Re: All-in Rule Question
Player 3 does not need to show his hand as he is not involved in an all-in pot. Player 1 is all in, but player 2 and player 3 both have chips left. Since there was no betting on the flop, turn, or river, the cards are turned over starting from the left of the dealer. If player 3 is in last position, he can muck his hand without showing. Even player 1, who is all in, does not have to show his hand if player 2 shows a better hand first.
The only time player 3 must show his hand is when he is the first person to the left of the dealer AND no one has bet on the river AND no one has shown their hand. He can still choose to muck at that point, but he cannot wait for others to show before mucking.
I believe that the rule you are quoting is when all players involved in a hand are all in before the river is dealt.
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