indifference, given that the coin lands tails, her credence that it is Monday should equal her credence that it is Tuesday, since being in one situation would be subjectively indistinguishable from the other. In other words, P(Monday Tails) = P(Tuesday | Tails), and thus P(Tails and Tuesday) = P(Tails and Monday). Suppose now that Sleeping Beauty is told upon awakening and comes to fully believe that it is Monday. Guided by the objective chance of heads landing being equal to the chance of tails landing, it should hold that P(Tails | Monday) = P(Heads | Monday), and thus P(Tails and Tuesday) = P(Tails and Monday) = P(Heads and Monday). Since these three outcomes are exhaustive and exclusive for one trial (and thus their probabilities must add to 1), the probability of each is then 1/3 by the previous two steps in the argument. An alternative argument is as follows: Credence can be viewed as the amount a rational risk-neutral bettor would wager if the payoff for being correct is 1 unit (the wager itself being lost either way). In the heads scenario, Sleeping Beauty would spend her wager amount one time, and receive 1 money for being correct. In the tails scenario, she would spend her wager amount twice, and receive nothing. Her expected value is therefore to gain 0.5 but also lose 1.5 times her wager, thus she should break even if her wager is 1/3. Halfer position David Lewis responded to Elga's paper with the position that Sleeping Beauty's credence that the coin landed heads should be 1/2. Sleeping Beauty receives no new non-self-locating information throughout the experiment because she is told the details of the experiment. Since her credence before the experiment is P(Heads) = 1/2, she ought to continue to have a credence of P(Heads) = 1/2 since she gains no new relevant evidence when she wakes up during the experiment. This directly contradicts one of the thirder's premises, since it means P(Tails | Monday) = 1/3 and P(Heads | Monday) = 2/3. Double halfer position The double halfer position argues that both P(Heads) and P(Heads | Monday) equal 1/2. Mikaël Cozic, in particular, argues that context-sensitive propositions like "it is Monday" are in general problematic for conditionalization and proposes the use of an imaging rule instead, which supports the double halfer position. Connections to other problems Credence about what precedes awakenings is a core question