Systematic N-tuple Networks for Position Evaluation: Exceeding 90% in the Othello League

TL;DR

This paper introduces a systematic approach to designing N-tuple networks for Othello, demonstrating that using many short, straight n-tuples of size 2 significantly improves position evaluation, achieving over 96% performance in the Othello League.

Contribution

The study shows that systematically placed short n-tuples outperform random long sequences, and a simple network with size 2 n-tuples can achieve state-of-the-art results.

Findings

Achieved nearly 96% performance in the Othello League.

Systematic placement of short n-tuples outperforms random long sequences.

A network with only 288 weights is sufficient for high performance.

Abstract

N-tuple networks have been successfully used as position evaluation functions for board games such as Othello or Connect Four. The effectiveness of such networks depends on their architecture, which is determined by the placement of constituent n-tuples, sequences of board locations, providing input to the network. The most popular method of placing n-tuples consists in randomly generating a small number of long, snake-shaped board location sequences. In comparison, we show that learning n-tuple networks is significantly more effective if they involve a large number of systematically placed, short, straight n-tuples. Moreover, we demonstrate that in order to obtain the best performance and the steepest learning curve for Othello it is enough to use n-tuples of size just 2, yielding a network consisting of only 288 weights. The best such network evolved in this study has been evaluated in the online Othello League, obtaining the performance of nearly 96% --- more than any other player to date.