Five Card Draw

Rules: Deal five cards to each player; bet. Each player in turn discards up to three cards, or optionally four if they show that the remaining card is an Ace, and receives fill-in cards. Discards are shuffled if necessary. Bet.

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Variants

Drunken Sailor: Five draw, but you can count pip cards as having one more or fewer pips than they show. Aces can be zero; tens can be 11.
Details: you can use zeroes and 11s in straights; the 11 goes between the 10 and the Jack. An 11 is slightly higher than a 10 for purposes of, eg, comparing pairs, but is still lower than a Jack. A pair of zeroes is legal, but is the lowest possible pair. (And I can't quite figure out why you would ever want that, but we decided it was legal.)
Fuck Your Friends: Deal five cards to each player. Those are all the cards that will be dealt. Bet.
In order, each player leads a round. The lead declares how many cards they want to draw. All other players hold up fingers, up to the specified number. The lead chooses which cards ze will exchange with; they may include multiple players. Make the exchange, and bet. Repeat for each player.
Leftovers: Five draw. After the draw and second round, before the showdown, shuffle the discards, and deal five up in the middle of the table. Everyone gets their five cards and one from the middle, so a six card hand. If the middle is the high hand, nobody wins, and the pot is held over.
Pig: Five Card Stud, but after the last round of betting everyone picks up their cards and plays like Five Card Draw -- discard and take in cards, and one more round of betting.
Resurrection Man: Five draw, but you may pay ten cents each to retain your discards.
Six Down to Five: Deal six cards to each player. At the discard phase, you must discard at least one card; you receive one fewer card than you discarded.
Vice President: Five draw, but the second highest hand wins.