Card Games

By Gough, John | Australian Primary Mathematics Classroom, Fall 2001 | Go to article overview

Card Games


Gough, John, Australian Primary Mathematics Classroom


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A recent article in New Scientist by Bryant Furlow argues that children's intelligence is boosted by playing games. In this article, the third in a series, the mathematics behind common card games will be examined.

Happy Families

The traditional pack of cards for Happy Families is even fun to look at and read: Mr Bun the Baker, Mrs Bun the Baker's wife, and little Master (or Miss Bun), happy, smiling, white-coated chef-hatted, roly-poly bun-shaped bakers--and many others--a happy community of tradespeople.

Here are the basic rules of Happy Families. The aim is to be the player who succeeds in making the most complete sets of families.

Other games have a related format. For example, in Authors (see Gough, 2000), the sets of matching cards consist of an author, and three of his or her works--a general knowledge work-out. The Shakespeare set, for example, might consist of a card showing the Bard of Avon musing, quill poised, and three other cards, one for 'Hamlet', another for 'Macbeth' and a third for 'Midsummer Night's Dream'.

Clearly the Happy Families and Authors format is equivalent to the standard 52-card pack, with four suites ([heart], [club], [spade], [diamond]), and four of each type of card, for example, a 6 of Hearts ([heart]), a 6 of Diamonds ([diamond]), a 6 of Clubs ([club]), and a 6 of Spades ([spade]). This is not as appealing as pictures of book-writers and characters from books, and is not suitable for developing a lot of general knowledge or trivia, but is readily available and very adaptable for other uses.

Old Maid

The children's card game Old Maid (or Old Bachelor, in the gender-reversal version) has a format of matched pairs, such as two identical Cyclists, two identical Butchers, and so on, as well as one single card which has no matching pair, a grim (or cheerful) spinster. The aim is to collect as many matching pairs as possible, while not being the losing player who is left at the end with the unmatchable solitary old person. A French version, using an ordinary card pack, but with the Jacks of Hearts, Diamonds and Clubs removed, is called 'Le Vieux Garcon'--The Old Boy--the Jack of Spades. A German version uses a special pack of pairs of cards, with one singleton called 'Black Peter'--the name of the game--often showing a fierce black cat wearing boots and a hat (The Way to Play, p. 309).

The rules for playing Singleton (a non-ageist name for the otherwise traditional but not so politically-correct game, Old Maid) are similar to those for Happy Families.

A further modification occurs with the game Fish (or Go Fish). Using a Happy Families pack, or a standard pack of cards, the usual rules for Happy Families apply, with two exceptions.

* When dealing the cards at the start, an extra hand is dealt. For example, if 4 people are playing, the pack is shuffled, and dealt out as fairly as possible, as though there were 5 players. The extra hand becomes the 'pond' where players 'fish'.

* When a player asks for a particular card, and gets the answer 'No', that player is told to 'Fish'. This means the player picks up the top card of the extra hand (unless all the cards in the fish-pond have already been taken up in this way).

The rules of Fish may vary considerably. For example, rather than forming an extra hand, players start with a deal of, say, seven cards each, and all the remaining cards are placed face-down in the middle as the 'stock' or 'fish-pond'. Also, if a player asks, for example, 'Do you have a three?', if the player who is asked has any threes, these must all be handed over (Frey, 1970, p. 281).

Several important features arise with these familiar games. Notice the large amount of luck or chance in Singleton: luck in the original deal, and luck in choosing a card from the player on the left. This is not a game of skill, except the skill of keeping a straight face. …

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