Two-agent IDA*

Abstract

The article presents an algorithm that combines Minimax's alpha-beta pruning with IDA*'s depth-first iteration and forward pruning. We prove that the algorithm, which we call Two - agent IDA* (TIDA*), is correct and is guaranteed to terminate—provided its heuristic is consistent. Minimax search has been applied with other ‘forward’ pruning or selective search techniques, but none of these techniques is guaranteed to compute the correct minimax result. We also prove that TIDA*'s accuracy monotonically increases with search depth, thus avoiding certain pathologies. Empirical results with 3×3, 4×4 and 5×5 Tic-Tac-Tff grids show that TIDA* outperforms MAB, provided both algorithms use the same consistent heuristic. However, results on a more complex search space—the 3D version of Tic-Tac-Tff—show that MAB with a good inconsistent heuristic can outperform TIDA* with a consistent heuristic even though TIDA* searches 1 to 1·5 levels deeper. This result and other empirical results suggest that an algorithm that starts with MAB and an inconsistent heuristic and then shifts near the end of the game to TIDA* with a consistent heuristic can outperform either algorithm. Finally, we present results on a forward-pruning version of MAB and show that under certain conditions it can outperform TIDA*, provided both use the same consistent heuristic.