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A computational agent-based model is proposed to study the historical naval battle of Trafalgar. The model, implemented using the Swarm simulation system, allows a dynamical study of system evolution at a high level of detail. Results agree in a very strict way with historical data. A comparison between the computational model and Lanchesters analytical model is proposed. Lanchesters forecasts and analysis of the battle are in substantial contrast with results obtained by the computational model. Moreover, counterfactual experiments have also been performed in order to investigate the possibility that a different outcome of the battle might have occurred: Nelsons strategy turned out to be not only the winning strategy, but the safest as well. The proposed model appears to be a very flexible tool for a quantitative analysis of a conflict and an interesting conceptual framework for the general study of conflict resolution.