I think I’ve got a fix for your lifespan-gamble dilemma. Omega (who is absolutely trustworthy) is offering indefinite, unbounded life extension, which means the universe will continue being capable of supporting sufficiently-human life indefinitely. So, the value of additional lifespan is not the lifespan itself, but the chance that during that time I will have the opportunity to create at least one sufficiently-similar copy of myself, which then exceeds the gambled-for lifespan. It’s more of a calculus problem than a statistics problem, and involves a lot of poorly-evidenced assumptions about how long it would take to establish a bloodline capable of surviving into perpetuity.
Or, if you don’t care about offspring, consider this: the one-in-a-million chance of near-instant death is actually a bigger cost each time, since you’re throwing away a longer potential lifespan. The richer you get, the more cautious you should be about throwing it all away on one roll of the dice.
Or, if you don’t care about offspring, consider this: the one-in-a-million chance of near-instant death is actually a bigger cost each time, since you’re throwing away a longer potential lifespan. The richer you get, the more cautious you should be about throwing it all away on one roll of the dice.
Upvoted for cleverness, but I don’t think that actually works. The expected loss grows at each step, but it’s always proportional to the output of the last tetration step, which isn’t enough to keep up with the next one; −1 10^10 + 10^(10^10)) is a hell of a lot smaller than −1 10^(10^10) + 10^(10^(10^10)), and it only gets worse from there. The growth rate is even large enough to swamp your losses if your utility is logarithmic in expected life years; that just hacks off one level of exponentiation at the initial step.
I don’t see a level of caution here that allows you to turn down this particular devil’s offer without leading you to some frankly insane conclusions elsewhere. In the absence of any better ideas, and assuming that utility as a function of life years isn’t bounded above anywhere and that my Mephistopheles does credibly have the diabolical powers that’d allow him to run such a scam, I think I’m going to have to bite the bullet and say that it’s not a scam at all. Just highly counterintuitive.
I think I’ve got a fix for your lifespan-gamble dilemma. Omega (who is absolutely trustworthy) is offering indefinite, unbounded life extension, which means the universe will continue being capable of supporting sufficiently-human life indefinitely. So, the value of additional lifespan is not the lifespan itself, but the chance that during that time I will have the opportunity to create at least one sufficiently-similar copy of myself, which then exceeds the gambled-for lifespan. It’s more of a calculus problem than a statistics problem, and involves a lot of poorly-evidenced assumptions about how long it would take to establish a bloodline capable of surviving into perpetuity.
Or, if you don’t care about offspring, consider this: the one-in-a-million chance of near-instant death is actually a bigger cost each time, since you’re throwing away a longer potential lifespan. The richer you get, the more cautious you should be about throwing it all away on one roll of the dice.
Upvoted for cleverness, but I don’t think that actually works. The expected loss grows at each step, but it’s always proportional to the output of the last tetration step, which isn’t enough to keep up with the next one; −1 10^10 + 10^(10^10)) is a hell of a lot smaller than −1 10^(10^10) + 10^(10^(10^10)), and it only gets worse from there. The growth rate is even large enough to swamp your losses if your utility is logarithmic in expected life years; that just hacks off one level of exponentiation at the initial step.
I don’t see a level of caution here that allows you to turn down this particular devil’s offer without leading you to some frankly insane conclusions elsewhere. In the absence of any better ideas, and assuming that utility as a function of life years isn’t bounded above anywhere and that my Mephistopheles does credibly have the diabolical powers that’d allow him to run such a scam, I think I’m going to have to bite the bullet and say that it’s not a scam at all. Just highly counterintuitive.