This North American Rummy game exists in many versions and has many different names. The play is similar to 500 Rummy in that a player may take several cards from the discard pile, but there two major differences.
I have collected over 25 descriptions of this game from different players, and no two of them agree in every detail. The variants affect every part of the game: the number of cards used, the deal, the card values, the wild cards, the melds that are allowed, the rules of play and the scoring. I will try to cover these variants by first describing a game that uses the commonest version of each rule, and then listing the variants I have seen.
The name 5000 Rummy reflects the fact that the game is often played to a target score of 5000, but many players use other targets and the game may be named accordingly: 1500 Rummy, 2000 Rummy, 2200 Rummy, 2500 Rummy, 2800 Rummy or 10000 Rummy. Other names include Backwards Rummy, Bitchin' Rummy, Circle Rummy, Crazy Rummy (though this name is more commonly used for a different variant with fixed hand sizes), Dumbbell Rummy, Dummy Rummy, George, Hillbilly Rummy, Polish Rummy and Wild One. I would like to thank the many contributors who over several years have sent me descriptions of these different versions of this game.
3 or 4 players use a standard 52-card pack; from 5 to 8 players use two 52-card packs (104 cards) shuffled together. Deal and play are clockwise.
The first dealer is chosen by a random method: for example all draw cards and the lowest deals. The turn to deal passes to the left after each hand. Before the deal, the dealer shuffles and the player to dealer's right cuts the cards.
Instead of dealing the cards around the table one or a few at a time as in many games, the dealer gives each player in turn their whole hand of cards before moving on to the next player. For each player, starting to the dealer's left:
The dealer will be the last to receive cards. The dealer's first (face up) card is wild for the current deal. For example if the dealer gets a 4 face up, the dealer takes four more cards face down, and fours are wild.
The dealer stacks the remainder of the cards in a neat face down pile to form a stock from which cards can be drawn. The top card of the stock is turned face up and placed next to the stock to begin the discard pile.
All players pick up their cards, both the face up one and the face down ones, and play begins.
As in all forms of rummy, the aim is to form combinations: sets of three or more equal cards and runs of three or more consecutive cards of the same suit.
5-5-
5 is a valid set.A wild card can be used as a substitute for any missing card needed to form a set or run. For example if 6's are wild, 
8-
6-10 is a valid run.
The player to dealer's left begins, and players take turns in clockwise order around the table. A turn consists of three parts:
6-7-8 and player B had added 9 to it, other players need to be aware that a 5 or a 10 can now be added (but not another 9), even though the 9 on the table is lying in front of player B and not next to player A's run.Players score the value of all the cards they have melded. For this purpose:
Also, if the play ended by one of the players going out, that player scores the value of all the cards remaining in the other players' hands, which they failed to meld.
Further deals are played until one or more players reaches a cumulative score of 5000 or more. At that point, the player who has most points is the winner.
There are numerous variations of this game: no two descriptions that I have seen agree in every detail. Below I have tried to list all the variants I have seen. Please note that some combinations of variants work better together than others, and in some places I have noted which variants should or should not be combined.
Depending on exactly how the deal is managed, there is the possibility that some players may begin with hands of only 3 or even 2 cards, which may be undesirable. To avoid this, some groups omit some small cards from the pack. It seems to be quite common to play without twos, so that a double deck contains 96 cards. Some take this further: I have seen variants played with 2×44 cards, where the lowest card is a 4, and with 2 or more decks of 36 cards containing nothing below a 6. If low cards are omitted, aces are always high in runs, next to the king.
Another way to avoid the smallest hands is to make all the twos permanent wild cards. In this case a player who receives a two as an upcard will be dealt another 15 or 20 cards, according to what dealing variant is used.
Many players add jokers to the deck. These act as permanent wild cards. Some groups have other permanent wild cards such as tens or one-eyed jacks.
To reduce the chances of running out of cards some players add extra decks. For example three or four players can play with a double deck (with 4 jokers if used) and five or more could use a triple deck (with 6 jokers if wanted).
Some players have a lower value of 50 for aces. If aces are 50 and wild cards are 100, then wild aces would normally be worth 150, but some groups do not allow aces to be wild - see below. Some play that wild cards are always worth 200, whether they are aces or not, and that aces are 100 when not wild.
Some groups value 9's and 8's as 10 points instead of 5. Some have special high values for other particular cards, for example 45 for the queen of spades.
Some groups treat the face up card dealt to each player as indicating the total number of cards that player should receive, rather than the number of additional cards. In this version, for example, a player who was dealt a 6 first would get only 5 cards face down, not 6.
In some groups a jack indicates 11 cards, a queen 12 cards and a king 13 cards, rather than pictures all indicating 10 cards. Some give 14 or 15 cards rather than 11 for an ace.
When permanent wild cards are used, they usually correspond to a larger number of cards, such as 15, 20 or even 25. Alternatively, some play that a wild card dealt as an upcard is buried in the pack and replaced by another card. One description with 2's as permanent wild cards says that the player receiving a 2 can choose whether to be dealt 2 or 12 cards in total.
Some avoid dealing hands with very few cards by burying any small card dealt as an upcard - for example if a 2, 3 or 4 is dealt it is buried and replaced.
Some groups determine the wild card for the hand by exposing the dealer's last card rather than the first card. Some determine the wild card by an extra card dealt face up to the dealer, after the number of cards indicated by the dealer's initial upcard have been dealt.
If the indicator card is a permanent wild card, some give the dealer additional cards until a card that is not a permanent wild card is found. Others bury the permanent wild card in the deck and deal a replacement indicator card.
In one description the wild card for the hand is determined by a separate card dealt after the dealer's hand is complete: this indicator card is not used in the game: it does not belong to the dealer, nor is it part of the discard pile.
The play mechanism is essentially similar to that of 500 Rummy, and all the variants of 500 Rummy play can in principle be used in this game as well.
Some groups have restrictions on the use of wild cards in melds. Some play that the number of natural cards in a meld must always be greater than the number of wild cards. Some play that only one wild card is allowed in a meld, but that a meld of six cards or more can be split into two parts, so that one wild card can be used in each. When playing with these restrictions, players need to agree to how to treat wild cards that represent themselves: for example if sixes are wild, some treat the run 6-7-8 as already containing a wild card, while other groups treat the six as natural since it is the correct value and suit to fit into the run, even though it keeps its "wild" value of 100 points.
Some players recognise a set of three or more wild cards as a special kind of combination, which can be extended only by adding further wild cards.
Some allow the real card that a wild card represents in a meld to be traded for the wild card. That is, during the melding part of on's turn, one can play the card that corresponds to a wild card on the table, take that wild card and meld it elsewhere or add it to one's hand.
Some require a player who takes more than one card from the discard pile to meld the deepest buried card along with two natural cards from the player's hand.
Some always require the card taken from the discard pile to be melded, even when only the top card is taken.
Many groups play that a player cannot 'lay off' cards, adding them to other players' melds on the table, until after they have melded at least one set or run of their own. Having melded a set or run, a player can then lay off single cards in the same or subsequent turns.
Some do not allow players to call 'rummy' when a playable card is discarded.
One the other hand, some allow a player to call 'rummy' when any meld can be made or added to using cards anywhere in the discard pile. This is known as 'rummy in the pile'. The calling player must take all the cards above the deepest card in the pile that is being melded. This rule is not recommended.
In the variant known by some as George and by others as 2500 Rummy, no runs can be melded, only sets of equal cards. A set can contain at most one wild card, and cards can only be taken from the discard pile when a player has two natural cards in hand that match the deepest buried card that is taken. This version is usually played with a double 48-card pack without twos, and a player's first card indicates the total number of cards to be dealt to the player, counting jack as 11, queen 12, king 13, ace 14 or 15.
Some allow a player to go out by melding all his or her cards, leaving no card to discard.
Some play that if a player goes out while one or more other players are floating, the floating player(s) must draw one card from the stock.
Some play that if a player goes out on his or her first turn to play, any other players who have not yet played take one turn before the hand is scored. If another player also goes out, any bonus for going out is given to the first player who did so.
When scoring, some play that instead of giving unmelded cards to the winner to score, each player subtracts the value of the cards remaining in his or her hand from the amount scored for melded cards. In this version scores will be lower and a player can have a negative score. With this type of scoring some add a bonus of, for example, 200 points to the score of the player who went out.
The game ends when a player reaches or exceeds the target score, which may be set at 1500, 2000, 2200, 2500, 2800, 5000 or even 10000. Clearly a higher target leads to a longer game, but the game length is also strongly affected by the card values. Games with permanent wild cards are higher scoring so a higher target is appropriate. Also, games in which unmelded cards are given to the player who goes out are higher scoring and a higher target is appropriate than for a game in which unmelded cards are deducted from the owner's score, especially if there is no bonus for going out.
Some play that if more than one player reaches the target in the same deal, the winner of the game is not the player with the highest score, but the player who went out on that final deal, provided that that player has reached the target. If the player who went out is below the target, then the highest score among the players who have reached the target wins, and if there is a tie for highest score the tying players are joint winners.
This game, although evidently quite popular in North America, is surprisingly little documented: so far as I have noticed it is not described in any of the standard card game books.
Here are archive copies of Jim Davidson's former web pages on 5000 Rummy and 10,000 Rummy.
Another description of 5000 Rummy can be found on the Thirtysomething Gamers site.
The variant known as George, without runs, appeared in the Anyone for Cards package for Windows 3.1, published in 1993.
I would like to thank the many people, some of them wholly or partly anonymous, who have sent me descriptions of versions of this game. They include J.R. Arner, Jim Davidson, Judy-Ann Dvernychuk, Pauline Evans, Sam Finn, Jerry Frank, Woody Frank, Martin Glynn, Larry Hawkins, John Hill, Lois Hurst, Jeffrey Jacobs, Terry Jantz, Beverley Jenkins, Patricia King, Jodi Love, Randall Maden, Lisa Miller, Theodore L Mullett, Glenda Ritter, D'Andrea Spann, Bryan Stout, Debby Warren and Tim Vannote.