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In everyday life, people routinely make decisions that involve irredeemable risks such as death (e.g., while driving). Even though these decisions under extinction risk are common, practically important, and have different properties compared to the types of decisions typically studied by decision scientists, they have received little research attention. The present work advances the formal understanding of decision making under extinction risk by introducing a novel experimental paradigm, the Extinction Gambling Task (EGT). We derive optimal strategies for three different types of extinction and near-extinction events, and compare them to participants’ choices in three experiments. Leveraging computational modelling to describe strategies at the individual level, we document strengths and shortcomings in participants’ decisions under extinction risk. Specifically, we find that, while participants are relatively good in terms of the qualitative strategies they employ, their decisions are nevertheless affected by loss chasing, scope insensitivity, and opportunity cost neglect. We hope that by formalising decisions under extinction risk and providing a task to study them, this work will facilitate future research on an important topic that has been largely ignored.