Unknown expected value vacation themed lotto scratcher
I got the idea from real world lotto scratchers, which by design are all losers, except some rare edge cases. The other half of the idea comes from a quote from "War Games" - "The only way to win is to not play"
You start with $10,000. You decide if you want to play (again). If you play, you go on vacation. The machine generates a series of random events that make up a plausible vacation. You spend money and earn joy, which converts directly back into money via magic.
Unknown to you, the expected value of the game is either more than or less than one. EV is the sum of all probabilities of the possibilities times the value, in this case dollars of joy.
You have to decide when to stop playing. If the game's EV is <1, stop playing immediately! If the game's EV is >1, stop playing when you think you are going to go bust or you just never stop. Some possible variations- games that have a constant EV on each replay, or games that have an EV that starts at a EV>1 but eventually switches permanently to <1, in which case that would be the best time to stop.
You have traveled to Atlanta by Amtrak. It cost -$400, but you got +$500 joy You stayed at a DoubleTree Hotel - $200, +$205 joy The restaurant burt your food. -$50, -$75 joy etc. And that was yor trip to Atlanta
Do you want to play again?