check/call check/call check/raise the river

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At the Party .25/.50 tables I've seen cases where someone will do this with TP and a weak kicker so short of reads and depending on how scary the board is I'll make the crying call. I think I'm ahead doing it but I might just be remembering the times I won and forgetting the times I got rivered...

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I agree.

This is not an uncommon way to play TP weak kicker at many limits. The idea is to lose the least but not let the aggressor check thru at the river (in case they don't have TP). If raised after the donk bet, they would fold.