Uncertainty is intrinsic to decision-making. Decisions regarding the use of road networks in the transportation of hazardous materials are no exception. Commonly, cautious shipment of hazardous materials is focused on identifying a single safest route between a pair of points. Here we demonstrate that for repeated shipments, where there is complete uncertainty about link incident probabilities, the safest strategy is in general to use a mix of routes determined by the worst case scenario probabilities. Using game-theoretic approach embedded in a Defender-Attacker-Defender framework, it is shown that maximum exposure to risk can be significantly reduced by sharing shipments between routes. The approach posits predefined disruption, attack or failure scenarios and then considers how to use road network so as to minimize the maximum expected loss in the event these scenarios materialise. The properties of the optimality conditions are explored leading to the formulation of an equivalent linear programming problem. A solution algorithm suitable for use with standard traffic assignment software is presented together with a numerical example relating to the central London road network.