Re: ATs
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why aren't you betting the turn for value? is c/c getting more value? i think c/c looks like exactly what he has, a heart draw.
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Assuming villain has a pair lower than T, then c/c wins the amount you call (or 0 if he checks) + the amount of your bet on the river that he will likely call with his 1-pair hand.
Assuming villain has a flush draw and takes a free card, you make more on flush over flush if you let him get there.
I really think c/c might make more when you are ahead, and lose less when you're behind than betting the turn. The only disaster from checking would be that the free card gives villain an unlikely non-heart 2-pair or hits a J/K/Q on you.
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