[The Dude]

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The other thing I've seen done is UTG whispers his hand into the floor's ear. If the floor can pick them out of the muck, UTG keeps it, the deck is reshuffled, and the two go heads up to a flop.

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This would be reasonable if the deck were still intact and UTG's cards were at least semi-distinguishable from the muck. But as is, other players' mucked cards, the deck, and UTG's hand are all indistinguishable. No way we can pull a hand out of that mess now.

FWIW, this is pretty much the only time I've ever said to myself, "Hmm. I'm not sure what I'd do if I were the floor." After some thought I know what I'd do, but it's a tough spot.