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

Markus Böck
7/1/2025
cs.AI

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Abstract

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.

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Cite this paper

@article{bck2025strongly,
  title  = {Strongly Solving $7 \times 6$ Connect-Four on Consumer Grade Hardware},
  author = {Markus Böck},
  year   = {2025},
  eprint = {2507.05267},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2507.05267v1}
}

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