TB: This is an extremely uncomfortable position for you, but you have learned a thing or two about his range.
1. He doesn't have AK, AA or KK. It's very unlikely that he would not have checkraised you seeing that the other two had already folded anyway.
2. Whatever that jack did to his hand meant that he was prepared for it, or at least you seem to indicate this (with the instant check).
What does it mean that he's prepared for it? Well, let's see:
* He could be holding A-rag and intends to call you down, but isn't willing to make it any more expensive than he has to.
* He could be on a flushdraw and has already decided to checkraise you if he hits
* He could be on a straightdraw and has already decided to checkraise you if he hits and to check if he doesn't
* He has a medium/large pair and has decided to check/call you down with it, and to checkraise if he hits a set.
* He has K-something and likes to think that you're
bluffing.
I find the flush draw extremely unlikely. With that pot size and your bet, calling is not a difficult decision, especially not when he has - like you - a decent stack left. The other possibilities I find about as likely, each. What does that mean for you?
25% of the time he has an ace and will call you down (or raise if he pairs his kicker)
25% of the time he has a king and will call you down, unless you scare him off (or he pairs his kicker)
25% of the time he has either hit his straight, or a pair larger than yours
You're, in other words, behind at least 75% of the time.
The positive aspect of this turn card is that if another heart hits the river, there are now only two cards in the deck can give him a higher flush. Your hand's value increased somewhat due to this.
In my opinion, your best (only?) chance of winning this hand unimproved on the river is if you push all-in on the turn, as it's extremely unlikely that you're ahead now, so you need him to fold the best hand. With a hand like K8, JT, TT or QQ, he might fold. I wouldn't believe an ace to lay it down on the turn though, especially not with a decent heart kicker.
Check and hope for the T of hearts, which would make your hand the second nuts.
