Fanorona

Fanorona is a board game indigenous to Madagascar.

Introduction
Fanorona has three standard versions: Fanoron-Telo, Fanoron-Dimy, and Fanoron-Tsivy. The difference between these variants is the size of board played on. Fanoron-Telo is played on a 3×3 board and the difficulty of this game can be compared to the game of tic-tac-toe. Fanoron-Dimy is played on a 5×5 board and Fanoron-Tsivy is played on a 9×5 board - Tsivy being the most popular. 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. According to one version of a popular legend, an astrologer had advised King Ralambo (1575-1610) to choose his successor by selecting a time when his sons were away from the capital to feign sickness and urge their return; his kingdom would be given to the first son who returned home to him. When the king's messenger reached Ralambo's elder son Prince Andriantompokondrindra, he was playing fanorona and trying to win a telo noho dimy (3 against 5) situation, one that is infamously difficult to resolve. As a result, his younger brother Prince Andrianjaka was the first to arrive and inherited the throne.

Board
The Fanorona board consists of lines and intersections, creating a grid with 5 rows and 9 columns. A line represents the path along which a stone can move during the game. There are weak and strong intersections. At a weak intersection it is only possible to move a stone horizontally and vertically, while on a strong intersection it is also possible to move a stone diagonally. A stone can only move from one intersection 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 ways, either (1) by approach or (2) by withdrawal.
 * An approach is moving the capturing stone to a point adjacent to an opponent stone provided that the stone is on the continuation of the capturing stone's movement line.
 * A withdrawal works analogously to an approach except 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 these 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 captures 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.