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If your going to bet and call a push, why not just c/r all in? Not sure, your beating almost nothing on that flop, although that almost min-raise preflop is pretty fishy. I would drop it, you kind of made it tough on yourself by betting the flop though.

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just looking at the betting and the stacks quickly ,it think the pot before the flop is up around 600 ,and hero bets 400 on the flop.i would hardly call that a min raise.
i like that cuz hero as an over pair and is giving the villian a chance to get away from just over cards.
if hero just checks ,villian is gonna bet no matter what,then you have no idea where you stand.if you check raise,you have to go all in and you still dont know if he has an over pair.
based on the read on villian he is a solid player,and solid players dont go all in with over cards unless they have a great confident read that they can move you of a hand like this.