Best-First and Depth-First Minimax Search in Practice
This work addresses a long-standing debate in game-playing AI by providing a simpler, more efficient framework for practitioners, though it is incremental in refining existing search algorithms.
The paper tackles the practical inefficiency of the best-first SSS* algorithm compared to depth-first Alpha-Beta in minimax search, showing that Alpha-Beta variants often evaluate fewer nodes and introducing MTD(f), which outperforms both SSS* and NegaScout.
Most practitioners use a variant of the Alpha-Beta algorithm, a simple depth-first pro- cedure, for searching minimax trees. SSS*, with its best-first search strategy, reportedly offers the potential for more efficient search. However, the complex formulation of the al- gorithm and its alleged excessive memory requirements preclude its use in practice. For two decades, the search efficiency of "smart" best-first SSS* has cast doubt on the effectiveness of "dumb" depth-first Alpha-Beta. This paper presents a simple framework for calling Alpha-Beta that allows us to create a variety of algorithms, including SSS* and DUAL*. In effect, we formulate a best-first algorithm using depth-first search. Expressed in this framework SSS* is just a special case of Alpha-Beta, solving all of the perceived drawbacks of the algorithm. In practice, Alpha-Beta variants typically evaluate less nodes than SSS*. A new instance of this framework, MTD(f), out-performs SSS* and NegaScout, the Alpha-Beta variant of choice by practitioners.