Any finite collective eventually loses almost surely, but the larger the collective, the longer it takes, and the greater the inequality in the meantime, before

Any finite collective eventually loses almost surely, but the larger the collective, the longer it takes, and the greater the inequality in the meantime, before everyone loses. In the limit, an infinite collective exhibits the paradoxical behavior from the article: expected value goes up forever, but almost every individual eventually loses. An ever smaller slice of huge winners is pulling up the average, but in any finite population this slice disappears in finite time. Only in an infinite population can it persist indefinitely. All of this is fairly straightforward for a mature student of probability. If enough folks want, maybe I could write up the details to prove these things.