Fanorona

Fanorona is a board game indigenous to Madagascar and derived from Alquerque.

Introduction

Fanorona is played on a board of 5 rows × 9 columns, with lines connecting the intersections. Black and white pieces, twenty-two each, are arranged on all points but the center. The objective of the game is to capture all the opponents pieces. The game is a draw if neither player succeeds in this. Capturing is done by either approaching or withdrawing from opponent's pieces. Fanorona is very popular in Madagascar. The legend of King Ralambo (1575-1610) states that the King wanted to give his lands to the first son who arrived at his castle. The oldest son was trying to win a "telo noho dimy" (3 against 5) situation and arrived too late to inherit his father's kingdom.

There also exist smaller variants of Fanorona. Fanoron-Telo is played on a 3 × 3 board and is comparable with tic-tac-toe. Fanoron-Dimyand is played on a 5 × 5 board. Fanoron-Tsivy, which is normally called Fanorona is played on the 5 × 9 board.

Board

The Fanorona board consists of lines andintersections, creating a grid with 5 rows and 9 columns. A line represents the path along which a stone canmove during the game. There are weak and strong intersections. At aweak intersection it is only possible to move a stone horizontallyand vertically, while on a strong intersection it is also possibleto move a stone diagonally. A stone can only move from oneintersection to an adjacent intersection.

Rules of Play

There exist variations of the rules; this is the main variant.

*Players alternate turns, starting with White.

*We distinguish two kinds of moves, non-capturing and capturing moves. A non-capturing move is called a "paika" move.

*A paika move consists of moving one stone along a line to an adjacent intersection.

*Capturing moves are obligatory and have to be played in preference to paika moves.

*Capturing implies removing one or more pieces of the opponent. It can be done in two different ways, either (1) by approach or (2) by withdrawal.
**An approach is the movement of the capturing stone to a point adjacent to an opponent stone provided that the stone is situated on the continuation of the capturing stone's movement line.
**A withdrawal works analogously to an approach but the difference is that the movement is away from the opponent stone.

*When an opponent stone is captured, all opponent pieces in line behind that stone (as long as there is no interruption by an empty point or an own stone) are captured as well.

*If a player can do an approach and a withdrawal at the same time, he has to choose which one he plays.

*As in checkers, the capturing piece is allowed to continue making successive captures, with the following restrictions:
**The piece is not allowed to arrive at the same position twice.
**It is not allowed to move a piece in the same direction as directly before in the capturing sequence. This can happen if an approach follows on a withdrawal.

*The game ends when one player succeeded in capturing all stones of the opponent. If neither player can achieve this, the game is a draw.

Analysis

Using 10.000 games with Alpha-beta pruning players the game-tree complexity and state-space complexity can be computed. It turns out that Fanorona has a game-tree complexity of 10⁴⁶ and a state-space complexity of 10²¹.

In 2007 the game of Fanorona and smaller variants has been solved weakly. It turns out that this game is a draw. Both the moves f2-e3A and d3-e3A lead to a draw.cite journal| author = M.P.D. Schadd, M.H.M. Winands, J.W.H.M. Uitweijk, H.J. van den Herik and M.H.J. Bergsma | year = 2008 | title = Best Play in Fanorona leads to Draw | journal = New Journal of New Mathematics and Natural Compuational | volume = 4 |issue = 3 | pages = 369–387| url = http://www.cs.unimaas.nl/maarten.schadd/Papers/2008FanoronaJNMNC.pdf | doi = 10.1142/S1793005708001124]

Notes and references

=See also= Fanorona can be played by email, using Richard Rognlie's Play-By-eMail Server.

External links

* [http://www.boardspace.net/ Play "Fanorona"] online at Boardspace.net, against human or robot opponents.
* [http://www.ics.uci.edu/~eppstein/180a/projects/fanorona/ Web applet and Java source]
*Visit [http://www.cs.unimaas.nl/maarten.schadd/Fanorona/ Maarten Schadd's Fanorona website] for a detailed analysis of the game and more information on how the game was solved.
*Fanorona can also be found on the website of the [http://www.icga.org/ ICGA] . (Click on game-specific info)
* [http://home.gna.org/fanorona/ A Python implementation of Fanorona 9 (Fanoron-tsivy)] .