Hi Pepper,
Showdown's are governed by several rules in the TDA:
Pots / Showdown
10. Declarations. Cards speak. Verbal declarations regarding the content of a player's hand are not binding; however, any player deliberately miscalling her hand may be penalized.
11. Face Up for All-Ins. All cards will be turned face up once a player is all-in and all betting action for the hand is complete. The dealer & players should insist on timely compliance with this rule.
12. Showdown Order. In a non-all-in showdown, at the end of the last round of betting, the player who made the last aggressive action in that betting round must show first. If there was no bet in the last round, the player to the left of the button shows first and so on clockwise. In stud, the player with the high board must show first. In razz, the lowest board shows first.
13. Contested Showdown / Playing the Board. All hole cards must be shown to win a contested showdown, even if playing the board.
14. Uncontested Showdown. In a non all-in showdown, when all opponent(s) cards have been mucked without being revealed, the last live hand wins. Opponents who muck at showdown without revealing their hands also lose the right to ask to see the winning hand.
15. Asking to See a Hand. Except where house policy provides an express right to see a hand, asking to see a hand is a privilege granted at TD’s discretion to protect the integrity of the game (suspicion of invalid hand, collusion, etc). This privilege is not to be abused.
Now if you have a house rule that both cards must be shown during showdown in order to win the pot, then that supercedes what is written above, and a player who shows one card and mucks the remainder of his hole card does no longer have a live hand, which is the same for TDA rules.
RE Contested Showdowns, both hole cards must be tabled.
A CONTESTED SHOWDOWN Falls into generally two categories:
1) An all-in player, therefore rule 11 applies to this
2) More than one player tables BOTH their hole cards.
In an CONTESTED SHOWDOWN, players must show BOTH hole cards in order to claim the pot.
AN UNCONTESTED SHOWDOWN is generally as follows:
1) A Player states they have XX and all other opponents muck their hands without any tabled hands
2) A player shows ONE of their hole cards, retaining the other face down, and all other players muck their hands - ie NOT CONTESTING THE SHOWDOWN
Example A), player A is heads-up on the river, bets and is called, shows a King which completes a gut-shot 4 card broadway straight, but does not show his other hole card, the other player (B) then mucks his cards, therefore not contesting the pot. In this situation the pot goes to player A as he has the LAST LIVE HAND in an Uncontested Showdown, he is not claiming the pot by having a broadway straight, as he has not yet tabled his hand - he is claiming the pot by having the only live hand remaining at the table
Example B) the same two players, on the river, Ten, Jack, Queen, Ace, Seven on the Board, Four Colours, Player A Bets, Player B Raises, player A calls (which he can do because he doesn't have the exclusive nut hand!) Player B then tables Ace Queen for two pairs. Player A therefore MUST table both his King and his other hole card in order to claim the pot as Player B has tabled a hand of Two Pairs. Player A must table both cards to claim the HIGH HAND, not on this occasion the last live hand, as player B has already tabled.
RE tabling one card and mucking the other, only where they hold the last live hand would they claim the pot, in all other circumstances, where there are still players with 2 hole cards (In Hold'em) then they no longer have a hand and are unable to claim the pot.
Hope this helps
Stuart