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His calling range on the turn:
10-x
3-3
5-5
10-10
Q-Q+
Flush draws.
I feel made hands that beat me make up ~1/2 of his range, made hands i beat ~1/4th of his range, and draws that came in make up the rest. I think he will fold all hands other than a made draw almost always, and therefore i am folding out probably 3/4ths of his range, most which is ahead of me by the river.
If he is holding a drawing hand on the turn more than 33% of the time, then check/folding river is probably best. I just don't think villain would flat call the turn with a draw nearly as often as he would shove.
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