How long before you could tell?

What the video says

1. How long before you could tell a real edge from luck?

   Not whether it works. How many years of it you would need to see.

2. Here is the same strategy, run again and again.

   320 runs, and every one of them has the same real edge: 0.50 a year.

   Not one of these is a fake. The only thing that separates them is luck, and the line each one draws is what its owner would actually see.

3. Now draw the line they have to clear.

   At 2 years it sits at 1.39. At 25 years, at 0.39.

   The line comes down as the history lengthens, and that is the only reason waiting helps at all. Anything under it is indistinguishable from nothing.

4. So count the ones that got above it.

   After 5 years, 30%. After 10, 40%. After 25, 72%.

   The rest are real edges that look like nothing. Their owners gave up, or never started, and they were right about the evidence and wrong about the strategy.

5. The formula names a number, and it is not the answer.

   An edge this size needs 15.4 years. At 16, 53% have got there.

   About half have not. The formula describes the average run, and nobody gets the average run — they get one of these.

6. Everything depends on how big the edge is.

   An edge of 1.00 takes 3.8 years. An edge of 0.25 takes 61.5.

   Halve the edge and you do not double the wait. You quadruple it, every time, exactly.

7. There is only one lever here.

   You cannot shorten the wait by being more careful, or more rigorous, or more patient. You shorten it by finding a bigger edge. Nothing else in this arithmetic moves.

8. And this is the generous version.

   The edge here never changes, each year is drawn independently of the last, and exactly one thing is being tested. Loosen any of the three and this arithmetic stops applying — it does not bend in your favour.

9. What this rests on.

   The edge is chosen. The seed is fixed, so the runs redraw identically.

10. Where this stops.

    The edge, and the way the years are drawn around it: ASSUMED. The runs are a seeded simulation, worth exactly what that assumption is worth: ASSUMED. And nothing here was measured: MISSING.

11. Nothing here was measured.

    The waiting time is one line of arithmetic you can check on a calculator. The spread around it is simulated, and the seed is printed under every frame above. Not investment advice.

Evidence behind it

• The arithmeticCONFIRMED
• The edge, and how the years are drawnESTIMATED
• The runs shown (a seeded simulation)ESTIMATED
• Anything measuredMISSING

Marks open only as wide as each input’s evidence class allows. See Method.