The showdown is the final stage of a hand of poker, after the last card has been dealt and after the last round of betting, where the players remaining in the hand expose their cards and the winner(s) and loser(s) are determined.
Showdowns are not required to be held for any particular hand of poker (though they are a part of the rules for all variants), and indeed in many high-stakes no-limit tournaments, showdowns are not even particularly common: if all players except for one fold their hands prior to the showdown, the remaining player wins the pot and does not have to expose their cards.
Showdown Rules Edit
The showdown has a few rules to follow for the order of exposing cards. Technically, these are house rules and may be changed by any particular poker establishment, but in practice, all poker rooms adhere to these rules as they are consistent and fair. Since exposing one's cards can give extra information to opponents, players generally do not expose their cards unless they are required to do so.
Rule 1: Side pots are resolved first, in reverse order of creation. Side pots are created when one player goes all-in but two or more players remain in the hand and continue to bet without the all-in player participating. If later in the hand, another player goes all-in while two or more players remain, yet another side pot is created. These side pots are awarded to their winner(s) first, before considering the main pot.
Starting with the most recently-created side pot, the dealer instructs the players to expose their hands according to rules 2-3 (below) until that side pot is awarded. Once that side pot is awarded, the next-most-recently-created side pot is considered, and the additional player(s) who participated in that pot expose their cards according to rule 3 until that pot is awarded.
This procedure continues right down to the main pot, where the first player who went all-in joins the mix and exposes their cards according to rule 3 and that main pot is finally awarded.
Rule 2: The player who took the most recent aggressive action on the most recent betting round only exposes their hand first. Aggressive action, in this case, means to bet or raise. If no player bets or raises on the final betting round (that is, if all remaining players check), then rule 3 is used (see below). If a player bets or raises on an earlier betting round (e.g. on the flop), but there is no betting on the final betting round, they are not considered to have made any aggressive action on this round, and rule 3 is used.
A betting round is only considered to be a valid betting round for purposes of rule 2 if there were two or more players remaining in it who both had chips available for betting. If, instead, only one player had chips remaining on the river, that round is not considered a betting round, and the player who took the most recent aggressive action on the previous betting round would expose their cards first.
Rule 3: Players are addressed in a clockwise fashion starting to the left of the dealer. Each player, when addressed, must either expose their cards or discard them A player may not keep their cards hidden when addressed; they must be either exposed or mucked. Typically, once a hand is exposed, it is then compared to the already-exposed hand, and the lower of the two hands (the one which cannot win) is mucked. In hi-lo games, take care to ensure that the mucked hand can win neither high nor low for the hand before mucking it!
In Practice Edit
In practice, frequently, one player has initiated aggressive action on the final round (indeed, it is often the player who initiated aggressive action throughout the hand) and will expose their hand first. Typically, that will indeed be the best hand and all other players will muck theirs (unless another player has requested to see a calling hand; see the discussion about IWTSTH in the article on folding). Any other player who ends up with a higher hand will then expose it, regardless of "acting in turn" according to rule 3 above, and players who cannot beat that new high hand will muck theirs.
So, in nearly all cases, the high hand is exposed "naturally", by the aggressive bettor exposing, and then possibly some other player beating them. But if there is a reluctance among players to expose their cards and yet also a reluctance to muck them, the dealer must enforce the showdown rules above to force exposure to occur in a timely fashion so everyone can get on with the game.
A player being reluctant to expose a winning hand even after other players have exposed their hopeful winners is a form of slow-rolling, and is generally considered rude and frowned upon in poker etiquette.