> if you model the stock market as a machine that simply gives random payouts drawn from some distribution, what is the probability that a set of 1,551 groups o

> if you model the stock market as a machine that simply gives random payouts drawn from some distribution, what is the probability that a set of 1,551 groups of 300 random draws from that distribution would contain at least one set that averages more than $310? If the paper ran such a model, I didn't see it. The abstract says the trader who made $310/day had a standard deviation of $2560 (presumably per day). Over 300 samples, that's a standard deviation of 2560/sqrt(300) or $150/day. So if he really had a breakeven strategy and got lucky, he was 2 standard deviations from the mean, or in the top 2.5%, and you'd expect 40 other traders to have done just as well, and it would be vanishingly unlikely that nobody else did. Not quite what you were asking, but I don't think there's enough information at least in the abstract to answer your question. The payout distribution will be largely dependent on the size of the traders' positions and riskiness of their strategies.