The Motivation

Why implement a computerized opponent for a Mancala variant?

Games within the Mancala family are played all over the world. However, as of now, KDE doesn’t offer any Mancala games to people looking for a challenging opponent.

Considerations

There are two core aspects to have in mind.

Firstly, the implementation must be designed in a way that suits the needs of KDE frontend developers. This ensures that programming a GUI for a Mancala game that utilizes this opponent is straightforward.

Secondly, this opponent must be easily extensible. The Mancala family of games comprises numerous variants, so designing this opponent with that in mind is of great value. By providing an engine that’s easy to understand and extend, we encourage developers to use it in future implementations of Mancala variants. This accelerates the process of implementing a new Mancala variant and it’s opponent, as all the core algorithms are readily available for their use.

The Game

Bohnenspiel is played on a board with 2 rows, each with 6 holes, and 2 end-holes, called stores. Each player owns the store to their right hand and controls the holes on their side of the board.

At the beginning, all holes are filled with 6 counters. The starting player chooses one of the holes under their control and removes all counters in it. The player goes through the holes next to the chosen one anticlockwise, placing one counter in each one until they have no more counters in their hand. Both stores are skipped. This is called sowing.

If the last counter falls into a hole, bringing the total number of counters in the hole to 2, 4, or 6, these counters are captured and put in the player’s store. When a capture is made, the preceding hole is checked and captured according to the same rule. The captures are repeated until the previous hole has some number of counters other than 2, 4, or 6.

The game ends when a player cannot move anymore; the remaining seeds on the board are given to the opposing player, and the winner is the one with more seeds [1].

The Algorithm

The final engine will use the MTD(f) Minimax Search algorithm with iterative-deepening. Optimizations like move ordering may be implemented, depending on the performance of the base algorithm.

MTD(f) was previously used to solve Kalah [2], another Mancala game, and consistently outperformed other algorithms in a variety of board games [3].

Closing Remarks

This project not only aims to introduce a new game into KDE’s repertoire, but also to lay the groundwork for future additions to the Mancala family within the community.

The development of this opponent will be done in the open, documented through blog posts and status reports, ensuring transparency and fostering community feedback. I invite the KDE community and all interested developers to engage with this project, suggest improvements, and contribute to the development of an opponent for one of the most popular and oldest board games in the world.

Development will take place in KDE Invent.

References

1. “Bohnenspiel : igGameCenter.” https://www.iggamecenter.com/en/rules/bohnenspiel.

2. G. Irving, J. Donkers, and J. Uiterwijk, “Solving Kalah”, Icga journal, vol. 23, no. 3, pp. 139--147.

3. A. Plaat, J. Schaeffer, W. Pijls, and A. de Bruin, “A New Paradigm for Minimax Search”.