I'll go ahead and do my own hypotheticals.
Assuming I didn't know what the mystery option is, I'd take the billion. If it's possible to live on fifty thousand dollars a year, my fortune would last me twenty thousand years if I lived off that much per year. Or I can live on a hundred thousand dollars per year for ten thousand years. Two hundred thousand dollars per year for five thousand years. Four hundred thousand dollars per year for two thousand five hundred years. It goes on and on. Eight hundred thousand dollars a year for one thousand two hundred and fifty years. 1.6 million dollars a year for six hundred and twenty five years. 3.2 million per year for three hundred twelve and a half years. 6.4 million per year for one hundred six and a fourth years. I could live in luxury for that. Assuming inflation doesn't become too much of an issue or we don't develop super anti-aging tech, I'll be fine.
With regards to the mystery option,
Yeah, that is the trick. The problem is doing that setting up. Maybe you can purchase indefinite hotel access for an arbitrarily large amount of money, but it might be a bit hard to set that up. The same goes for indefinite food deliveries, indefinite chauffeur service, etc.
With regards to hunting down the seven:
There's no guarantee the seven will value the lives of their families over ending my own life.
Possession and Rebellion are very dangerous for subverting the population, but Photomancy's dangerous in his own way if he manages to get ahold of original photographs of nuclear weapons. Competence can definitely acquire the skills necessary to set one off.
I'd make public all information I had on the seven, and offer massive rewards to those who supply info about their location. Tactical drone strikes do seem like a good idea, they're immune to basically anything the seven can do aside from escaping. As soon as I have a location, missile the heck out of them, prioritizing...
Actually, that's a good hypothetical.
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With regards to the seven enemies described in my earlier hypothetical, how would you rank them on the danger scale?