On a long, slow trip to Mars, Virgin Galactic is entertaining it's passengers with a prize drawing.
Every hour there is a 40% chance you'll win. If you don't win, then you have the same odds to try again and again each hour. Prizes follow this sequence: $1, 1, 2, 2, 5, 5, 100, 100.
The sequence restarts after not winning 8 straight or if the passenger wins before then. The ship's computer automatically enters you in the contest. Passengers need not be present or awake to play, nor is there a cost to play.
What is Virgin's expected cost per hour, per passenger? (Or, what is the expected value of each hour of your travel?)