arXiv:2507.05267cs.AI2025-07

用消费级硬件生成7×6连四棋强解表,47小时完成89.6GB数据构建。

Strongly Solving $7 \times 6$ Connect-Four on Consumer Grade Hardware

  • 基于二元决策图的符号化搜索,高效生成强解查表。
  • 在单核CPU上47小时完成89.6GB查表,支持胜负平评估。
  • 开源包含快速取胜/慢速败局策略,适合博弈研究者使用。

尽管连四棋在数学上已被解决,且可通过搜索方法有效计算最优走法,但以查表形式实现强解曾被认为不可行。本文重新审视基于二元决策图的符号化搜索方法,通过高效实现,在单个CPU核心、128GB内存条件下,47小时内为标准7×6棋盘生成了89.6GB的查表。除胜负平评估外,开源代码还包含α-β搜索,可找出最快获胜或最慢失败的走法。

原文摘要 · Abstract (English)

While the game Connect-Four has been solved mathematically and the best move can be effectively computed with search based methods, a strong solution in the form of a look-up table was believed to be infeasible. In this paper, we revisit a symbolic search method based on binary decision diagrams to produce strong solutions. With our efficient implementation we were able to produce a 89.6 GB large look-up table in 47 hours on a single CPU core with 128 GB main memory for the standard $7 \times 6$ board size. In addition to this win-draw-loss evaluation, we include an alpha-beta search in our open source artifact to find the move which achieves the fastest win or slowest loss.

博弈求解查表法符号计算

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