[Wongboy]

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I understand that if someone only shows one card and the other player wants to see both cards before mucking, the first player must show both. But what happens if someone shows one card, the other guy mucks? Doesn't the first guy who mucks forfeit his claim to the pot?

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Yes that is correct. The guy who mucks forfeits the pot AND his right to see both cards.

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Consider the following situation:
The board is AAQQ4. Player A tables JJ. Player B shows just an Ace. Player A then says "nice hand" and mucks his cards followed by Player B mucking his cards.

Technically Player A should win the pot since he was the only player to table a valid hand. This would be a douche move by Player A, however.