In many board games, AlphaZero has demonstrated superhuman abilities. Dots-and-Boxes is a classic board game with simple rules but requiring skills to win. This paper proposes Dotsformer, which extracts chain-loop structures from the game board. These structures connect distant boxes, providing long-range relational information as input to the Transformer. We employ multiple convolutional kernels to generate Q, K, and V, and incorporate information about the box structure itself into the attention scores. We also incorporate auxiliary training tasks, including an initiative task and a classification task. These tasks determine whether to retain or relinquish the initiative in the current situation, and classify actions into forbidden, conceding, safe, and scoring moves. They provide additional supervisory signals and accelerate learning. The experimental results show that Dotsformer outperforms AlphaZero in both rollback speed and playing strength: it achieved a winning rate of 87.6% and an ELO rating lead of 340 points against the baseline. Additionally, ablation studies verify the effectiveness of each key module.