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2014-05-26 · última modificação 2014-05-26 16:06

International Colloquium
April 17-21, 2001,
University of Fribourg (Switzerland)

Jeroen Donkers, Jos Uiterwijk, Univ. Maastricht, 
& Alex de Voogt, Univ. Leiden (Netherlands)

Mancala Games

The large group of Mancala games offer many possibilities for academic research. In the field of game history, Mancala games have been studied because of their enormous geographical spread and the large diversity in boards and game rules. The goal of our talk is to present some of the research in various other directions that has been done by us, but mainly by others. In the field of psychology, Mancala games play a special role among other board games. The effect of a single move can be so large that it becomes incalculable for humans, especially when multiple leaps of sowing are allowed. The way in which players cope with this has been studied in the game of Dakon. Mancala games are also of interest to mathematicians. Some Mancala games have special properties like the existence of infinite move sequences in Bao.

Mathematical research has also been performed on solitair Mancala games, leading into the series of Tchoukaillon positions. Finally, Mancala games have been studied early in the field of Artificial Intelligence as a model of human reasoning, but they are still subject of research in computer games. Kalah has recently been solved and Awari is bound to be solved very soon.

N'Guessan Assande, Univ. d'Abidjan (Ivory Coast)
& Jean Retschitzki, Univ. Fribourg (Switzerland)

Learning awale strategies

Awale is well known in many parts of Western Africa with almost the same set of rules. Most men and boys know the rules, as well as a significant number of adult women and girls. However the game is not played every day and it was even difficult to find a board for our research in the village of Kpouebo. In our study conducted in this village and in Abidjan, we found a great diversity in the mastery of strategies in ivorean boys and men.

In this paper we present our understanding of how players learn the strategies they use. The data on which we base these ideas were produced through reseach projects conducted in Ivory Coast with experienced players (boys and men) on the one hand, and in Switzerland with novice boys and chess players learning the game while playing against a computer program, on the other hand.

It is almost impossible to learn awele strategies through books and/or journals. The only available literature describes the basic rules and only a few elementary strategies. So we claim that practice and observation of other players are the only means by which players learn to become better players. We found no difference between the way novices in Switzerland began to learn the elementary tactics and those observed in young boys in Ivory Coast.

Bruce Whitehill, Rochester, NY (USA)

Halma and chinese checkers: 
Origins and variations

Halma, a game from the 19th century, is still played in countless countries.  Most written material on Halma suggests the game was developed in England, but Halma was invented by an American professor, George H. Monks. The game, inspired by the British game of Hoppity, was produced in the United States in 1885, following Monks’ trip to England.

Even in the U.S. there was controversy surrounding Halma, as both E.I. Horsman and Milton Bradley laid claim to the rights.  Bradley backed down, and marketed a modified version as Eckha.

Halma is considered the forerunner of Chinese Checkers.  Released in 1928 by J. Pressman & Company, Chinese Checkers did not receive a patent number until 1941.  Though the origin of Chinese Checkers–or the transition from Halma to Chinese Checkers–is still a mystery, one Pressman source calls its introduction to the US market somewhat "strange" and "a fluke."

This report deciphers the origins of Halma, and shows the links to it’s more modern successor, Chinese Checkers.  Interviews with the Monks family give some insight into the inventor. Rules of the game–including those rarely shown for three players–are explained in brief, and an examination is made of other games which can be considered variations of both Halma and Chinese Checkers.

M. T. de Souza, A.L. Petty, N. Passos, G. Escorel, 
& V. Carracedo Univ. São Paulo (Brazil)

Evaluating game activities: 
a study with brazilian children

Based on Piaget's theory, this study aimed to build up criteria to evaluate children in game activities. The contribution is to demonstrate the influence of the adopted procedures in school results. The research was held at the « Laboratory of Psychopedagogy » where we studied children between 7 and 12 years old with learning difficulties. We investigated the game "Four Colours" and two pedagogical evaluations, applied in two phases.

On phase I we defined three stages of development regarding rules, strategies and autonomy. On phase II we compared productions. In the game context, results show that: (a) there were more productions of stage three on phase II than on I; (b) the number of children that changed from an inferior to a superior level was bigger than the ones who remained at the same level or changed to an inferior level.

In the pedagogical evaluations: (a) the majority remained at the same level considering: personal and cultural references, interpreting and writing;  b) on logical thinking, most children changed to superior levels. The analysis of children’s performance in the game and the pedagogical evaluations showed that it was possible to confirm the initial hypothesis: the laboratory's proposals can influence school activities and vice-versa.

Don Beal, University of London (U.K.)

Learn from your opponent - but 
what if he knows less than you?

In recent years there has been growing interest in computer learning techniques for computer play of games. A fundamental technique, and one much studied, is that of computer learning of good weight sets for evaluation functions. Most of these algorithms are based on Temporal Differences (first described by Samuel for Checkers in 1948) and the more recent TD(l) algorithm published by Sutton in 1988, which spawned further research and some spectacular successes (e.g. Tesauro's World Championship class Backgammon program 1994).

Temporal Differences assume that evaluations early in the game should predict later evaluations. Weight adjustments are made if they don't. For both Samuel's and Sutton's mechanisms, this has the undesirable effect that learning from play against an inferior opponent will distort the evaluation, and degrade play.

This paper discusses how to avoid this problem, and looks at a new question - can learning be effective when witnessing only random play? Or is purposeful play a pre-requisite for learning to take place?

Karsten Kjer Michaelsen, Odense (Denmark)

Games and gaming pieces 
in Denmark’s Iron Age

Games played a major role in the Danish Iron Age and Viking society. The archaeological finds are many, and they have been made in graves, settlements and bogs. Among the most common artefacts are: gaming pieces made out of glass, bone, amber and rock, dice of Germanic and Roman types and wooden gaming boards.

Games seem to have been played by all classes of society ranging from the poorest children to the wealthiest chiefs. The Danes played local Germanic games as well as those imported from the Roman Empire, with glass gaming pieces and dice used with a dice cup. As a matter of fact, the gaming side of Danish Iron Age society is the best evidence we have of Roman impact, not only as far as the export of artefacts goes, but also – no doubt unintentionally – in difficult-to-document areas such as politics, religion and the rules of games.

Irving Finkel, British Museum (U.K.)

The Indian Board Game 
Survey: The first results

Some years ago a joint project was instituted between the Anthropological Survey of India in Calcutta and the British Museum in London, to investigate the traditional sedentary games still played in rural India. To this end the author produced a booklet summarising what is known of indian games, and including specimen questionaires for use in the field. Field researchers working for the Anthropological Survey have now submitted some thirty reports, which are being edited by the author for publication.

This lecture will cover the work of the investigation, giving some idea of the results so far, and describing certain new and most unexpected discoveries that have recently been made.

Giampaolo Dossena, Cremona (Italy)

Among the forerunners of roulette

Two italian wheels of fortune (end of XVIII century) looking very similar but offering different opportunities of bet.

Increasing opportunities of bet in Biribissi (XVIII-XX century).

Two-person Chaturanga and 
four-handed Chaturanga 
compared using computing analysis

Four-handed Chaturanga is an Indian game once thought to be the precursor of chess game, which was invented at the latest in the 7th century. The name (Chaturanga) refers to the four arms of the Indian army: the infantry, elephants, cavalry, and chariots. The game was played on an 8x8 square board. Each side had a Rajah (King), a Hasty (Elephant), an Ashwa (Horse), a Roca (Boat), and four Padatis (Foot soldiers).

In the previous study, for a two-person game G which has the average possible moves B and average game length D, we proposed an estimate of game strategic complexity E(G) as E(G) .

We hereby propose a measure of n-person game's strategic complexity. This is based on the fact that a player can give his direct effect to the outcome of the game only at his own turn. Given an n-person game G which has the average possible moves B and average game length D, an estimate of game strategic complexity E(G) is given by E(G) .

We can obtain such average values derived from the statistics of many grandmaster games in some domains such as chess. However, such statistics are only available for a few games. For games where no grandmaster games are available (e.g., Chaturanga), the statistics of specific features, such as the average number of possible moves and the average game length, are obtained by the method of semi-random self-play we proposed.

This paper proposes a game strategic complexity measure for n-person games, by which we hope to obtain more insight into the evolutionary history of chess-like games. Four-handed Chaturanga (which used a dice) is compared with two-person Chaturanga.

J. G. Ch. van de Riet, Markelo (Netherlands)

Ancient boardgames by the number, part 2

I will present a sequel to the idea expressed earlier (Proceedings BG in A III, Florence 1999), after which the game of mancala 2 x 6 [x 6] as played by Near Eastern rules complies with the 360 degrees "calendar" of the region; therefore the game seems an educational appliance of same (for initiates) before it turned divinatory (for initiates and commoners) and simply a game at last (for commoners).

The detailed reconstruction of the "calendar" on several levels, through its congruency with mancala, facilitated a similar insight into games like "mehen", "mahasna", "akhor", "senet", "tab", "dara", and others. So, naturally, I could not help but cast the net wider: if an entire cluster of games can be shown to match a single "sacred" pattern, then perhaps a few more games may have originated as vessels of "wisdom" of the ancient type?

That made for two more years of exciting research, with results I am almost as inordinately proud of as of my son Numa, who, upon his arrival late last year, reminded me of the basic rules of educational play: 1. one-to-one eye contact; 2. symmetry of action; 3. exchange. The ancients apparently knew what they were doing when they introduced (board) games as an educational appliance.

Flavio Santi, La Tour de Peilz (Switzerland)

The Swiss Museum of Games 
between interactivity and science

There are no toys in the Swiss Museum of Games. Restricting the collection to games creates a dilemma. In the visitor's mind, the words "game" and "museum" seem diametrically opposed to each other, the one implying interaction and pleasure, the other science and study.

For the last two years, the Swiss Museum of Games has been seeking to resolve the ambiguity inherent in the visitor's expectations. To play or to learn, that is the question. The desire to make the museum available to everyone in the region as well as the more ambitious aim of making the museum known in Switzerland, if not worldwide, is also a challenge the Museum has taken to heart.

The role of such a museum is therefore ambivalent: to surprise visitors of all ages, backgrounds and expectations and make no room for their disappointment.

Aviezri Fraenkel, Weizmann Institute (Israel)

Two-player cellular automata boardgames

We define a two-player virus game played on a finite cyclic directed graph G=(V,E). Each vertex is either occupied by a single virus, or is unoccupied. A move consists of transplanting a virus from some vertex u into a selected neighborhood N(u) of u, while devouring every virus inN(u), and replicating in N(u), i.e., placing a virus on all vertices of N(u) where there wasn't any virus. The player first killing all the virus wins, and the opponent loses. If there is no last move, the outcome is a draw.

Giving a minimum of the underlying theory, we exhibit the nature of the games on hand of examples. The 3-fold motivation for exploring these games stems from complexity considerations in combinatorial game theory, extending the hitherto 0-player and solitaire cellular automata games to two-player games, and the theory of linear error correcting codes.

Philipp v. Hilgers, Humboldt-Universität (Germany)

Games interrupted - from historical 
moments when mathematics comes into play

In Science, where the historical, cultural or epistemological sides of human beings and their social structures are studied, games tourned out to be a revealing subject. But the organisation of gaming rules is seldom taken immediately as a theoretical exploration of systems. Taking this step means, firstly to examine the knowledge of paradigmatic games; and secondly, to catch their relations to the founding of theories in general and in a decided historical moment.

Here, these relations will be described concretely by comparing the knowledge of games and two branches of mathematics, which belongs to her most recently offsprings: topology and probability theory. It will be focused, how turning points of the discourse and the point of view concerning games changed, to make the transfer of knowledge possible, while the games stimulating mathematical questions and problems were not at all new.

Although such prominent mathematician as Fermat, Pascal and Euler stand for the develpoment of probability theory and topology, the subject is not only examined in terms of a history of ideas. Rather stressing a method focusing on cultural practices and techniques than the role of an individual should make evident how posing of questions in field of mathematics can be are triggered by games. By that, games and their rules and mathematical theories can be discussed in a broder scope, exploring how they interfere, produce short circuits and how their differences become irreversible.

Erik Ostergaard, & Anne Gaston, Naestved (Denmark)


The age and origin of the war and race game Daldøs is unknown. The name appears in several distant coastal regions in Denmark e.g. Thy, Fanø and Bornholm which indicates that the game has been widely known. War and race games are most likely further developments of the ancient Egyptian game of Sen't. This type of game has been known from India (Tablan) to Senegal (Siga) and Benin to Samic areas of Scandinavia (Sakku). However we have no knowledge of any finds of the game in the area between North Africa and Northern Europe.

The origin of the name of the game is not fully established. The name may be French and has possibly been brought to Denmark by the Vikings who raided Normandy. The first part of the word 'dal' could originate from the french word 'dalle' meaning a flat stone or marble used for paving. In Arabic the word 'Tab' means a small ceramic tile, and all Arabic versions of the game starts with this word. The second part 'døs' almost certainly reflects the old French "doues" = two. If this is so the name describes that two dice is thrown. To reach France the game could have travelled two ways, either with the Romans or with the Moors.

The only example of the game known to us has been found in Northern Jutland and can be seen at the local museum in Thisted. It consists of a flat board with two outher rows of 16 holes and a middle row of 17 holes. There are 32 pegs cut into two different shapes making two sets of sixteen. When the game starts, the two sets are placed in the two outside rows. There are also two specially cut dice – longish with the ends shaped as pyramids so that they can only rest on four sides – which are marked A, II, III, IIII. The A has the value 1 and is called 'Dallen' (The Dal).

Mayari Granados-Steiert, Bad Homburg (Germany)

Games tables in France, England 
and the german-speaking countries

Games tables are a  type of furniture which became popular in Europe in the 15th century . The highest popularity they reached was in the 18th century. Game tables could be plain, like simple card tables, or very luxurious with many possibilities for transformation, to be used for several games, like chess, backgammon, cards and various games of chance.

Our project shall contain a survey of game tables as a type of furniture for the three chosen areas, England and France being the two most important influences regarding game tables for Germany. The first results will help to decide whether to choose a certain area, or maybe a certain court or reigning family. Questions to be discussed in that part are, which kinds of game tables were most popular; and where? Research so far has shown that simple game tables were not only used by the bourgeoisie or the lower gentry, but also at court, where they existed next to more representative, precious game tables. This thesis seems to be worth further research and might become one of the main thesis of the work.

Rosita Haddad Zubel, Univ. Fribourg (Switzerland)

Playing the board? 
Or playing other's minds?

Game theory holds that other peoples' minds are of no importance in strategic games. In fact game theory maintains that in interactive occasions such as a game of chess, people exclusively play the board. This is to say that players evaluate mathematically - at all moments - all possible outcomes following a move.

Due to the high complexity of its model, formalised game theory portraying a highly idealised mind computer has lost its impact in psychological research.

The present paper explores new avenues of modelling real player's games, leading to the understanding that whilst we play a board game, we not only play the board but a game on our partner's minds.

In order to show how we progressively combine both strategic and psychological procedures, we adopt developmental stance and talk about two experiments run with children from age 5 to 13. The first is a simplified version of a chess game. The second a marble game.

We shall present data of age characteristic types of games and show how a pluri-methodological approach can guide us both in the analysis of a board game and the games we play on other peoples' minds.

Rosely Palermo Brenelli, UNICAMP (Brasil)

Psycho-pedagogy and game of rules

The purpose of this work is to present some results that our research group has been developing with games of rules as a means of psycho-pedagogic and pedagogic interventions. The theoretical background is based on Piaget’s genetic psychology.

In our research with school children, we have used games such as:

  • "Cilada", in order to analyze the construction of logic and arithmetic notions;
  • the Mastermind, in order to both investigate the different forms of reasoning that children of different ages present when playing and the (possible and necessary) construction of logic creativity;
  • the Game of Rings, which has emphasized multiplicative relations,
  • and Close the Box, where we work on adding, operations.

We will present the different modalities of intervention with the games applied during our research as well as the results found, indicating the expressive contribution that games of rules have as a means of intervention towards favoring learning of children at school.

V. Balambal Ramaswamy, Channai (India)

Pallankuzhi, a traditional 
boardgame of women in Tamilnadu

There are many board games played in India especially in Tamilnadu. Most of these games are played as pastimes. Women who are busy with the household work in tradition oriented families do not go out and play. But from very early times, women of Tamilnadu are in the habit of playing Pallankuzhi, a traditional boardgame, at home during their leisure time.

The material required for this game is board in different shapes specially made of wood with 7 divisions on each of its 2 sides. The game pieces vary from seeds of tamarind to precious stones according to the economic status of the players. Different types of games are played with this board and game pieces. Though mainly played by two players, the rules allow 4 players or partnership too. Presence of mind, calculation and good memory are needed to win the game.

This game is played mainly for enjoyment but it contributes to the alertness and of better memory of the players. Even today, this game is being played both in urban and rural areas. This is one of the very traditional board games in Tamilnadu, mainly played by womenfolk.

Spartaco Albertarelli, Milano (Italy)

Senet rules: a "crazy hypothesis"

I have always been fascinated by the reconstruction of ancient games rules, by the patient work  needed to put together all the small clues discovered by the archaeologists.

I have read many books describing these games, and the way the archaeological finds have been interpreted, but I've always been uncertain about the reconstruction of the Senet rules. I've always found something "out of tune"; between the rules and the picture of the game that the ancient Egyptians leaved to us.

So I thought about a different "game concept" and, even if my reconstruction is not based on any new discovery, but simply on a different analysis of the documents we already know, I decided that this international colloquium is the best place to explain my "crazy hypothesis".

Yuri L. Averbakh, 
Russian Chess Museum (Russia)

About origin of chess

The main point of my research is that the game of chess has been evolutionary developed from an ancient Indian racegame with dice on the ashtapada (8x8) board. The approximate stages of this evolution are:

1. In a racegame the game pieces have been named chariots or presented chariots.

2. The racegame of the chariots has been transformed in a war game of the battle chariots.

3. The wargame of battle chariots has been transformed in a war game of the four main battle forces of the ancient Indian army.

4. This war game could be played by four or by two players. In the last case the conception of check-mate has arised.

5. The dice has been thrown away. It could happen because Indian people had been already acquainted with a wargame of the Greeks without dice petteia.

In my paper I will present many direct and inderect proofs in favor of this theory.

Fernand Gobet, & Guillermo Campitelli
University of Nottingham (U.K.)

Intelligence and chess

While chess is often seen as a domain requiring a high level of intelligence, the available empirical evidence is far from being clear cut. The results can be summarised as: (a) chessplayers have a higher general intelligence than the general population; (b) within the chess population, there is no correlation between general intelligence and skill level; and (c) surprisingly, there is little evidence that chessplayers have better visuo-spatial abilities than the general population. We present additional evidence from our laboratory: about laterality (chessplayers are more often left-handed than could be expected by chance), seasonal effect (chessplayers with an international rating were born more often in the first half of the year than expected by chance), and visual memory (chessplayers do not perform better than non-players). These results are discussed in the light of research into expert behaviour, which emphasises acquired knowledge, and of research into talent, which emphasises innate abilities. In the conclusion, we consider the difficulties of drawing causal links from these results.

Thierry Wendling, Univ. Neuchâtel (Switzerland)

Invention and transmission 
of chess knowledge

Although chess is known for its numerous technical books, it is not simply acquired through reading. Several factors are actually at stake in the player's acquisition of chess knowledge, such as socializing with other players, reinventing on the board of tactics and strokes already tested by others, playing against computers, etc. From an anthropological perspective, this paper examines the different ways of acquiring and transmitting chess knowledge. It is concerned by two issues. First, chess furnishes a case study for analyzing how, in contemporary society, knowledge is produced through reading specialized literature, relationship with peers, imitation of an elite (grand masters), consultation of web sites, etc. Second, chess expresses a particular concern given by the players to knowledge as a key to victory. That very fact raises the problem of the concrete relationships between knowledge and practice.

Piet Notebaert, KHBO-Spellenarchief, 
Brugge (Belgium)

Classification of board games: an easily 
adaptable system to classify board games

The department of Teachers Education of the Catholic College Brugge – Oostende (KHBO) in Belgium uses board games in their Teachers Education. The College works in association with the non-profit organisation ‘Flemish Games Archives’, well known within the gaming community. It has at its disposal the largest collection of board games, books and magazines in the Benelux.

One of the objectives of the Archive is to find a system to easily classify the thousands of different board games, so that students, teachers and researchers can use those games that have one or several similarities.

After researching in several Archives, studying of many books and drawing a comparison between many websites, the “KHBO  Games Archive” came up with a system that offers them an easy access to equivalent board games.

The question many researches ask is very simple: “I know that particular game and would like to know what other games are similar. Can you give me a list of equivalent games?” I will demonstrate the way games are classified in their database. This system proved to be very successful and is set up to be easily adapted to new game systems.

Koichi Masukawa, Hyogo-ken (Japan)

Spread of Go and Shogi 
(japanese chess) in Edo-era

My paper is about the spread of Go and Shogi (japanese chess) in Edo-era (1603-1868) in Japan.

One of the most important factors that played a role in this expansion was that professional Go-Shogi Families were allowed to be supported financially for generations and received the salaries from Tokugawa-government. These families litterally spread out Go and Shogi.

There was a rare system of Go-Shogi players in the world and it laid the foundation of present professional players. I will show true facts about Go-Shogi families based on recently discovered documents from the Edo-era.

Ulrich Schädler, Frankfurt am Main (Germany)

Little greek dogs in the East

In the discussion about the history of chess the question of the identity of two games mentioned in the Babylonian Talmud has been discussed. In Kethuboth V, 5 (fol. 61b) a board game played with little dogs – a fairly common designation of gaming counters in Egyptian, Babylonian and Greek sources – is mentioned together with “nardshir“. In Shebuoth 29a, Nedarim 25a and Kiddushin 21b a board game called “iskundrée“ is mentioned, the name of which is normally held to derive from Alexander the Great's name and which medieval commentators have identified with the game of little dogs. This points to a Greek origin of the game(s) mentioned in the Talmud.

A greek board game known from ancient sources was in fact played with "dogs": póleiz or póliz, the game of the "city". This game seems to have been the Greek version of the Roman, "ludus latrunculorum". In the near east, an area linked to the Greek world by reciprocal contacts centuries before Alexander's times, where Greek was the "international" language, the Greek game seems to have been very well known even at a later time when Firdowsi wrote his "Shaname".

R. Vasantha, Sri Krishnadevaraya University (India)

Deciphering the boardgames 
invented by the Raja of Mysore

India’s role in the history of the world’s board games can only be described as being of primary importance. Boards, dice and pieces are known from archaeological sites of the third millennium BC, and there is evidence of many kinds to show that games of chance and skill have persistently held an important place in Indian cultures over the intervening millennia. For anyone interested in the boardgames of India, the name of the Maharaja Krishnaraja Wodeyar III of Mysore (1794-1868) will always be held in high respect and admiration. He was not only a skillful player, but also responsible for the development of new games and in some cases, for enterprising new developments of old games. These new games are depicted as murals on the walls of the Mysore Palace and are in the form of "bandhas" (puzzles). These puzzles involve the knowledge of geometry, topology, logic, language, philosophy and military strategy. To understand these games is an intellectual challenge and my paper tries to unfurl the puzzles in the board games.

Renate Syed, Univ. München (Germany)

On the indian origin of backgammon

Old Indic texts mention a board game for two players that is played with thirty conical stones, fifteen white and fifteen black, and two dice. The stones are called shaara or shaarii; the board, with two rows of twelve squares each, is termed phalaka, and the dice are named golaka, paashaka or aksha.

The earliest accounts of the shaara game, from texts dating between the second century B.C. and the 6th century A.D., are fragmentary, but they do at least contain the information that shaara is a game of movement, in which the stones, only being allowed to move forward, first traverse the opponent’s half of the board and then one’s own half. It is a fight game, the aim being to "pursue" the adversary figures and to "kill" them, to play them off the board. It is significant that even in the earliest texts the figures of one colour may only move clockwise, the other colour only anti-clockwise.

A text entitled Maanasollaasa, written in the first half of the 12th century, describes the shaara game in detail (in 78 and a half verses) and leaves no doubt that this was the game that earlier provided the basis for the persian nard-game and western backgammon: Among the numerous ways of arranging the stones at the beginning of the game there is also that which still applies for backgammon; in Sanskrit it is called golakriidana. Visual representations from India depict the shaara game; an important relief from the year 530 A.D. shows the god Shiva and his wife playing shaara, but the game is also illustrated in the paintings in Ajanta, dating from the last quarter of the fifth century.

In the face of this evidence, we may doubt the persian sources stating that backgammon (called nard by the Persians) was a persian invention and came to India from Persia. This is backed by the fact that arabic sources, among them al-Yaquubi (ninth century), talk about an indian sage having invented nard.