An Adventurer is standing on the first of eight sequential platforms, ready to advance. But a Booby-trapper is positioning a trap to catch them in a game played over several rounds.
Each round, the Adventurer secretly chooses either 1, 2, or 3 and the Booby-trapper secretly picks a platform. Then, the choices are revealed and the Adventurer advances a number of platforms equal to their chosen number. Then, if the Adventurer is standing on the platform that the Booby-trapper picked for this round, the game is over and the Adventurer wins nothing. Then, if the Adventurer is standing on the 6th, 7th, or 8th platform, the game is over and the Booby-trapper pays the Adventurer $100. Then, if the game is not yet over, a new round begins.
How much should the Adventurer be willing to pay the Booby-trapper to play this game?
Assume that both players are perfectly rational gamblers trying to maximize their money, have access to random number generators, and are aware that both players know all of this.