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i think this is a good time for a rvr check. especially after you checked the turn.

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Why do you check the river in this spot? I am asking this not becuz I disagree with your decision but becuz im curious as to your thinking of checking the river vs betting the river. I think the hero bet the river becuz he felt he would get called by many hands he can beat given the way he played his hand on the turn. King highs, 3x,and 4x will probably call him but may check behind him if he checks. I am unsure as to what the right decision is on the river.