Is there a solid actuarial calculation behind either of the probabilistic claims you're making? Don't get me wrong, I certainly hope you're right and gp is wrong, but I imagine it's pretty hard to decide either way.

I think Bill Gates is a flawed example, since he is focused on philanthropic charity, which is unlikely to have a transformative/exponential effect on societal survivability proportionate to the effect his wealth could have on his personal survivability. But, if he were more focused on potentially transformative "moonshot" investments then I think it might be close.

In any event, I don't think you can really assert either way with confidence, so for any individual it's a more or less blind choice between being optimistic and altruistic or pessimistic and selfish. Unfortunately capitalist logic pushes us strongly away from altruism and towards maximizing individual outcomes. Of course as many have pointed out it's not actually a binary choice if you're sufficiently wealthy, the survivalism is just a form of hedging, but it does have a potentially significant opportunity cost.

Significant controlled influence on the world at large that leads back to a detectable benefit you? Not a chance. The probability of societal meltdown is small, but it's larger than any of our individual impacts. Heck, just the risk of meltdown through accidental nuclear war (easily 0.1%/century, and arguably at least 10 or 100 times that) is already large enough.

This is a question of altruism, or of whether all of these possibilities are too small to be worth spending spending time on.

Not the person you're responding to but being convinced that modern civilization is doomed - even if you're convinced it'll collapse during your own lifetime - doesn't preclude you from enjoying all of its benefits (like the Internet). If anything, it makes you more likely to enjoy them "while they last".