Um, what? If anything, applying the theorem in this case would say that profits should be normally distributed, whereas it's fairly common for market makers to have perfect/near-perfect trading records.
Sorry, that was vague. My point was that market participants who make many trades will rapidly converge on their mean return, with little fluctuation. If you sample a normal distribution 10M times with a mean of 0.01%, you will very rarely see a negative sum of the samples.
The theorem says nothing of the sort. By your argument, if I flip a coin 10M times, where heads is 1 and tails is -1, and get a mean of 0, then I will very rarely see tails. You're confusing mean and variance.
Ok, I think your main idea was that since they've achieved consistently positive returns, then they're likely to keep it up. Even if that were true, the 800lb gorilla question is how they've managed to achieve such consistency in the first place.
They have slightly positive return per trade, and they make millions of trades per day. Their PnL is the sum of their trades -- the expected values grows like O(n), while the volatility grows like O(sqrt(n)), so for n = several million, the probability their PnL will be negative is extraordinarily low.
