Concentration (game)

Last updated April 08, 2019

Concentration, also known as Match Match, Match Up, Memory, Pelmanism, Shinkei-suijaku, Pexeso or simply Pairs, is a card game in which all of the cards are laid face down on a surface and two cards are flipped face up over each turn. The object of the game is to turn over pairs of matching cards. Concentration can be played with any number of players or as solitaire. It is a particularly good game for young children, though adults may find it challenging and stimulating as well. The scheme is often used in quiz shows and can be employed as an educational game.

A card game is any game using playing cards as the primary device with which the game is played, be they traditional or game-specific. Countless card games exist, including families of related games. A small number of card games played with traditional decks have formally standardized rules, but most are folk games whose rules vary by region, culture, and person. Games using playing cards exploit the fact that cards are individually identifiable from one side only, so that each player knows only the cards he holds and not those held by anyone else. For this reason card games are often characterized as games of chance or “imperfect information”—as distinct from games of strategy or “perfect information,” where the current position is fully visible to all players throughout the game.

Playing card card used as one of a set for playing card games

A playing card is a piece of specially prepared heavy paper, thin cardboard, plastic-coated paper, cotton-paper blend, or thin plastic that is marked with distinguishing motifs and usually used as one of a set for playing card games, performing magic tricks and flourishes, for cardistry, and in card throwing. Playing cards are typically palm-sized for convenient handling, and usually are sold together as a deck of cards or pack of cards.

Game entertainment, activity; structured playing, usually undertaken for enjoyment

A game is a structured form of play, usually undertaken for enjoyment and sometimes used as an educational tool. Games are distinct from work, which is usually carried out for remuneration, and from art, which is more often an expression of aesthetic or ideological elements. However, the distinction is not clear-cut, and many games are also considered to be work or art.

Rules

Any deck of playing cards may be used, although there are also commercial sets of cards with images. The rules given here are for a standard deck of 52 cards, which are normally laid face down in four rows of 13 cards each. The two jokers may be included for a total of six rows of nine cards each.

The Joker is a playing card found in most modern card decks, as an addition to the standard four suits. The Joker originated in the United States during the Civil War and was created as a trump card for the game of Euchre. It has since been adopted into many other card games, where it may function as a wild card. The card is unique within the French pack in that it lacks an industry-wide standard appearance.

Additional packs can be used for added interest. Standard rules need not be followed: the cards can be spread out anywhere, such as all around a room.

In turn, each player chooses two cards and turns them face up. If they are of the same rank and color (e.g. six of hearts and six of diamonds, queen of clubs and queen of spades, or both jokers, if used) then that player wins the pair and plays again. If they are not of the same rank and color, they are turned face down again and play passes to the player on the left. Rules can be changed here too: it can be agreed before the game starts that matching pairs be any two cards of the same rank, a color-match being unnecessary, or that the match must be both rank and card suit.

The game ends when the last pair has been picked up. The winner is the person with the most pairs. There may be a tie for first place.

Solitaire

Concentration may be played solo either as a leisurely exercise, or with the following scoring method: play as normal, but keep track of the number of non-matching pairs turned over (this may be done using poker chips, pennies or by making marks on a sheet of paper). The object is to clear the tableau in the fewest turns, or to get the lowest possible score.

A penny is a coin or a unit of currency in various countries. Borrowed from the Carolingian denarius, it is usually the smallest denomination within a currency system. Presently, it is the formal name of the British penny (abbr. p) and the informal name of one American cent (abbr. ¢) as well as the informal Irish designation of 1 cent euro coin (abbr. c). It is the informal name of the cent unit of account in Canada, although one cent coins are no longer minted there. The name is also used in reference to various historical currencies also derived from the Carolingian system, such as the French denier and the German pfennig. It may also be informally used to refer to any similar smallest-denomination coin, such as the euro cent or Chinese fen.

With perfect memorization and using an optimal strategy, the expected number of moves needed for a game with $n$ cards converges to $\approx 0.8*n$ , with $n\to \infty$ .^[1] For a standard deck of 52 cards, the expected value is $\approx 41.4$ moves.^[2]

Strategy

Over the course of the game, it becomes known where certain cards are located, and so upon turning up one card, players with good memory will be able to remember where they have already seen its pair.

It is common for many players to think they know where pairs are and to turn over the one they are sure of first, then be stumped finding its mate. A better strategy is to turn over a less certain card first, so that if wrong, one knows not to bother turning a more certain card over.

An ideal strategy can be developed if we assume that players have perfect memory. For the One Flip variation below, this strategy is fairly simple. Before any turn in the game, there are t cards still in play, and n cards still in play but of known value. The current player should flip over an unknown card. If this card matches one of the known cards, the match is next chosen. Less obviously, if the card does not match any known card, one of the n known cards should still be chosen to minimize the information provided to other players. The mathematics follow:

If a remaining unknown card is chosen randomly, there is a 1/(t−1−n) chance of getting a match, but also a n/(t−1−n) chance of providing opponents with the information needed to make a match.

There are some exceptions to this rule that apply on the fringe cases, where n = 0 or 1 or towards the end of the game.

Variations

Many of these may be played in combination with one another:

Any Color: A version especially good for young children where matching pairs need only be of the same rank, not the same color. When playing with jokers, these count double because they are more difficult to match.
One Flip: Players who make a successful pair win these cards but do not go again until their next turn.
Zebra: Pairs may only be formed by cards of the same rank, but opposite in color (so 7 of diamonds would match with a 7 of clubs or spades, but not a 7 of hearts)
Two Decks: For a much longer game, shuffle together two 52-card decks and lay them out in 8 rows of 13 cards (9 rows of 12 cards if using jokers). Pairs must be identical (same rank and same suit, so the 10 of clubs would have to match the other 10 of clubs).
Two Decks Duel: Duel is a two-player game where the playing field is divided into two separate parts. Each player shuffle a full 52-card deck and lay it out in 4 rows of 13 cards. The players cannot access each other's cards. Player one starts, flipping one card face-up, then player two selects one card from his/her own side. If the pair is a match, cards are removed, if not, they are flipped back. Pairs must be identical (same rank and same suit, so the 10 of clubs would have to match the other 10 of clubs). After every turn roles are exchanged, in this case: player two flips a card and player one answers.
Double Decker Checkerboard: For a slightly easier version of the two-pack game, use decks with different backs and shuffle them separately. Deal them out in a checkerboard pattern (red, blue, red, blue, etc.) The different backs help identify the position in the grid and significantly reduce the possibility of which cards will match.
Fancy: The cards need not be laid out in a strict rectangular grid and many players have their own special layouts that include circular, triangular, or diamond-shaped formations. Dealers may select any layout they wish.
Spaghetti: Same rules as standard concentration, only the cards are not laid out in neat rows. They are strewn randomly about on the floor.

A checkerboard or chequerboard is a board of chequered pattern on which draughts (checkers) is played. Most commonly, it consists of 64 squares (8×8) of alternating dark and light color, typically green and buff, black and red, or black and white. An 8×8 checkerboard is used to play many other games, including chess, whereby it is known as a chessboard. Other rectangular square-tiled boards are also often called checkerboards.

If one of the players has a particularly good memory, she could play blindfolded. In this case, her opponent must say which cards have been turned up, turn the cards back down if she doesn't get a pair and take the cards out for her if she does get a pair.

Concentration is not limited to playing cards. Many versions of the game that are designed for children may have different themes. In some computer versions, the cards may randomly move to increase the difficulty.

Related Research Articles

Solitaire is any tabletop game which one can play by oneself. The term "solitaire" is also used for single-player games of concentration and skill using a set layout of tiles, pegs or stones rather than cards. These games include peg solitaire and mahjong solitaire. Most solitaire games function as a puzzle which, due to a different starting position, may be solved in a different fashion each time.

Spit, also referred to as Slam or Speed, is a game of the shedding family of card games for two players. The game is played until all of someone's cards are gone.

President is a westernized version of an originally Japanese card game named daifugō or daihinmin. It is a game for three or more, in which the players race to get rid of all of the cards in their hands in order to become "president" in the following round. It can also be played as a drinking game. A commercial version of the game exists under the name The Great Dalmuti, with a non-standard deck.

500 rum, also called pinochle rummy, Michigan rummy, Persian rummy, rummy 500 or 500 rummy, is a popular variant of rummy. The game of canasta and several other games are believed to have developed from this popular form of rummy. The distinctive feature of 500 Rum is that each player scores the value of the sets or cards they meld. It may be played by 2 to 8 players, but it is best for 3 to 5. The term "Michigan Rummy" may also refer to an unrelated game involving a playing board, chips, and accumulated pots that are awarded to players who play certain cards.

Old Maid is a Victorian card game for two or more players probably deriving from an ancient gambling game in which the loser pays for the drinks. It is known in Germany as Schwarzer Peter or Schwarze Dame, in Sweden as Svarte Petter, in Norway as Svarteper, in Denmark as Sorteper, in Croatia as Crni Petar, in Slovenia as Črni Peter, in Hungary as Fekete Péter, in Czech Republic as Černý Petr, in Slovakia as Čierny Peter, in Finland as Musta Pekka, in Italy as Asino, in France as Le Pouilleux or Vieux Garçon, or Mistigri, and in Japan as ババ抜き　(Babanuki). The game spawns an element of bluffing, commonly used in poker.

Cheat is a card game where the players aim to get rid of all of their cards. It is a game of deception, with cards being played face-down and players being permitted to lie about the cards they have played. A challenge is usually made by players calling out the name of the game, and the loser of a challenge has to pick up every card played so far. Cheat is classed as a party game. As with many card games, cheat has an oral tradition and so people are taught the game under different names. The game is called "I Doubt It" by Edmond Hoyle and is sometimes known as "Bullshit" or "Bologna" in the United States.

Slapjack, also known as Slaps, is a simple standard-deck card game, generally played among children. It can often be a child's first introduction to playing cards. The game is related to Egyptian Ratscrew and is also sometimes known as Heart Attack. It is also related to the simpler 'slap' card games often called snap.

Golf is a card game where players try to earn the lowest number of points over the course of nine deals. It is a game for four or more players using a double-deck of 108 cards, and has little in common with its solitaire cousin.

Rummy is a group of matching-card games notable for similar gameplay based on matching cards of the same rank or sequence and same suit. The basic goal in any form of rummy is to build melds which consists of sets, three or four of a kind of the same rank; or runs, three or more cards in sequence, of the same suit. If a player discards a card, making a run in the discard pile, it may not be taken up without taking all cards below the top card. The Mexican game of Conquian is considered by games scholar David Parlett to be ancestral to all rummy games, which itself is derived from a Chinese game called Khanhoo and, going further back, Mahjong. The Rummy principle of drawing and discarding with a view to melding appears in Chinese card games at least in the early 19th century, and perhaps as early as the 18th century, and is the essence of Mahjong.

Sheng ji is a family of point-based, trick-taking card games played in China and in Chinese immigrant communities. They have a dynamic trump, i.e., which cards are trump changes every round. As these games are played over a wide area with no standardization, rules vary widely from region to region.

Speed is a game for two players or more of the shedding family of card games, in which each player tries to get rid of all of his or her cards first.

Switch, also called Two Four Jacks, Black Jack or Irish Switch, is a shedding-type card game for two or more players that is popular in the United Kingdom, Ireland and as alternative incarnations in other regions. The sole aim of Switch is to discard all of the cards in one's hand; the first player to play his final card, and ergo have no cards left, wins the game. Switch is very similar to the games UNO, Flaps and Mau Mau, both belonging to the larger Crazy Eights or Shedding family of card games.

Ranter-Go-Round is a card game with bluffing elements.

Winner is a card game similar to the game President, the game Big Two, and other shedding games. It is the game from which Tien Len and other similar games are derived.

Mighty is a card game invented in the 1970s by Korean college students. Mighty is mostly played by Korean students, and also by some groups in North America. It is usually played by five people, but the number of cards can be modified so that it can be played by anywhere from 4 to 8 players. It is a point-trick game with bidding. It is similar to the card game Spades, but has more rules and, therefore, more strategies in playing. Mighty is also similar to Rook and Japanese Napoleon.

Buraco is a Rummy-type card game in the Canasta family for four players in fixed partnerships in which the aim is to lay down combinations in groups of cards of equal rank and suit sequences, there being a bonus for combinations of seven cards or more. Buraco is a variation of Canasta which allows both standard melds as well as sequences. It originated from Uruguay and Argentina in the mid-1940s, with apparent characteristics of simplicity and implications that are often unforeseeable and absolutely involving. Its name derives from the Portuguese word "buraco" which means “hole”, applied to the minus score of any of the two partnerships. The game is also popular in the Arab world, specifically in the Persian Gulf; where it is known as 'Baraziliya' (Brazilian).

Go Fish or Fish is a card game usually played by two to five players, although it can be played with up to 10 players. It can be played in about 5 to 15 minutes.

Euchre has many variations in game playing. Some of them are designed for two, three, five or even six hands. Described below are some of these variations. Some are called “Johann.”

Egyptian Ratscrew is a card game of the matching family of games. The game is similar to the 19th century British card game Beggar-My-Neighbour, with the added concept of "slapping" cards when certain combinations are played, similar to and perhaps borrowed from Slapjack.

References

↑ Daniel J. Velleman; Gregory S. Warrington (2013). "What to Expect in a Game of Memory". The American Mathematical Monthly. 120 (9): 787. doi:10.4169/amer.math.monthly.120.09.787.
↑ Foerster, K.-T.; Wattenhofer, R. (2013). The Solitaire Memory Game (Technical report). ETH Zurich.

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[1] Daniel J. Velleman; Gregory S. Warrington (2013). "What to Expect in a Game of Memory". The American Mathematical Monthly. 120 (9): 787. doi:10.4169/amer.math.monthly.120.09.787.

[2] Foerster, K.-T.; Wattenhofer, R. (2013). The Solitaire Memory Game (Technical report). ETH Zurich.