&quot;[…] to what degree should you believe that the outcome of the coin toss was Heads?&quot; is a terribly unrigorous way to phrase this question.  I suspect it&#x27;s where all the confusion sets in.<p>Are we adjusting the natural prior of a coin toss based on information we now have?  We have no information; 50%.<p>Are you placing a bet each time you are awake?  You get to bet <i>twice</i> if the coin comes up Tails; 2:1 (33%) odds against Heads balances the tables.<p>Are we judging how often we&#x27;d be correct if we guessed Heads every time we were awoken?  Depends on the number of trials.  With only 1 trial; 50%.  With 2 trials; 42%.  With infinite trials; 33%.<p>Nothing begets a paradox like an ill-posed question.