The Chef

You, a perfectly rational agent, awake in a lovely bed in a warm brightly lit room. You take stock of your surroundings, and find them delightfully cozy. On your bedside is a nicely bound book, entitled "Food for your Tummy". You open it and begin to read, it informs you that you have come to be as part of a lovely game run by "The Chef", an upright and well respected logician and cook. The Chef, whose motives you find impenetrable, will create in turn some group of N people, starting with one and doubling each time. Each group's fate, once created, will be determined by a complex mechanism tucked away deep in a mountain whose operation is unfathomable to you. However, the pamphlet assures you that the process is truly fair and random, no group will be favored over any other. The mechanism will output either TRICK or TREAT. The experiment ends once TREAT is output. Your fate, should the mechanism decide TREAT, will to be served a scrumptious dessert guaranteed to please your palate. The Chef reasons that since the group which receives the judgement of TREAT is always larger than the sum of all members of the groups that are harmlessly deceived, the tricksters (who are slightly fewer than the cooks) will not be overworked. You look around your lovely room, neither you nor it have any distinguishing features whatsoever. You consider that you are a perfectly rational agent, and try and decide exactly how much your tummy should rumble in anticipation. After you fix your answer in your mind, a soft soothing voice tells you that the mechanism has judged twelve trillion, four hundred and sixty-three billion, nine hundred and seven million, three hundred and four thousand, and five times before your upcoming judgement. Does your anticipation fade?

End of Part One

Part Two