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Evolution and Analysis of Strategies for Mancala Games
Damien Jordan and Colm O’Riordan
CIRG, Information Technology College of Engineering and Informatics
damojordan@gmail.com, colm.oriordan@nuigalway.ie
Abstract
Mancala games are are a range of strategy games.
This research attempts to better understand the variants
of the game by investigating heuristics to play the game
We then combine a number of heuristics together to
form a strategy. A genetic algorithm is used to evolve
the most successful strategy for this game.
1. Mancala Games
Mancala is a family of two-player board games that
are popular all over the world. There are over 300
documented variants of Mancala. The object of mancala
games is usually to capture more seeds than one’s
opponent.
The game begins with the players placing an equal
number of seeds, as per the variation in use, in each of
the bowls on the game board. A turn typically consists
of removing all seeds from a bowl, placing one seed in
each of the following bowls in sequence, and capturing
seeds based on the rules of the game. The exact rules
for capturing vary considerably among the variants.
For more than a century, board games and strategy
games have been the topic of many scientific studies by
psychologists and scientists. “Board games have long
fascinated as mirrors of intelligence, skill, cunning and
wisdom” [1]. Mancala games represent an interesting
topic of study given the wide range of rule variations
resulting in games of differing levels of difficulty
2. Hypothesis
Many interesting research questions exist in the
domain of mancala games. These include: are there
winning strategies? For which variants do these
strategies exist? Can these strategies be represented as
heuristics? Are heuristics developed for one game
transferrable to another? Which changes to the rules
change the difficulty?
In this paper we focus our studies on one variant of
the game, Bantumi. We hypothesise that a set of
heuristics can be developed and empirically tested to
measure their efficacy and secondly, that evolutionary
computation can be used to learn a robust strategy
3. Methodology
The methodology employed in this study includes:
design and development of a simulator, design and
development of heuristics, empirical testing of these
heuristics and the use of a genetic algorithm to evolve a
suitable strategy.
4. Current work/Results to date
A simulation for the mancala game Bantumi (and
variants) has been designed and implemented. Seven
5
heuristics have been designed (following analysis of the
literature and game play) and implemented for Bantumi.
These are:-
H1-Pick a bowl that allows the player to have another go
H2-Pick a bowl that allows the player to make a capture
H3-If the opponent has seeds in bowls that allow him another
go, disrupt it
H4-If the opponent can capture some of the player’s seeds on
the next go, move them
H5-Always pick the closest bowl to the score bowl
H6-Avoid picking a bowl that, after sowing, results in giving
the opponent another go
H7-Avoid picking a bowl that, after sowing, results in
allowing the opponent to capture some of the player’s seeds
All heuristics were tested against each other in a
round robin tournament. The results of these
experiments showed that H1 and H5 were the two
strongest heuristics of the group, while H3, H6 and H7
were the weakest. The results of this experiment are
shown below:
Win % after 100 games
100
80
60
40
20
0
H7
3 - F 3 - S 4 - F 4 - S 5 - F 5 - S 6 - F 6 - S
Rand
Digit = seeds/bowl, F = First move, S = Second
move
Combining heuristics H1, H2, H4 and H5 in a linear
order to form a new heuristic was shown to win an
average of 83% of games when played against all other
heuristics. A genetic algorithm was designed and
implemented in our simulator for Bantumi. After
numerous generations, and millions of games played, a
strategy has evolved when using 3 seeds per bowl that
wins an average of 96% of games when played against
all other heuristics.
5. References
[1] J. Retschitzki, A. J. de Voogt & F. Gobet, “Moves
in Mind: The Psychology of Board Games.” Psychology
Press Ltd, Hove UK, 2004.
H1
H2
H3
H4
H5
H6