$5-10 QQ bad river

[W. Deranged]

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This is an easy c/fold.
Bet/fold is the second best line.
c/calling is terrible.

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I really have a very hard time seeing why check-call is "terrible" here.

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I guess he feels a J or T is highly likely given read of villain and the raise on the flop.

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I agree with that but that does not explain why bet-folding is so much better than check-calling (it is not, in my opinion, and I don't think it's that close).

[toss]

I think given the sparse read on villain he'll be more likely to call with A-high rather than raise it. By bet-folding we can extract value from an A-high and safely fold when we get raised.