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Yield and variance: how many bets you need before you know
With a true 2% yield at odds of 2.00 you need 9,600 bets before it separates from zero. After 100, the margin of error is ±19.6%: almost everything you see is still noise.
Pubblicato il 14 settembre 2026
Yield is return per unit staked: what you made divided by what you put through. Stake 1,000 euros in total and finish 20 up, and your yield is +2%. It is the right measure, because it doesn't depend on how much you stake each time.
The question almost nobody asks is how many bets it takes for that number to mean anything. The answer is: far more than people place.
How many bets it takes
A bet at 2.00 returns +1 unit if it wins and −1 if it loses. If your true win probability is 51%, your true yield is +2%: you are ahead. But the standard deviation of a single bet is 1.0 units, fifty times your edge.
For the edge to emerge from the noise it has to accumulate. This table says how many bets are needed for a true yield to be distinguishable from zero at the usual 95% confidence.
| Odds | +1% | +2% | +3% | +5% | +10% |
|---|---|---|---|---|---|
| 1.20 | 7,372 | 1,764 | 748 | 243 | 43 |
| 1.50 | 19,012 | 4,702 | 2,067 | 727 | 170 |
| 2.00 | 38,411 | 9,600 | 4,265 | 1,533 | 381 |
| 3.00 | 77,210 | 19,396 | 8,661 | 3,147 | 803 |
| 4.00 | 116,009 | 29,192 | 13,058 | 4,760 | 1,226 |
| 6.00 | 193,606 | 48,783 | 21,850 | 7,987 | 2,071 |
| 10.00 | 348,801 | 87,966 | 39,436 | 14,441 | 3,761 |
The arithmetic is the standard one: a bet at odds q with probability p returns p·q − 1 on average, with standard deviation q·√(p(1−p)). After n bets the standard deviation of the mean divides by √n, and the true yield has to exceed 1.96 of those.
Two things the table says immediately
First: a small edge requires a number of bets beyond almost anyone's reach. At 2.00, proving a +2% takes 9,600 bets. At five a week, that is thirty-seven years.
Second, less obviously: the odds you play matter enormously. The same +2% takes 1,764 bets at 1.20 and 87,966 at 10.00, fifty times as many. Long odds carry huge variance, and variance is the time it takes to know.
And in reverse: how wrong the number you see can be
The same arithmetic, turned around: after n bets at 2.00, how far the observed yield can sit from the true one.
| Bets | Margin of error |
|---|---|
| 50 | ± 27.7% |
| 100 | ± 19.6% |
| 250 | ± 12.4% |
| 500 | ± 8.8% |
| 1,000 | ± 6.2% |
| 2,500 | ± 3.9% |
| 5,000 | ± 2.8% |
| 10,000 | ± 2.0% |
After a hundred bets the margin is ±19.6 points. That means an observed +15% is consistent with a true −4%, and a −10% is consistent with a true +9%. Across a hundred bets, almost everything you see is noise.
It is why a winning run isn't proof, and neither is a losing one. And why anyone selling «three months at +30%» is showing a number that, at that sample size, cannot tell a method from a coin.
What to do with it
- Track the number of bets, not just the balance. The balance doesn't say where you are on the curve; the count does.
- Look at the interval your yield sits in, not its point value. With 250 bets and +5% observed, the honest answer is «between −7% and +17%».
- If you play long odds, accept that you won't know for a long time. That isn't a flaw in the method: it is the mathematics of long odds.
- ⚠ Don't use these figures to decide stake sizes. They say how long measuring takes, not that there is something to measure.
The OddSonar log records the stake and the odds of every bet, and computes turnover, profit, ROI, win rate and bet count. ⚠ It does not produce the odds-band split or the interval on this page: to get those, export the log to CSV and separate the bands in a spreadsheet.