In Brief Most studies assessing decision-making under uncertainty use events with probabilities that are above 10-20 %. Here, to study decision-making in radical uncertainty conditions, Degoulet, Willem, Baunez, Luchini and Pintus provide a novel experimental design that aims at measuring the extent to which rats are sensitive - and how they respond - to extremely rare (below 1% of probability) but extreme events in a four-armed bandit task. Gains (sugar pellets) and losses (time-out punishments) are such that large - but rare - values materialize or not depending on the option chosen. The results show that all rats diversify their choices across options. However, most rats exhibit sensitivity to rare and extreme events despite their sparse occurrence, by combining more often options with extreme gains (Jackpots) and/or avoidance of extreme losses (Black Swans). In general, most rats’ choices feature one-sided sensitivity in favor of trying more often to avoid extreme losses than to seek extreme gains - that is, they feature Black Swan Avoidance. Highlights - A novel experiment is proposed to measure whether rats are sensitive - and how they respond - to radical uncertainty materialized by extremely rare and extreme events in a four-armed bandit task; - Most rats exhibit sensitivity to rare and extreme events; - Most rats opt more often to avoid rare and extreme losses than to seek rare and extreme gains: they feature Black Swan avoidance.