Mapping the Safest Routes: A Clustering Study of the French Defense - Wijayanto, Feri (Department of Informatics Universitas Islam Indonesia, 2025)
This study explores the safest variations in the French Defense using 5,156 artificially generated chess games with Stockfish 17. Unlike prior work reliant on historical data, this method reduces theory bias by randomly selecting from the engine's top five moves at each position. We applied k-means clustering with cosine similarity to group move sequences based on evaluation scores. Both two-cluster and three-cluster models were tested. Stability was assessed via 50 resamples using 50% of the data. The three-cluster model, which includes a neutral group, had excellent stability (ARI = 0.99) but moderate cohesion (silhouette = 0.53). The two-cluster model showed better cohesion (silhouette = 0.65) but lower stability (ARI = 0.68). Among the variations, e5 (Advance) and exd5 (Exchange) stood out, with about 54% of games in each line falling into clusters favoring White. This suggests they are the safest and most reliable options. In contrast, Bb5+ performed well in simulations but poorly in real-world data, indicating theoretical risks. In summary, clustering on simulated games reveals hidden strategic insights, confirming e5 and exd5 as strong, low-risk choices for White in the French Defense.