Overview
This page presents all known fair starting positions by moving 1 or 2 pieces for the Mancala (Kalah) variant without empty capture. These states are not included directly in the paper due to space limitations and are instead archived here for presentation use.
These positions were generated through full-state computational analysis and evaluated under the modified rule set where empty captures are disabled.
For the analysis of the standard (usual) version of Mancala, please refer to the primary FairKalah research page: Prof. Todd W. Neller’s FairKalah Site .
Research Supervision & Affiliation
This project is conducted under the supervision of Prof. Todd W. Neller , Gettysburg College.
This page is hosted as a subsection of the primary FairKalah research site.
Research Paper
Title: FairKalah Without Empty Capture
Authors: Phong Pham, Todd W. Neller
Abstract:
Kalah (a.k.a. Mancala) is a two-player game of perfect information
that has been a popular game for over half a century despite a strong first player
advantage. Previous AI research concerns Kalah with empty captures, yet a common variation disallows empty captures. In this paper, we present the first analysis
of the fairness of Kalah without empty captures, initial game states that are fair,
as well as optimal play insights from analysis of optimal and suboptimal states.
Status: Manuscript in preparation
Fair State Archive
A total of 323 provably fair starting positions were identified for the no-null-capture Mancala variant. Due to space and performance constraints, the full set of boards is hosted on a separate archive page.
Longest fair optimal game
This is one of the longest games played optimally with a fair starting position. Try to guess how long it is?
Read the game from left to right, row by row.
Really long game