Games || Universal Games

Universal GamesAuthor(s): Helen MorrisSource: Mathematics in School, Vol. 26, No. 4, Games (Sep., 1997), pp. 35-40Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30215304 .

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Universal

Games

by Helen Morris

Alquerque (Africa) A game that has been played for centuries in North Africa and the Middle East. On the West Bank of the River Nile in Egypt there is a temple at Al-Qurna, where an engraving of an Alquerque board has been found, dating back to 1400 BC. The game then spread, by the Moors of Africa, to Spain.

Games have been played for thousands of years, for power, for money, for amusement, all over the world. They began very simply, using the resources available at the time - sand, pebbles, coloured sticks, shells. Most of the games that we play today have descended from these simple ancient pas- times, although we now have access to superior resources, including computers programmed to beat us, and commer- cially manufactured packages. We cannot always afford to purchase the more sophisticated offerings, but we can always find items around that will still be able to provide children with the experiences and excitement enjoyed around the world for the past 3000 years.

Fig. 1

Two players each have 12 pieces, starting in the positions shown. Pieces can move along a line to an empty point. Pieces can be captured by being jumped over onto an empty point. More than one capture can be made in one move, and the direction of movement can also be changed. If a player misses a chance to capture an opponent's piece, then the offending piece can be removed from the board. The winner is the first person to capture all of the opponent's pieces.

FROM A TO Z Mathematics in School, September 1997

Ba-awa (Africa) A Mancala game, played to the same rules as Wari, with one exception. Two players have 6 cups containing 4 seeds in each. The first player lifts the seeds from one of their cups and sowing one into each cup in an anti-clockwise direction. Where the last seed falls, the same player lifts and sows those seeds. This continues until the last seed falls into an empty cup. The second player now starts from any of their own cups. From now on, if any seed makes a cup up to 4 seeds, the owner of the cup immediately transfers them to their store. If the last bean makes up a 4 the turn ends. The player with the most seeds wins.

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Chatatha (Native America) Originally played by Native Americans using sea shells and a shallow basket. The players toss six shells in the basket, and win sticks according to their score. Three shells facing up and three down score 1 stick, six shells up or six down score 2 sticks. The winner is the first person to score 8 sticks.

Dara (Nigeria)

Played by the Dakarkari people in Nigeria using stones, pieces of pottery or shaped sticks. The board consists of 5 rows of 6 holes. Each player has 12 pieces, which are placed, in turn, into the holes. Once all of the pieces have been placed moves are made. A piece can be moved into an adjacent empty hole (not diagonally). The aim is to make a row of three pieces, not diagonally. When a line of 3 is formed the player removes one of the opponent's pieces from the board. The game ends when a player is unable to make a line of 3 pieces.

Exchange Kono (Korea)

Fig. 2

Each player has 8 pieces, with the starting position as shown. The players take turns to move a counter one space diagonally onto a black spot. The aim is to be the first to occupy the opponent's starting positions. There are no jumps or captures.

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Fox and Geese (Iceland)

Fig. 3

This game was played by the Vikings in Iceland. There are 13 geese and 1 fox. The geese start in the positions shown; the fox starts on any empty spot. Geese move first, along a line. The fox kills a goose by jumping over it to a vacant point. The geese win if they surround the fox. The fox wins if there are so many geese killed that it cannot be surrounded.

Go Bang (Japan)

In Japan the most popular game is Go, with professional players earning a lot of money from the game. Go Bang is a simpler version of Go, arriving in England in 1885. Counters are placed alternately on the intersections of a 10 x 10 square board. The aim is to form 5 counters in a row in any direction.

Mathematics in School, September 1997



Hyena Game (Sudan) Kungser (Tibet)

A game that has been played for centuries by the Baggara tribe in North Africa. The Baggara tribe were nomadic and the game portrays the perils of nomadic life.

The game can be played with 2 to 6 players. Each player has a counter which represents their mother. There is also a bowl with 50 counters (Taba beans). Scoring is made with 3 coins. One head - take 1 Taba from the bowl. Two heads - move 2 places and the go ends. Three heads - move 3 places. No heads - move 6 places. A go only ends when two heads have been thrown.

You start with one Taba. A mother must reach the well with an exact throw, or make up the difference with Taba's. She then pays 4 Taba's to wash her clothes and starts back again. If she is short of Taba's she must throw them, but she can count up her scores while she is waiting and use them all at once when she starts back. The first mother back (does not have to be an exact throw) pays 2 Taba's and releases the Hyena, which doubles its coin scores. At the well it needs 10 Taba's for a drink and then it races back, eating any mothers it overtakes. So a mother can win, lose or be eaten.

A battle game between 2 Princes and 24 Lamas (the priests, not the animals!). The Princes and 8 Lamas are placed as shown. The first player (the Prince) can move a Prince one space or capture a Lama by jumping over it to an empty space beyond. The second player (the Lama) plays by placing a Lama on the board until all 24 have been used. Then the second player continues play by moving Lamas on the board. The Prince wins if only 8 Lamas remain. The Lama wins if the Princes are trapped. Lamas can force a capture in order to help trap a Prince. Multiple captures are allowed.

Ludus Latrunculorum (Italy) Popular with Roman soldiers, this game was used when they were resting.

An 8 x 8 chessboard is used. Each player needs 16 men, plus a Dux or King (special counter). The players take it in turns to place their men, two at a time, on the squares of the board. The Dux is placed last. After all pieces have been placed, the second player goes first, moving any piece one square (not diagonally). If an enemy piece is sandwiched between two opposing pieces, it is captured and removed from the board. The moving piece can continue with another move, after a capture. Comer pieces can be captured by being surrounded on either side. A piece can be moved in between two enemy pieces in safety. If an opponent cannot move then a player must move again. The Dux can also jump over any single piece. If this ends up in a sandwich the sandwiched man is captured. The Dux can be captured. The player with the most men left at the end is the winner.

Ise-Ozin-Egbe (Nigeria)

Fig. 4

The player starts by lifting the 10 beans in the bottom row and sowing one at a time. The next moves start from the hole where the last sowing finished. The aim is to arrive back to the original position.


Mu Torere (New Zealand) A blockade board game played in New Zealand by the Ngati Porou people. It is the only native Maori board game known. The board would have been marked on the ground with twigs or stones used as counters.

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Putah

Fig. 5

Two players have 4 pieces (known as perepere) each placed on adjacent points of the star (called the kewai). The aim is to block the opponent from moving. The centre space is called the putahi. Moves can be made (a) from one kewai to an adjacent empty kewai, (b) from the putahi to a kewai, (c) from a kewai to the putahi as long as either one or both of the adjacent points is occupied by an enemy piece. Only one piece can occupy the same place at the same time. Jumping is not allowed.

Nyout (Korea)

A racing game from Korea, for 2 to 4 players, from probably before 1100 BC. It is still a very popular gambling game. These games made their way to America by 800 AD.

The board consists of points made into a cross and a circle. Each player can use four counters (Mal) which stand for horses. The players take turns to toss a dice (called Pam-Ny- out) and move their horses anti-clockwise around the board, starting at N, aiming to finish at N. If a player's horse lands on E, S or W, they may take a short cut through the middle of the board to the exit or Ch'ut (N). If a horse lands on the same square as another of it's own horses they can join

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together and move as one horse. Three or four horses can join together. If a player's horse lands on a square occupied by an opponent, then the opponent is sent back to the start, but not if the opponent has a joined horse there greater than the landing horse. If a score of 4 or 5 are thrown, the player has another throw; the scores are added together and can be used for one horse or split between two or more horses. The winner is the first player to land on the Ch'ut.

Ou-moul-ko-no (Korea) The Korean name for Pong Hau K'i.

Pong Hau K'i (China)

Fig. 6

Traditionally played by children in Canton, usually with scraps of paper.

A game for two players, one with two white counters, the

other with two black counters. Players take it in turns to move one counter along a line to an empty space. The aim is to block the opponent from being able to move.

Quirkat (Arabia) The original Arabian name given to Alquerque.

Rithmomachia

Rithmomachia

Fig. 7

Popular game played by intellectuals in the Middle Ages. It is played on a board of 8 x 16 squares. Each player has 'round', 'triangle', 'square' pieces in their colour, and one 'pyramid' piece. Players take turns and move one piece at a time. A 'round' can move to any adjacent, empty space. A 'triangle' can move 3 empty spaces in any direction. A 'square' can move 4 empty spaces in any direction. A 'pyramid' can move in any of the previous 3 ways.

The aim is to capture the opponent's pieces, which can be done in 4 different ways.




(1) By landing on an occupied square. (2) By surrounding a piece on 4 sides. (3) By moving to a position so that the number on the piece multiplied by the number of vacant squares between this piece and an opponent's piece is equal to the number on the opponent's piece. (4) By moving pieces to either side of an opponent's piece so that the sum of the pieces is equal to the opponent's number.

There are several ways of winning and players need to agree in advance the Victory method that they are playing to. Some common Victory rules follow.

(1) Capturing a certain number of pieces. (2) Capturing pieces to a total value of, say, 160. (3) Capturing pieces to a total value but with a specified number of pieces.

For the more advanced player, Victory can be gained on achieving any of the following outcomes (made up of own and at least one captured piece).

(1) Having 3 pieces which form an arithmetic progression (eg 3,6,9) or a geometric progression (eg 2,4,8) or a harmonic progression (eg 2,3,6 as the reciprocals form an arithmetic progression). (2) Having 4 pieces which form two different progressions (eg 2,3,4,6 gives an A.P. with 2,3,4 and an H.P. with 2,3,6). (3) Having 4 pieces which form 3 different progressions (eg 4,6,9,12 gives 6,9,12 as an A.P., 4,6,9 as a G.P., and 4,6,12 as an H.P.)

Shap Luk Kon Tseung Kwan (China)

Fig. 8


The name means 'sixteen pursue the general'. It is played on an Alquerque board with a triangular extension at the top. One player is the general and the other controls the 16 soldiers. They can all move one step along any line in any direction. The general can enter the triangle but the soldiers cannot. The general and the soldiers can capture. The general can capture two soldiers by moving to an empty point between them. Both soldiers are then captured and removed from the board. If the soldiers can position themselves so that they are directly beside the general on the same line the general is captured and loses. If the general is trapped inside the triangle he is captured and loses.

Tabula (Italy) Tabula

Fig. 9

Played by the Emperor Claudius (50 AD) and Zeno (450 AD). Each player has 15 counters of their colour. All pieces go onto the board at 1 and leave at 24, moving anti-clockwise. Three dice are thrown, the total of which can be used to move one piece, or used separately to move 3 pieces, or two of the dice can be combined to move two pieces. If a player has two or more pieces on a square the opponent cannot land on that square. If a player lands on a square occupied by only one opponent's piece, that piece is sent back to the beginning. The winner is the first person to get all 15 counters safely round and off the board, with an exact throw needed to leave the board.

Ur (Iraq)

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Fig. 10

The Royal Game of Ur is sometimes called the Sumerian Game, and dates from 3000 BC. A board and pieces were found in the Royal Cemetery at Ur.

Each player has 7 counters. 3 coins are used. No heads scores 0. One head scores 1. Two heads scores 4. Three heads scores 5. When 3 heads are thrown, have another go. Throw 1 to enter the board. One player follows route A, the other route B. Two or more men on a square are safe, but single men can be hit and sent back to the start. Rosettes can be shared by opposing players, and are safe. The exact score must be thrown to leave the board.

Vultures and Crows (India)

Also called Kaooa, it uses a Pentalpha board, and involves one vulture and seven crows. A crow is placed, then the vulture, then another crow, then the vulture can move one space, until all crows have been placed on the board. The vulture captures the crows by jumping over them to a vacant spot. The crows can pen in the vulture to stop it from moving.

Wari (Arabia)

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Also known as Mancala, and has become the general name for all 'transferring' games where counters (or seeds) are moved from one cup to another. Two players have 6 cups containing 4 seeds in each. Players take turns, lifting the seeds from one of their cups and sowing one into each hole in an anti-clockwise direction. If the last seed drops into an enemy cup to make a final total of 2 or 3, the seeds are captured, along with the seeds of any unbroken sequence of 2's or 3's on the opponents side adjacent to and behind the plundered hole. The player with the most seeds at the end is the winner.

Yote (West Africa) Players take turns to place twelve counters of their own colour. Once all of their counters are placed the pieces can be moved one space up or down. A capture is made by jumping over an enemy piece to a space directly beyond. Any player who makes a capture can also remove another counter belonging to the opponent. Multiple jumping is not allowed.

Zamma (Sahara)

This game is sometimes called 'quadruple Alquerque', with similar rules. Each player has 40 pieces - moves can be made directly or diagonally forward. When a piece reaches the opposite side of the board it becomes a mullah, and can be 'crowned' with another piece. A mullah can move any amount of spaces in any direction, and can jump across empty spaces between itself and an opponent's piece to an empty space immediately on the other side. F*

References Bell, R. and Cornelius, M. (1988) Board Games Round the World, Cambridge

University Press, Cambridge. Cornelius, C. and Parr, A. (1991) What's Your Game?, Cambridge Univer-

sity Press, Cambridge. Irons, C. and Burnett, J. (1995) Mathematics from Many Cultures, Kingscourt

Publishing, London. Krause, M. C. (1983) Multicultural Mathematics Materials, The National

Council of Teachers of Mathematics, Virginia, USA. Sheppard, R. and Wilkinson, J. (1989) The Strategy Games File, Tarquin

Publications, Diss.

Author Helen Morris, Balshaw's High School, Church Road, Leyland, PR5 2AH




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