Hobbit on Quest
But, that's the thing about randomness. Sure, you might get an even distribution, but, there's no guarantee of that. It's equally possible that you get group in random choices, meaning that you might wind up wiping out everyone with any medical training, for example, simply through random chance.
It really is a mad idea.
Well, he is the Mad Titan. Would it seem less mad if all the destruction were still essentially Thanos's love letter to the personification of Death? It may seem like that's, at least, is a bit better thought out than annihilating half the population for population management - but it's still madder than a hatter.