Thanks for the kind words. I always enjoy hearing from high school math teachers out there because I almost became one myself. Based on seeing par sheets and speaking to industry insiders I can confidently say that if the alternative choices are shown at the conclusion of a bonus round then the game is honest about them. In other words the prizes were randomly determined and what you see at the end is truly how they were hidden. However in games where the alternative choices are not shown the odds are likely similar to a prize wheel, with lower probabilities for the higher wins. I played Price is Right enough to see the Showcase Showdown twice. As you said, the values behind the price tags are revealed at the end. So I maintain that the game is indeed truthful and speculate that you have just been unlucky.