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But do you prefer pushing yourself or check/calling, or irrelevant? Also, how does preflop and flop look, if you don't mind?

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I'm pushing this turn myself 100% of the time, because you don't want AKhearts to catch up to you for free. Also, if you push, villain's getting about 3:1 to call you so you're probably getting his money anyway, so it's better to get it in there than risk giving him a free card.

Preflop, I'd just limp 88, because in early position you're probably going to play it for set value, so you'd be chopping your implied odds down considerably by raising it yourself. Calling the pf reraise is good, if you're fairly sure you can stack him.

On the flop, check raising may be a little risky, again with two hearts on the board. I'd pot the flop, and go from there. As played, the check raise looks great.