We investigate the dynamics of voluntary cooperation to either reduce the size or the probability of a stochastic shock. For variants of a repeated four-person prisoner’s dilemma game, we show that cooperation is larger and more stable when it affects the probability rather than the size of damages. We provide crucial insights on behavioral adaptation following adverse events: defecting players are more likely to switch to cooperation after experiencing an adverse event, while existing cooperation is reinforced when the damage does not occur. This behavior is consistent with simple learning dynamics based on ex post evaluations of the chosen strategy.