Hmmm, I wonder if the ratio of "insane billionaires : insane people in mental institutions" correlates to the ratio of "sane billionaires : sane people (presumably not in mental institutions)"?

Are you more or less likely too be a billionaire if you're insane?

(Is there even such a thing as a "sane billionaire"?)

It depends on how we define "sane", doesn't it?

If we just mean "not evidently delusional or psychotic", then probably a billionaire is no less likely to be sane than anyone - probably if anything more so, one power of money being that of reliable access to medical care.

If we instead by 'sane' mean "firmly grounded and operating within consensus reality", as I once heard the term defined, then I think the question becomes considerably more interesting. (Whose consensus?)