This paper deals with the search for a dynamic run-based optimal travel strategy, to be supplied through mobile devices to travelers on a stochastic multi-service transit network, which includes a forecasting system of bus arrival times at stops. The paper first analyses some existing run-based optimal strategy search methods, then a new procedure is proposed and applied. The optimal strategy is obtained as a heuristic solution of a Markovian decision problem (MDP). The hallmarks of the proposal are to use only traveler state spaces (which allows the curse of dimensionality, one of the main problems of optimal policy search, to be reduced) and to use a real-time error distribution of bus travel time forecasts and at-stop bus arrival time fo...