Set Card Game
BENJAMIN LENT DAVIS AND DIANE MACLAGAN
SET is an extremely addictive, fast-paced card game found in toy stores nationwide. Although children often beat adults, the game has a rich mathematical structure linking it to the combinatorics of inite affine and projective spaces and the theory of error-correcting codes. Last year an unexpected connection to Fourier analysis was used to settle a basic question directly related to the game of SET, and many related questions remain open.
The game of SET was invented by population geneticist Marsha Jean Falco in 1974. She was studying epilepsy in German Shepherds and began representing genetic data on the dogs by drawing symbols on cards and then searching for patterns in the data. After realizing the potential as a challenging puzzle, with encouragement from friends and family she developed and marketed the card game. Since then, SET has become a huge hit both inside and outside the mathematical community.
I love to add math games to our curriculum and today I want to show you how to play one of my favorite card games. SET was introduced to me years ago by a go. I've made a few card games before but this is the first Solitaire game I've done. It's been fun to make, I hope you enjoy playing it. If you have any questions, comments or requests for other solitaire games you can send them to admin@cardgames.io or tweet at me @cardgamesio. In Peter Norvig’s interesting post The Odds of Finding a Set in The Card Game SET, he concludes that the odds against there being no set in 12 cards, during a game, is 16:1. This is an average value, but it doesn’t tell the whole story. A more detailed analysis shows that the odds when playing a game of SET start off at 30:1 for the first. America's Favorite Card Games®. SET Puzzle Rules. Download our interactive flash tutorial. Play SET at The New York Times. FOR MORE INFORMATION, SEE.
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This page is partly based on contributions from Magnus and Greg Petras.
Introduction
Contract Rummy is a version of Rummy consisting of a series of rounds. In each round there is a different contract: players have to collect a particular combination of groups and sequences before they are allowed to meld. The contracts become progressively more demanding on each deal.
Alternative Names and Variants
This page describes several games which are so similar that they can almost be regarded as variations of or alternative names for the same game. They are:
The original game of the group was Zioncheck, invented by Ruth Armson in the 1930's, which had just six contracts.
Links to several other web pages with rules of various Contract Rummy games can be found at the end of this page.
Contract Rummy
This description is based on a contribution from Magnus.
Players
The game is best played by three to five players; the optimum number is four.
Cards
Contract Rummy is played with two standard decks of 52 cards, plus jokers.The number of jokers used should be one fewer than the number of players, sothree players play with 106 cards, four players with 107 and five with 108.
Playset Card Game Online
The Deal
There are seven rounds altogether. The first dealer is chosen randomly, and thereafter the turn to deal rotates clockwise. The deal itself is clockwise, one card at a time. In the first three rounds, the players receive 10 cards each; in the last four they receive 12 cards each.
The cards remaining after the deal are placed face down on the table to form thestock pile, the top card of which is turned face up and placed alongsideto start the discard pile.
Object of the Game
The object of each round is to dispose of all your cards by acombination of melding, laying off, and discarding. In order to do anymelding or laying off, you must begin by fulfilling your contract for the round currently being played.
There are two kind of melds, sequences (also called runs) and groups (also called sets or books).
- A sequence or run, in this game, consists of at least four consecutive cards of the same suit, such as 4 5 6 7. An ace can count as low or high but not both at the same time. So A 2 3 4 and J Q K A are both valid sequences, but Q K A 2 is not valid.
- A group, set or book consists three cards of the same rank, irrespective of suit, such as 5 5 5.
Once it has been melded, a sequence can be extended by adding further consecutive cards at either end, as far as the ace in either direction; the longest theoretically possible sequence being 14 cards long with an ace at each end. A group can be extended by adding further equal ranking cards.
When a player goes out, by disposing of all their cards, the other players score penaltypoints for all the cards remaining in their hands. The object of the game is to be the player with the lowest score at the end of the series of seven rounds.
The Contracts
The contracts in each successive round are as the following.
- Two Groups of 3 (6 cards)
- One Group of 3 and One Sequence of 4 (7 cards)
- Two Sequences of 4 (8 cards)
- Three Groups of 3 (9 cards)
- Two Groups of 3 and One Sequence of 4 (10 cards)
- One Group of 3 and Two Sequences of 4 (11 cards)
- Three Sequences of 4 and No Discard (explained later)
The Play
The player to dealer's left takes the first turn. A turn consists of:
- 1. The Draw
- The player must either draw the top card of the stock pileor take the top card of the discard pile. A player who chooses to draw a card from thestock pile must first give any other player who wishes the opportunity to take thediscard (see below).
- 2. Melding
- The player may place groups or sequences from hand face up on the table. This can only be done once by each player during each round. When melding, you mustlay down exactly the combination of groups or sequences which is required by the contract for the round you are in. For example, you cannot lay down one group if you need two, or if you need asequence also. When you meld, you can only meld the minimum number of cards required. For example if you have a sequence of a greater number of cards than four, or a group of more than three, you must wait until your next turn before you can lay off the additional cards.Melding is optional - you are not required to meld as soon as you are able to.
- 3. Laying off.
- Laying off is adding cards to groups or sequences which have already been melded - both your own and those melded by your opponents. You may lay off only if you have already melded in some previous turn of the current round. You may not lay off before or on the same turn in which you meld. There is no limit as to how many cards you may lay off in one turn. Laying off is optional - you are never obliged to lay off cardsif you do not wish to.
- 4. The Discard.
- At the end of your turn, you must discard one card from your hand and placed it face up on top of the discard pile (except at the end of round 7 - see below).
It can occasionally happen that the stock pile runs out of cards. If a player wishes to draw a card when there are no cards left in the stock pile, then you take all the cards of the discard pile except the top one, shuffle them together, and place them face down to make a new stock. The top card of the old discard pile remains face up to start the new discard pile. Play then continues as before.
If there are a lot of 'May I?'s (see below), it is just conceivable that both the stock pile and the discard pile might run out of cards. In that case the play ends. There is no winner and everyone scores penalty points according to the cards that they have in their hands (see scoring).
Taking the Discard Out of Turn (the 'May I?')
If at the start of your turn you choose to draw from the stock rather than take the discard, any player who desires the card on the top of the discard pile may ask for it (hence the name 'May I?' of the version described later). If several people want the discard, it goes to the earliest in turn to play after the person who is about to draw from the stock. The player who takes the discard in this way must take in addition the top card from the stock as a penalty card.
After someone has taken the discard out of turn, it is possible for a different player to take the next card of the discard pile in the same way, also taking a penalty card from the stock pile along with it. There is no limit as to how many times this can be done, but the same player is not allowed to take two successive cards from the discard pile in this way.
Only when the other players have had the opportunity to take any cards they want from the top of the discard pile does the person who was about to play draw from the stock and continue their turn. Note that the play resumes from its original point - the turn to play does not jump to the person who takes the discard.
Note also that if the player whose turn it is to play wishes to take the card at the top of the discard pile they may do so, without taking a penalty card from the stock pile, and no one else then has the chance to take any discards.
Jokers
Jokers may be used in either sequences or groups, to substitute for any missing card.
If a joker is played in a sequence, any player who has the card which the joker is representing, and who has already melded their contract on a previous turn, may, during the laying off phase of their turn to play, take the joker, replacing it in the meld with the card it represents. Any joker gained in this manner must be laid off in the current turn - it cannot be saved for play in a later turn.
Jokers played as part of a group are considered 'dead'; they cannot be reclaimed and played elsewhere.
Special Rules for Particular Rounds
- 3 4 5 6 and 5 6 7 8
- 3 4 5 6 and 8 9 10 J
Scoring
When someone goes out by getting rid of all their cards, play ends and the other players score penalty points for all the cards remaining in their hands, the cards scoring as follows:
| Face cards (K,Q,J) | 10 Points |
| Ace | 15 Points |
| Joker | 15 Points |
| Number Cards are worth their spot (index) value. | |
At the end of the seventh and last round, the player with the lowest total score wins.
Variation
The game can be played without jokers.
Liverpool Rummy
Paul Welty reports that Liverpool Rummy is the same as Contract Rummy, except that the player to the right of the dealer must cut the deck before the deal. If this player manages to cut the exact number of cards required to deal the hand and leave a face-up card, then the cutting player's score is reduced by 50 points (which is good).
May I?
Set Card Game Directions
This is related to Contract Rummy, described above, but according to Greg Petras there are the following differences:
- In 'May-I?', one deck of cards is used per 2 people playing, including both jokers from each deck of cards.
- The sequences or groups in your initial meld can contain more than the minimum number of cards. For example, in round 3, if you have, say, 3-4-5-6-7 and 2-3-4-5-6-7, you may lay down all of these cards at once in your melding turn. You do not have to put down, for example, just 3-4-5-6 and 2-3-4-5 first and then wait until your next turn to then to lay off the left over 7 and 6-7. The same applies to groups - the initial meld may have as many cards as you like (minimum 3) of the same rank.
- Jokers which have been melded cannot be reused. For example, if someone has put down a sequence 3-4-joker-6, and you have the 5 of that suit, you may not take the joker out in exchange for your 5.
- In the rounds where the contract has more than one sequence (rounds 3, 6, and 7)there is no prohibition against contiguous sequences. For example it is acceptable to meld 3-4-5-6 and 7-8-9-10 of the same suit as two sequences.
- The special rules for round 7 do not apply. The player melding may have more than 12 cards: if they have said 'May-I?' during that round they will have two extra cards in their hand for each 'May-I?' they said. It is not necessary to use all the cards in your hand in your 3 sequences, and if the player melding has cards left over, then play continues as in other rounds.
- The Joker is worth 25 points, not 15 points.
Shanghai Rummy
There are several versions of Shanghai Rummy. There is also a rummy game known to some people as Shanghai, which is not a contract game, but a type of Carousel or Manipulation rummy - this will be found on the Carousel page.
The description below has been put together mainly from a description by Mark Allen Davis, with variations supplied by Tahelia Powe and Deb Kolsov.
The basic rules are as in Contract Rummy; the description below concentrates on the differences.
Players, Cards, Deal and Contracts
The game is for 3 to 5 players. The game is played with two standard decks including four jokers (108 cards). As in Contract Rummy, 11 cards are dealt to each player and there are seven contracts:
- two books
- one book, one run
- two runs
- three books
- two books, one run
- one book, two runs
- three runs with no discard
Melding Rules
In a run, aces are high only. A-2-3-4 is not a run. When putting down runs, consecutive runs in the same suit (such as 6-7-8-9 and 10-J-Q-K) cannot be put down by the same player in the initial meld. Runs can, however, become consecutive later, when they are extended by adding extra cards.
A player cannot put down two books of the same rank - six eights do not make two books.
A joker can be used in a meld as a substitute for a missing card. A book or run cannot contain more than one joker (but a player can meld more than one joker provided that they are used in different books or runs).
Further cards can be added to your initial meld and to other players melds in the same turn that the initial meld is laid down or in later turns.
The 'May I?'
Each player can take the discard out of turn at most two times in each round. It is convenient to use pennies or other tokens to keep track of this. The player who wants the discard must also take the top two cards from the face down stock, and does not meld or discard. Play then reverts to the person whose turn was interrupted.
You can only take the discard by a 'May I?' if the player whose turn it is does not want it. If more than one player wants to 'May I?' the same card, the one whose turn to play would be sooner has priority.
The Shanghai
This occurs when a card is discarded which could be added to one of the melds that is already on the table. There are two situations:
- If you deliberately discard a card which could be added to an existing meld, you can call 'Shanghai' as you discard it. This prevents it from being picked up by the next player or being 'May I?'d in that player's turn. This can happen, for example, when you have not yet made your initial meld, but wish to get rid of a card from your hand which happens to fit one of the other players' melds.
- If you discard a card which could be added to an existing meld without calling Shanghai, then any other player (even a player who has not yet put down their contract) may call 'Shanghai', and add the discard to a meld. The calling player then offers their hand to you face down, and you must draw a card from it and place it in your own hand. The player to your left then takes their turn as normal.
Note that a 'Shanghai' takes precedence over a 'May I?'. If a player calls 'Shanghai' to protect a discard or to take a discard and add it to a meld on the table, this stops any other player taking that card with a 'May I?' on that turn.
The Scoring
The penalty points for cards remaining in players' hands when someone goes out are as follows:
| 2 - 7 | 5 points each |
| 8 - K | 10 points each |
| aces | 20 points each |
| jokers | 50 points each |
Variations
Tahelia Powe's version has the following differences:
- Only 10 cards are dealt to each player.
- There is an additional contract of 4 books of 3 inserted at the seventh deal; on the eighth and last deal you need three runs of 4.
- When going out, you are never allowed to discard; all the cards from your hand must be played on the table.
- A player cannot meld more than one run in the same suit.
- 'May I?'s are called buys.
- There is no Shanghai.
Deb Kolsov's version has a different sequence of contracts:
- two sets of 3
- set of 3, run of 4
- two runs of 4
- three sets of 3
- set of 3, run of 7
- two sets of 3, run of 5
- three runs of 4
- set of 3, run of 10
- three sets of 3, run of 5
- three runs of 5
Progressive Rummy
This section is based on a contribution from John Eveleigh
Unless otherwise stated the rules are the same as for Contract Rummy.
Players, Cards, Deal and Contracts
Two packs of cards are used, with 4 jokers (108 cards in all). 11 cards are dealt to each player.
There are fifteen contracts; the sequence is as follows:
| ROUND | CONTRACT | BUYING |
|---|---|---|
| 1 | 2 sets of 3 | |
| 2 | 1 set of 3 and 1 run of 4 | |
| 3 | 2 sets of 4 | |
| 4 | 2 runs of 4 | |
| 5 | 2 sets of 3 and 1 run of 4 | |
| 6 | 1 set of 4 and 1 run of 5 | |
| 7 | 2 sets of 5 | |
| 8 | 2 runs of 5 | |
| 9 | 4 sets of 3 | BUY 1 |
| 10 | 3 runs of 4 | BUY 1 |
| 11 | 3 sets of 4 | BUY 1 |
| 12 | 5 runs of 3 | BUY 2 and TAKE 2 |
| 13 | 5 sets of 3 | BUY 2 and TAKE 2 |
| 14 | 1 set of 5, 1 run of 5 and 1 pair | BUY 1 |
| 15 | 2 sets of 3 and 1 run of 5 |
Melding Rules
The above table shows the initial meld requirements. Having laid down your initial meld you can add more cards to your own and other players' melds in the same or subsequent turns.
In runs, aces count high or low but not both. J-Q-K-A and A-2-3-4 are allowed but K-A-2-3 is not. There is no rule against a player laying down two consecutive runs in the same suit, such as 3-4-5-6 and 7-8-9-10 of hearts, as separate runs, but once they are on the table separate runs must remain separate - runs cannot be joined or split.
A set can consist of any three or more cards of the same rank - identical cards can be included. A pair (needed for hand 14) is two cards of the same rank. There is no rule against a player melding two sets of the same rank.
Jokers and twos are wild. A set or run may contain any number of wild cards to substitute for missing cards. The player must specify (if it is not clear) whether the meld is a run or a set, the rank of the set, and the rank and suit of a run. Wild cards once melded cannot be moved - a player who holds the real card represented by a melded wild card is not allowed to substitute the real card for the wild card.
Buying
To make up the number of cards required for hands 9-14 it is necessary to 'buy' the face-up card from the discard pile. Each card bought costs one penny, paid to a kitty, and you place the bought card in your hand. In hands 9-11 and 14 you can buy on one occasion during the hand; in hands 12 and 13 you are allowed to buy twice. In hands 12 and 13, at the same time you buy the up-card you also take the next blind card from the face-down stock.
If it is your turn you have the right to buy first if you wish and then take your normal turn. If it is not your turn you have to state that you wish to buy the card. The current player may only stop you if they wish to take (or buy) the card themselves. If several players want to buy the face up card, the one whose next turn to play comes soonest has priority, so any player to your right, up to the current player can opt to buy the card you wanted.
When a card has been bought, the face up card underneath it is then available to be bought.
You can only buy in hands 9-14, and you only get one or two opportunities to buy depending on the hand, as detailed on the score sheet.
Scoring
Play ends when a player 'goes out' by getting rid of all the cards from their hand. This can be done by putting down all the cards in melds or by discarding one's last card. Each of the other players scores penalty points for the cards they are holding:
| Wild cards (Jokers and 2s) | 20 |
| Aces | 15 |
| Picture cards | 10 |
| 3s to 10s | 5 |
At the end of the 15 deals, the player with the lowest score is the winner, the next lowest is second, etc. The players settle up in pennies according to their position - for example for a four player game the payments are as follows:
- Winner: Receives 12
- 2nd: Pays 2
- 3rd: Pays 4
- 4th: Pays 6
In addition the winner takes all the pennies paid to the kitty for buying cards.
Other schedules of amounts are possible. Also, by prior agreement, the kitty can be split between the winner and second player - two thirds for the winner and one third for second.
Other Contract Rummy web pages
The variation 6-7-8-9-10 - which was played in Pittsburgh in the late 1940's, is described on a web page by Alan Hoyle.
A variation called Continental Rummy is described on an archive copy of Mike Gaston's page.
Rummy.com (archive copy) had rules for Contract Rummy and Russian Rummy.
12-Step Rummy is described on Kate Hanratty's page.
Archive copy of Bill Whitnack's description of a version which he calls Rummy Rummy.
The Contract Rummy pages of Randy Rasa'a Rummy-Games.com site describe several versions.
Rummy.ch is a German language site offering rules for Contract Rummy and many other rummy games, plus strategy articles and reviews of online rummy sites and a forum.
Several games described on other pages of pagat.com are closely related to Contract Rummy but with definite differences.
Software for Contract Rummy
How To Play Set Card Game
Malcolm Bain has written Windows programs for two versions of this game: Contract Rummy and California Rummy. These are available from Card Games Galore.