Why patience is mathematical rather than moral

Expected profit grows in proportion to the number of bets, while the spread of possible outcomes grows only with its square root. Four times as many bets means four times the expected profit and twice the noise.

That divergence is what eventually makes an edge visible. It is also why nothing is visible early: at small numbers the noise term dominates completely, and the result carries almost no information about the process.

It also means an unprofitable process takes just as long to reveal itself, and will produce winning months on the way. The mathematics is symmetric and offers no early warning in either direction.

Which is where it goes wrong. Short records prove nothing in either direction, which is inconvenient for everybody — the person selling a good month and the person abandoning a bad one are making the same error.

What to do with it. Set the review horizon in hundreds of bets rather than in weeks, and refuse to draw conclusions before reaching it.