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Everyone that said check-calling is wrong here were talking about this situation specifically.

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um
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river depends on how he plays Ahigh/Khigh(other assorted nopair hands) if he always bets if you check, you are better served to check/call

if he checks behind Ahigh, but will call with it, bet/fold

if he checks behind Ahigh/Khigh, and doesn't call a river bet ... check/fold

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its not a simple hey one is bad, its dependent on how this player plays, and its kinda a feel thing, that you get with time, practice(and looking stupid a few million times)