Okay, I've finally figured out what I'd do with the non-me money: Crowd-sourced humanitarian initiatives.
$10mil: buy a SuperBowl 30-sec slot ($5mil) and a few other global and extremely high-profile bits where a competition to submit the "best" idea of how to use a half-billion dollars to help humanity would be cleverly advertised. The top nine ideas (chosen exclusively by a secret committee) each win a million dollar cash prize, and 91 second-place ideas win $10K each. Obviously, some lawyers would go over the contest rules ensuring no patents or other entanglements, submissions are the property of me, "best" and "help humanity" is interpreted only by me for prize selection purposes, etc etc etc.
I'd expect ideas to cover typical efforts toward space exploration/colonization, disease eradication, global peace efforts, max-efficiency charity, and certainly some unexpected and clever possibilities.
I pick the top idea among the nine and actually execute on it (possibly tweaking to suit me) with a half-billion.
And, I'll see if I can pull in the highest-net-worth global multibillionaires (Gates, Buffett, Carlos Slim, Amancio Ortega, Larry Ellison, the Kochs, the Waltons, etc) or other notable billionaires (CEOs of Google, Facebook, SpaceX, Amazon, etc) to do any matching on the idea execution, or whether they'd agree to execute on one of the other eight finalists - perhaps even see in advance if they would be part of the competition secret committee, which would add to the visibility of the ad campaign.