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Well, the complete air part of his range will almost certainly fold to a raise of 53, as this looks like you are setting yourself up for a turn shove, and it's optimistic to think villain would try and re-bluff you off the air in your range when you use this size, so you miss you out on value from that.
He's going to be peeling with hands such as A10 a lot more when you raise to 34 as opposed to 53, which is of course what you want, when you raise here.
Raising to 53 will get him to continue with a range that you are doing well enough against but not that you'll be making a lot of money against. (overpairs/draws)
Against his overpairs (good ones anyway) the outcome will likely be the same = he'll reraise and it'll get in on the flop so there's no difference here, apart from he will be more likely to reraise if you raise to 53 than if you raise to 34 - (I assume he'll put more air in your range and sometimes turn to bluffcatch mode when you make it 34, and he'll prob just assume you aren't folding when you make it 53)
On a non heart 3 or 4 I would probably check assuming he just flatted my raise, as I don't think it'd likely he'll fold anything that I would want him to fold on that turn. (1010+) I would be more likely to bet the turn if I thought that he would also bet river with his Ax hands that he called the flop with, but we don't have that info.
If I did bet it'd probably be quite small again, maybe 30-40, as protection isn't an issue here and I would want him to continue with as wide a range as possible which includes hands like Ax as mentioned earlier.
If the turn was a J or Q, I'd probably bet intending to get him to fold 99/1010/8x by the river - depending on timing etc. (I'd be more inclined to use a smaller betsize here too) for example, say you bet $4 on the turn and he called, then you bombed river, you are going to get a ton more folds then if you bet $80 and bombed river (not just because of pot odds either) when he C/C a small bet it all but takes his monsters out of his range, the more you bet - the more inclined people are too slowplay, so when your small bet gets called, you can be happier about betting the river.
If the turn is an ace, I'd probably check here as it makes it less likely that you'll be able to get a bet on both the turn and river from one pair hands such as tens or w/e, that he would be more likely to call with on the river if you checked the turn, and again, protecting against these hands isn't a big factor. Even though you do lose a potential 2 streets from an Ax that he peels the flop with - it's less likely he has these hands combo wise when it comes on the turn.
Not really sure if that rambling makes sense but it's what comes to mind.
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