provided that you don't have heirs and all your remaining money magically disappears when you die. What do you think?
Just have it so you only have to pay if you win. That makes it less confusing.
Case 1: You have a 50% chance of paying $x to give a 16.7% increase in the probability of surviving. Case 2: You have a 100% chance of paying $x to give a 33.3% increase in the probability of surviving.
In either case, the amount you pay would be 1/3 the value of your life.
Imagine you're playing Russian roulette. Case 1: a six-shooter contains four bullets, and you're asked how much you'll pay to remove one of them. Case 2: a six-shooter contains two bullets, and you're asked how much you'll pay to remove both of them. Steven Landsburg describes an argument by Richard Zeckhauser and Richard Jeffrey saying you should pay the same amount in both cases, provided that you don't have heirs and all your remaining money magically disappears when you die. What do you think?