An Adventurer is standing on the primary of eight sequential platforms, able to advance. But a Booby-trapper is positioning a lure to catch them in a sport performed over a number of rounds.

Each spherical, the Adventurer secretly chooses both 1, 2, or 3 and the Booby-trapper secretly picks a platform. Then, the alternatives are revealed and the Adventurer advances quite a lot of platforms equal to their chosen quantity. Then, if the Adventurer is standing on the platform that the Booby-trapper picked for this spherical, the sport is over and the Adventurer wins nothing. Then, if the Adventurer is standing on the sixth, seventh, or eighth platform, the sport is over and the Booby-trapper pays the Adventurer $100. Then, if the sport just isn’t but over, a brand new spherical begins.

How a lot ought to the Adventurer be prepared to pay the Booby-trapper to play this sport?

Assume that each gamers are completely rational gamblers attempting to maximise their cash, have entry to random quantity mills, and are conscious that each gamers know all of this.