Monte-Carlo engines (like AlphaZero, Leela) use self-play simulations guided by neural networks, repeatedly exploring random playouts and statistically backing up results, while alpha-beta engines (like Stockfish) systematically eliminate inferior lines through precise pruning and exact search. Monte-Carlo search excels in long-term planning, pattern recognition, and positional intuition because it uses deep neural nets to evaluate and guide rollouts. Alpha-beta engines excel in calculation-heavy positions, tactics, and exactness because they compute minimax results directly.

Monte-Carlo methods are more “human-like,” while alpha-beta methods are more “tactically brute-force precise.”