Concentration, also known as 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 and is an especially 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.

**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.

**Computerized versions**

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.

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