I just ran some monte carlo simulations. Turns out I was totally wrong, at least for a uniform distribution. I now suspect it's probably true for any distribu

I just ran some monte carlo simulations. Turns out I was totally wrong, at least for a uniform distribution. I now suspect it's probably true for any distribution, but I can't prove it yet. It just seems really odd to me: It seems like because you get 9x the number of dice rolls for one group you would end up with a final distribution that favors the majority group, but that is obviously not the case. I need to wrap my brain around that one.