| Sumario: | We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. Reckless theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; timid theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; non‐transitive theories deny the principle that, if A$A$ is better than B$B$ and B$B$ is better than C$C$, then A$A$ must be better than C$C$. Having set up this trilemma, we study its horns. Non‐transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty.
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