This is the question that decides whether you have a method or a hobby. It has a real answer, and the answer is larger than almost anyone expects.
Bet one unit at decimal odds o with true win probability p.
The outcome is + (o-1) or -1. The variance is
var = p(o-1-e)² + (1-p)(-1-e)², e = p(o-1) - (1-p)Over n independent bets the standard deviation of your average result shrinks
with 1/√n. That square root is the whole story: to halve the noise you need
four times the sample.
True probability 52%, price 2.00, 100 bets. Your edge is 4% per bet. The standard deviation of your realised ROI after 100 bets is about 10 points.
Read that again. A genuinely profitable method, after a hundred bets, is expected to show anything between a 16% loss and a 24% gain. If you stop at 100 bets you have learned almost nothing — and if you quit after a losing run, you may have quit a good method.
The standard question: how many bets to tell a 55% edge from a coin flip, with 80% power at the usual 5% significance?
| Target | Bets needed (approximately) |
|---|---|
| 55% vs 50% | 850 – 1,050 |
| 52% vs 50% | about 3,000 |
| 57% vs 52% | about 1,500 |
Those are the numbers. Not fifty. Not two hundred.
Suppose you win 55 of 100 at average odds 1.90. Your break-even is 52.6%, so you are 3.4 points ahead — but the standard error of a proportion of 0.55 at n = 100 is
se = √(0.55 × 0.45 / 100) = 0.0497So the 95% interval on your true hit rate is roughly 45% to 65%. That interval contains break-even. You have not demonstrated an edge; you have demonstrated a sample.
Write the interval, not the point estimate. When someone shows you "74% over 21 picks", the honest interval is about 53% to 89%. It contains both skill and luck, and no viewing of the picks will separate them.
This is not a reason to avoid measuring. It is a reason to measure longer, and to state the uncertainty instead of hiding it.