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Interesting hand. I wonder what he has on the turn? Maybe some two pair type hand, maybe a straight? He obviously puts you on a draw, and correctly so. I doubt he will put in a lot of money on the river if you make your hand there, so a turn push would be the only way to get your draw paid off IMO.
However, zook makes a valid point that profitably pushing with draws requires some FE, which you don't likely have much of. I am fine with folding the turn since you are probably behind his most likely range, and it doesn't look like he is willing to fold.
1,452 games 0.031 secs 46,838 games/sec
Board: Qs Ts Kc 8c
Dead:
equity win tie pots won pots tied
Hand 0: 33.919% 23.97% 09.95% 348 144.50 { QcJc }
Hand 1: 66.081% 56.13% 09.95% 815 144.50 { AJs, KJs+, QJs, AJo, KJo+, QJo }
You aren't getting pot odds to call either, though it is close and if you think you could get $15 off of Villan on the river if you make your hand a call on the turn might actually be profitable.
($10 to win $16 ; you would need to be at least a 38% favorite to win the hand at showdown to be getting correct pot odds).
So, my answer to your question is; fold or call, but going AI on the turn is not +EV. Folding would be best unless you believe villan will pay off a value bet on the river if you make your hand.
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