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Other 196's:
I think you would HAVE to pull it right? Regardless of how many times the lever can be given to the next person, you are either killing 1/3rd lives in the scenario, or you are killing 1/8bil.
What if no one ever pulls it?
You win the game
Assuming the problem is infinite and considers physical factors, then it would happen at one point
Actually, if it doubles every time and we assume 8 billion is the max, you only need 32 people to not pull it. Maybe I'd bet on that. If I was in the middle I'd let it pass no question.