Let’s Make a Deal: Sleeping Beauty and Monty Hall Are the Same “Paradox”

The Monty Hall problem and the Sleeping Beauty paradox are two of the best-known problems in probability theory and information theory. The essence of both is asking what credence a player should give to one of two options, when the options presented have been informed by a decision made by another intelligent agent, based on information unavailable to the player. The solution to the Monty Hall problem is largely well established, but there is no such consensus for Sleeping Beauty. While most commenters advocate for the so-called thirder solution, there remains a robust defence of the dissenting halfer viewpoint. Here, we demonstrate that these two famous problems can be simulated from the same simple experiment and thus are, in fact, entirely equivalent. As such, we also advocate for the thirder solution to Sleeping Beauty, in line with the equivalent result for Monty Hall. Despite this defence of the thirder position, we argue that many of the published statements made in favour of this conclusion are either misleading or incorrect, owing to ambiguous notation regarding frames of reference and knowledge. Similar issues have led to flawed attempts at resolving other paradoxes, including the Two Envelope paradox and the Absent-Minded Driver paradox.