April 17-21, 2001,
University of Fribourg (Switzerland)
Donkers, Jos Uiterwijk, Univ. Maastricht,
& Alex de Voogt, Univ. Leiden (Netherlands)
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.
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
Assande, Univ. d'Abidjan (Ivory Coast)
Jean Retschitzki, Univ. Fribourg (Switzerland)
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
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.
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.
Whitehill, Rochester, NY (USA)
and chinese checkers:
Origins and variations
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.
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.
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."
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.
T. de Souza, A.L. Petty, N. Passos, G. Escorel,
& V. Carracedo Univ. São Paulo (Brazil)
a study with brazilian children
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.
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.
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.
Beal, University of London (U.K.)
from your opponent - but
what if he knows less than you?
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
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.
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?
Kjer Michaelsen, Odense (Denmark)
and gaming pieces
in Denmark’s Iron Age
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
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.
Finkel, British Museum (U.K.)
Indian Board Game
Survey: The first results
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.
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.
Dossena, Cremona (Italy)
the forerunners of roulette
italian wheels of fortune (end of XVIII century) looking very similar
but offering different opportunities of bet.
opportunities of bet in Biribissi (XVIII-XX century).
compared using computing analysis
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).
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)
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) = .
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.
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.
G. Ch. van de Riet, Markelo (Netherlands)
boardgames by the number, part 2
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).
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?
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
Santi, La Tour de Peilz (Switzerland)
Swiss Museum of Games
between interactivity and science
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.
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.
role of such a museum is therefore ambivalent: to surprise visitors
of all ages, backgrounds and expectations and make no room for their
Fraenkel, Weizmann Institute (Israel)
cellular automata boardgames
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 in N(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.
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.
v. Hilgers, Humboldt-Universität (Germany)
interrupted - from historical
moments when mathematics comes into play
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.
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
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.
Ostergaard, & Anne Gaston, Naestved (Denmark)
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.
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.
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
Granados-Steiert, Bad Homburg (Germany)
tables in France, England
and the german-speaking countries
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.
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.
Haddad Zubel, Univ. Fribourg (Switzerland)
Or playing other's minds?
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.
to the high complexity of its model, formalised game theory portraying
a highly idealised mind computer has lost its impact in psychological
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.
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.
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.
Palermo Brenelli, UNICAMP (Brasil)
and game of rules
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.
our research with school children, we have used games such as:
in order to analyze the construction of logic and arithmetic notions;
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;
Game of Rings, which has emphasized multiplicative relations,
Close the Box, where we work on adding, operations.
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.
Balambal Ramaswamy, Channai (India)
boardgame of women in Tamilnadu
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.
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.
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.
Albertarelli, Milano (Italy)
rules: a "crazy hypothesis"
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.
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.
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".
Russian Chess Museum (Russia)
origin of chess
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:
In a racegame the game pieces have been named chariots or presented
The racegame of the chariots has been transformed in a war game of the
The wargame of battle chariots has been transformed in a war game of
the four main battle forces of the ancient Indian army.
This war game could be played by four or by two players. In the last
case the conception of check-mate has arised.
The dice has been thrown away. It could happen because Indian people
had been already acquainted with a wargame of the Greeks without dice
my paper I will present many direct and inderect proofs in favor of
Gobet, & Guillermo Campitelli
University of Nottingham (U.K.)
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.
Wendling, Univ. Neuchâtel (Switzerland)
of chess knowledge
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.
of board games: an easily
adaptable system to classify board games
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.
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.
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.
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.
Masukawa, Hyogo-ken (Japan)
of Go and Shogi
(japanese chess) in Edo-era
paper is about the spread of Go and Shogi (japanese chess) in Edo-era
(1603-1868) in Japan.
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.
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.
Schädler, Frankfurt am Main (Germany)
greek dogs in the East
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.
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
Vasantha, Sri Krishnadevaraya University (India)
invented by the Raja of Mysore
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.
Syed, Univ. München (Germany)
the indian origin of backgammon
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.
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.
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.
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.