Good points, but continuing with the thought experiment, I think you fail to consider what might be a reality for your psychics. What if the psychics don't have

Good points, but continuing with the thought experiment, I think you fail to consider what might be a reality for your psychics. What if the psychics don't have perfect information, nor perfect control, but have, perhaps varying on the psychic in question, some amount of power that lets them see or control future numbers with some amount of probability, but not certainty? In that case, they might win more often, but not every time. Given that so many things in nature follow a power curve or a bell curve, I think your presumed psychic abilities, we can assume, follow the same curves, and if most of your psychics then have "some ability" to predict these numbers, but not a certainty, then I think they are more likely to be frequent smaller winners. For example, if you have an ability that let's you see a 4/8 of the future numbers, with 33% certainty, then one time out of three, you will win 4/8 of the numbers, and sometimes more than 4/8 if you're lucky. TL;DR -- your presumed psychic abilities probably exist on a spectrum ( bell / power curve ) and likely most of your psychics do not have "perfect" future information. PS - I have a feeling that psychics would prefer to play the stock market, than lottery. I just sense their expected payoff is higher in that case, probably because there are a lot more factors that affect a stock price, so even partial information across a lot of these seems to provide a better advantage, than partial information on 1 single list of numbers.