>>>The odds of her results being "luck" have been calculated at 31 Trillion to one.
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>Right, but calling it "luck" is a straw man. E.g. consider that in the banking crisis, people who bet against/contributed to the fall of the US economy made billions. Nobody called that luck- so why attribute HRC's wins to luck rather than accurate market prediction by competent advisors? She never said it was just fabulous good luck, she attributed it to good advice and stopping when she was pregnant with Chelsea. The only "luck" reasonably attributed is that she stepped away at the perfect time, unlike her advisers who came a cropper when the market changed. IOW she followed the oldest gambling advice to quit while you're ahead. And she gave a perfectly plausible explanation for why she stopped when she did.
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>Also I'd note that one of her advisors was a regular finalist in one of those Las Vegas card playing events. You could argue that the fall of cards is just luck, but every year the same names make it through thousands of other players to appear in the finals. The chances of the same 5 or 6 always appearing together at the end also are astronomical, except that nobody says "you can't be that lucky" and attributes it to corruption.

Your first paragraph is ok, adding in a non-random influence skews random calculations. Second example just shows that in some card games knowledge of the game is more important than card distributions encounterd via the random process. Germans participating would have to tax winnings, as our IRS equivalent says it is NOT chance (lottery-like winnings are tax free)

The fact that HRC had not to cover - hmmm, that is more similar to a card dealer allowing her to keep some cards she wants to ;-)