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Robust Decision Making (RDM) is an established framework for decision making under deep uncertainty. RDM relies on the idea of scenario neutrality , namely that decision robustness is not affected by how scenarios are generated if these are uniformly distributed and span a sufficiently large range of future states of the world. Several authors have shown that scenario neutrality may not hold, but they did so by adopting either new or computationally expensive modeling. We introduce the Belief-Informed Robust Decision Making (BIRDM) framework to assess how robustness might change under an arbitrary large number of non-uniform distributions at virtually no additional costs with respect to RDM. We apply BIRDM to a flood management problem and find that alternative distributions change the robustness and ranking of measures. BIRDM allows identifying what distributions lead to these changes and under what set of distributions a measure has a specific robustness and rank. • The Belief-Informed Robust Decision Making (BIRDM) framework integrates probabilistic information into Robust Decision Making. • BIRDM does not require new modeling nor additional computational costs with respect to Robust Decision Making. • BIRDM allows exploring changes in decision robustness under alternative distributions of deep uncertainties. • We apply BIRDM to a flood management planning problem along the Po River in Italy. • We find that alternative distributions of deep uncertainties change decision robustness and alter the ranking of measures. [ABSTRACT FROM AUTHOR]