Development and Application of a Monte Carlo Tree Search Algorithm for Simulating Da Vinci Code Game Strategies

TL;DR

This work addresses efficient decision-making with $MCTS$ for the Da Vinci Code game under branch-divergent GPU parallelism. It implements two parallel variants, $MCTS$-cpu with OpenMP and $MCTS$-gpu with CUDA, and introduces a simplified $MCTS$-dvc that reduces branching by omitting plausible-number sets and fixing guess sequences. Evaluation shows linear CPU scaling with the number of threads up to about the physical core limit, while $MCTS$ on GPU exhibits non-linear gains with noticeable troughs due to cache misses and memory contention. The results inform architectural choices for parallel game-AI systems, highlighting that CPU-based parallelization can outperform GPU-based approaches for divergent-branch strategic tasks on current hardware.

Abstract

In this study, we explore the efficiency of the Monte Carlo Tree Search (MCTS), a prominent decision-making algorithm renowned for its effectiveness in complex decision environments, contingent upon the volume of simulations conducted. Notwithstanding its broad applicability, the algorithm's performance can be adversely impacted in certain scenarios, particularly within the domain of game strategy development. This research posits that the inherent branch divergence within the Da Vinci Code board game significantly impedes parallelism when executed on Graphics Processing Units (GPUs). To investigate this hypothesis, we implemented and meticulously evaluated two variants of the MCTS algorithm, specifically designed to assess the impact of branch divergence on computational performance. Our comparative analysis reveals a linear improvement in performance with the CPU-based implementation, in stark contrast to the GPU implementation, which exhibits a non-linear enhancement pattern and discernible performance troughs. These findings contribute to a deeper understanding of the MCTS algorithm's behavior in divergent branch scenarios, highlighting critical considerations for optimizing game strategy algorithms on parallel computing architectures.

Figures (10)

• Figure 1: Play example of Da Vinci Code
• Figure 2: Simplification: not to keep guessing
• Figure 3: Four steps of MCTS
• Figure 4: Simplification: limited expansion
• Figure 5: Overall process of creating MCTS