Showdown Scenario where bluffer does not want to show

[AngusThermopyle]

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Just a question as I didn't see it get asked yet.

In the OP's scenario, what if villain says "I bluffed, you win" but doesn't release his hand - and you say something like "thanks" muck your hand and start gathering chips.

What's the ruling here? Am I right to think that only the physical act of mucking cards actually counts, so villain gets the pot?

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Depends. On the house and the floor and the villain's 'history'.
If he just says "I bluffed" or "Nice call", be prepared to lose. Those are not concessions.
But "You win" or "Take the pot", you might get the pot. If you don't, please don't post it here.