We discuss the extension of the classic dynamic programming approach to hybrid control systems, where a continuous controller can switch between a finite collection of states, paying a cost of switching. This approach requires the resolution of a system of quasi-variational Hamilton-Jacobi inequalities that we propose to approximate via a semi-Lagrangian scheme obtained by the direct discretization of the dynamical programming principle. We discuss the application of such a framework to model a sailing boat navigation problem for the optimization of the strategic choices on a race course. The model can be extended to the non-zero sum games, naturally including the presence of 3 or more players. For the number of players going to infinity, it is possible to introduce a new model as its mean-field limit. This is the case of very crowded races, where the interaction between many players would be impossible to model correctly with other techniques.