Gin Rummy is one of the most popular forms of rummy. The game is generally played by two players, each receiving ten cards. Here is an article by David Parlett on the History of Gin Rummy, which was originally published on the Game Account site.
Note: I have been told that among some players the name Gin Rummy in fact refers to not to the game described below, but to the game which is called 500 Rum on this web site.
One standard deck of 52 cards is used. Cards in each suit rank, from low to high:
Ace 2 3 4 5 6 7 8 9 10 Jack Queen King.
The cards have values as follows:
Face cards (K,Q,J) 10 points Ace 1 point Number cards are worth their spot (index) value.
The first dealer is chosen randomly by drawing cards from the shuffled pack - the player who draws the lower card deals. Subsequently, the dealer is the loser of the previous hand (but see variations). In a serious game, both players should shuffle, the non-dealer shuffling last, and the non-dealer must then cut.
Each player is dealt ten cards, one at a time. The twenty-first card is turned face up to start the discard pile and the remainder of the deck is placed face down beside it to form the stock. The players look at and sort their cards.
The object of the game is to collect a hand where most or all of the cards can be combined into sets and runs and the point value of the remaining unmatched cards is low.
4, 5, 6 or 
7, 8, 9, 10, J.
7, 7, 
7.A card can belong to only one combination at a time - you cannot use the same card as part of both a set of equal cards and a sequence of consecutive cards at the same time. For example if you have 7, 7, 7, 8, 9 you can use
the 7 either to make a set of three sevens or a heart sequence, but not both at once. To form a set and a sequence you would need a sixth card - either a 7 or a10.
Note that in Gin Rummy the Ace is always low. A-2-3 is a valid sequence but A-K-Q is not.
A normal turn consists of two parts:
For the first turn of the hand, the draw is done in a special way. First, the person who did not deal chooses whether to take the turned up-card. If the non-dealer declines it, the dealer may take the card. If both players refuse the turned-up card, the non-dealer draws the top card from the stock pile. Whichever player took a card completes their turn by discarding and then it is the other player's turn to play.
You can end the play at your turn if, after drawing a card, you can form sufficient of your cards into valid combinations: sets and runs. This is done by discarding one card face down on the discard pile and exposing your whole hand, arranging it as far as possible into sets (groups of equal cards) and runs (sequences). Any remaining cards from your hand which are not part of a valid combination are called unmatched cards or deadwood. and the total value of your deadwood must be 10 points or less. Ending the play in this way is known as knocking, presumably because it used to be signalled by the player knocking on the table, though nowadays it is usual just to discard face down. Knocking with no unmatched cards at all is called going gin, and earns a special bonus. (Note. Although most hands that go gin have three combinations of 4, 3 and 3 cards, it is possible and perfectly legal to go gin with two 5-card sequences.)
A player who can meet the requirement of not more than 10 deadwood can knock on any turn, including the first. A player is never forced to knock if able to, but may choose instead to carry on playing, to try to get a better score.
The opponent of the player who knocked must spread their cards face-up, arranging them into sets and runs where possible. Provided that the knocker did not go gin, the opponent is also allowed to lay off any unmatched cards by using them to extend the sets and runs laid down by the knocker - by adding a fourth card of the same rank to a group of three, or further consecutive cards of the same suit to either end of a sequence. (Note. Cards cannot be laid off on deadwood. For example if the knocker has a pair of twos as deadwood and the opponent has a third two, this cannot be laid off on the twos to make a set.)
If a player goes gin, the opponent is not allowed to lay off any cards.
Note that the knocker is never allowed to lay off cards on the opponent's sets or runs.
The play also ends if the stock pile is reduced to two cards, and the player who took the third last card discards without knocking. In this case the hand is cancelled, there is no score, and the same dealer deals again. Some play that after the player who took the third last stock card discards, the other player can take this discard for the purpose of going gin or knocking after discarding a different card, but if the other player does neither of these the hand is cancelled.
Each player counts the total value of their unmatched cards. If the knocker's count is lower, the knocker scores the difference between the two counts.
If the knocker did not go gin, and the counts are equal, or the knocker's count is greater than that of the opponent, the knocker has been undercut. In this case the knocker's opponent scores the difference between the counts plus a 10 point bonus.
A player who goes gin scores a bonus 20 points, plus the opponent's count in unmatched cards, if any. A player who goes gin can never be undercut. Even if the other player has no unmatched cards at all, the person going gin gets the 20 point bonus the other player scores nothing.
The game continues with further deals until one player's cumulative score reaches 100 points or more. This player then receives an additional bonus of 100 points. If the loser failed to score anything at all during the game, then the winner's bonus is 200 points rather than 100.
In addition, each player adds a further 20 points for each hand they won. This is called the line bonus or box bonus. These additional points cannot be counted as part of the 100 needed to win the game.
After the bonuses have been added, the player with the lower score pays the player with the higher score an amount proportional to the difference between their scores.
Many books give the rule that the winner of each hand deals the next. Some play that the turn to deal alternates.
Some players begin the game differently: the non-dealer receives 11 cards and the dealer 10, and no card is turned up. The non-dealer's first turn is simply to discard a card, after which the dealer takes a normal turn, drawing the discard or from the stock, and play alternates as usual.
Although the traditional rules prohibit a player from taking the previous player's discard and discarding the same card, it is hard to think of a situation where it would be advantageous to do this if it were allowed. The Gin Rummy Association Rules do explicitly allow this play, but the player who originally discarded the card is then not allowed to retake it unless knocking on that turn. The Game Colony Rules allow it in one specific situation - "action on the 50th card". When a player takes the third last card of the stock and discards without knocking, leaving two cards in the stock, the other player has one final chance to take the discard and knock. In this position, this same card can be discarded - if it does not improve his hand, the player simply turns it over on the pile to knock.
Some people play that the bonus for going gin is 25 (rather than 20) and the bonus for an undercut is 20 (rather than 10). Some play that the bonus for an undercut, the bonus for going gin, and the box bonus for each game won are all 25 points.
Some play that if the loser failed to score during the whole game, the winner's entire score is doubled (rather than just doubling the 100 game bonus to 200).
A collection of variations submitted by readers can be found on the Gin Rummy Variations page.
In this popular variation the value of the original face up card determines the maximum count of unmatched cards with which it is possible to knock. Pictures denote 10 as usual. So if a seven is turned up, in order to knock you must reduce your count to 7 or fewer.
If the original face up card is a spade, the final score for that deal (including any undercut or gin bonus) is doubled.
The target score for winning Oklahoma Gin is generally set at 150 rather than 100.
Some play that if an ace is turned up you may only knock if you can go gin.
Some play that a player who undercuts the knocker scores an extra box in addition to the undercut bonus. Also a player who goes gin scores two extra boxes. These extra boxes are recorded on the scorepad; they do not count towards winning the game, but at the end of the game they translate into 20 or 25 points each, along with the normal boxes for hands won. If the up-card was a spade, you get two extra boxes for an undercut and four extra boxes for going gin.
When three people play gin rummy, the dealer deals to the other two players but does not take part in the play. The loser of each hand deals the next, which is therefore played between the winner and the dealer of the previous hand.
Four people can play as two partnerships. In this case, each player in a team plays a separate game with one of the opposing pair. Players alternate opponents, but stay in the same teams. At the end of each hand, if both players on a team won, the team scores the total of their points. If one player from each team won, the team with the higher score scores the difference. The first team whose cumulative score reaches 125 points or more wins.