Climate change requires reconsideration of flood risk management strategies. Cost-benefit analysis (CBA), an economic decision-support tool, has been widely applied to assess these strategies. This paper aims to describe and discuss probabilistic extensions of CBA to identify welfare-maximising flood risk management strategies under climate change. First, uncertainty about the changes in return periods of hydro-meteorological extremes is introduced by probability-weighted climate scenarios. Second, the analysis is extended by learning about climate change impacts. Learning occurs upon the probabilistic arrival of information. We distinguish between learning from scientific progress, from statistical evidence and from flood disasters. These probabilistic extensions can be used to analyse and compare the economic efficiency and flexibility of flood risk management strategies under climate change. We offer a critical discussion of the scope of such extensions and options for increasing flexibility. We find that uncertainty reduction from scientific progress may reduce initial investments, while other types of learning may increase initial investments. This requires analysing effects of different types of learning. We also find that probabilistic information about climate change impacts and learning is imprecise. We conclude that risk-based CBA with learning improves the flexibility of flood risk management strategies under climate change. However, CBA provides subjective estimates of expected outcomes and reflects different decision-maker preferences than those captured in robustness analyses. We therefore advocate robustness analysis in addition to, or combined with, cost-benefit analysis to support local investment decisions on flood risk reduction and global strategies on allocation of adaptation funds for flood risk management.