Abstract
If an agent believes that the probability of E being true is 1/2, should she accept a bet on E at
even odds or better? Yes, but only given certain conditions. This paper is about what those
conditions are. In particular, we think that there is a condition that has been overlooked so far in
the literature. We discovered it in response to a paper by Hitchcock (2004) in which he argues
for the 1/3 answer to the Sleeping Beauty problem. Hitchcock argues that this credence follows
from calculating her fair betting odds, plus the assumption that Sleeping Beauty’s credences
should track her fair betting odds. We will show that this last assumption is false. Sleeping
Beauty’s credences should not follow her fair betting odds due to a peculiar feature of her
epistemic situation.