A New Paradigm for Minimax Search

TL;DR

This paper presents a new memory-enhanced minimax search paradigm that improves game-tree search efficiency by integrating iterative deepening and memory, outperforming traditional algorithms in practical game-playing programs.

Contribution

Introduces MT, a memory-enhanced minimax framework enabling simple construction of best-first algorithms like SSS*, with experimental validation across multiple games.

Findings

MTD-f outperforms NegaScout in leaf nodes, nodes, and time

Memory and iterative deepening significantly improve move ordering

Results differ from previous simulations, showing less node expansion in practice

Abstract

This paper introduces a new paradigm for minimax game-tree search algo- rithms. MT is a memory-enhanced version of Pearls Test procedure. By changing the way MT is called, a number of best-first game-tree search algorithms can be simply and elegantly constructed (including SSS*). Most of the assessments of minimax search algorithms have been based on simulations. However, these simulations generally do not address two of the key ingredients of high performance game-playing programs: iterative deepening and memory usage. This paper presents experimental data from three game-playing programs (checkers, Othello and chess), covering the range from low to high branching factor. The improved move ordering due to iterative deepening and memory usage results in significantly different results from those portrayed in the literature. Whereas some simulations show Alpha-Beta expanding almost 100% more leaf nodes than other algorithms [12], our results showed variations of less than 20%. One new instance of our framework (MTD-f) out-performs our best alpha- beta searcher (aspiration NegaScout) on leaf nodes, total nodes and execution time. To our knowledge, these are the first reported results that compare both depth-first and best-first algorithms given the same amount of memory