn't so big that giving a free card to a 4 outer is a huge mistake.
Are there arguments against Betting?
Yes, the simplest being that, if we are behind it is foolish to not take a free card with so many outs. By betting we give our opponent the most action we will give unimproved to a middling 1 Pair hand, and open ourselves up to being charged the most for our draw from Sets, Straights, and the small percentage of made Flushes.
Another reason to check the Turn is the possibility that villain may semi-bluff CR the turn with a decent heart. This creates the possibility of us folding what may be the best hand on the river, and makes our decision making harder if we improve on the river without making our flush. The aggressiveness of our opponent makes this a decent possibility.
My vote is check, raising if a heart or 5 that falls on the river and calling if we improve with a non-heart 9 or A. Whether or not to call the river unimproved is a judgment call based on what falls on the river and opponent reads. I lean most towards folding unimproved most of the time. I think we will end up paying off too many hands and foregoing some of the advantages of checking the Turn.
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