RE: Could it be possible to profitably trade a random walk?
The key for why he gets this result is in the original article:
Let us set a take-profit order on the upper Bollinger line at a distance of two standard deviations and a stop-loss order – on the bottom line at a distance of four standard deviations from the 15-bar moving average line of closing prices.
Essentially he's saying that when his random price gets through a 2 SD entropy barrier he wins, when the price gets through a 4 SD entropy barrier he loses, otherwise he lets it ride. If the entropy barrier for accepting a loss is 2 SD higher than for accepting a win, it's entirely reasonable that N = 30 is too small a sample to see any losses.
This is similar to the martingale system -- if you set the criterion for quitting to be either a small win or a large loss, then it's entirely possible to see a long run of wins for zero or negative EV, because the balance to those modest positive outcomes of very high probability gets concentrated into a single disastrous outcome of very low probability.
It's even worse than this. For the system that profited on all 30 series, he used a 1SD profit target and a 5SD stop loss. And he did make thousands of trades, with many losses. It's hard to read this blurry image, but it looks like he optimized on those two parameters:
With #OptVar1 50 and #OptVar2 10 corresponding to the 5SD stop and 1SD target. So it could be an issue of curve fitting, where he just kept optimizing until he found a set of parameters that worked.