A perfectly rational Sleeping Beauty is put to sleep on Sunday night, and intermittently awoken either on Monday only (if a fair coin shows Heads) or on both Monday and Tuesday (if the fair coin shows Tails). According to experimental conditions, she neither remembers previous awakenings nor knows about passage of time, but she is aware of experimental conditions. Her credence for the coin having come up Heads is at the center of a scientific (mostly philosophical) controversy: halfers insist it (...) should be 1/2, while thirders claim it should be 1/3. Winkler (2017) reviewed the literature, in terminology accessible to statisticians. This paper presents a comprehensive treatment of the probability side of the problem, from the perspective of a frequentist applied statistician. Perceived contradictions are resolved (in line with Groisman 2008) or traced back to violation of model assumptions. Modeling was at the heart of the confusion and is also at the heart of the solution. (shrink)