Guide · 6 min read
Betting variance: why results scatter around expected value
A real edge can sit in the red for hundreds of bets. That is not bad luck in the dramatic sense; it is what variance looks like at betting margins. Here is the maths behind it, a worked 1,000-bet example checked with a simulation, how long losing runs and drawdowns typically last, and why sure bets and value bets behave so differently.
Updated 22 October 2026
Contents
Expected value and results are two different things
Expected value (EV) tells you what a bet returns on average over a very large number of repetitions. A single bet never returns the average: at odds of 2.00 and a €10 stake you get +€10 or −€10, never the +€0.30 that an EV of +3% implies.
For example, if the true probability is 51.5% and the odds are 2.00, EV is 0.515 × 2.00 − 1 = +3% of the stake. Variance describes how far actual results scatter around that average. In sports betting it is huge relative to the edge.
The standard deviation of a bet
For a single bet with decimal odds O, win probability p and a stake of 1, you either win O − 1 or lose 1. It follows that:
σ per bet = O × √(p × (1 − p))
σ after n bets = σ × √n
EV after n bets = n × (p × O − 1)
The key lies in the last two lines: EV grows with the number of bets n, the spread only with its square root. That is why a small edge only shows through the noise after a very large number of bets. And the higher the odds, the bigger the spread: at odds of 3.00 with the same +3% EV, σ per bet is about 1.42 instead of 1.00.
Worked example: 1,000 bets at 2.00 with +3% EV
You stake one unit (for example €10) 1,000 times at odds of 2.00, each time with a true win probability of 51.5%.
σ per bet = 2.00 × √(0.515 × 0.485) = 2.00 × 0.4998 = 0.9995 units.
σ after 1,000 bets = 0.9995 × √1,000 = about 31.6 units.
EV after 1,000 bets = 1,000 × 0.03 = +30 units.
About two thirds of all paths end between −1.6 and +61.6 units, about 95% between −33 and +93 units. At €10 a unit, that means being €330 down or €930 up after 1,000 bets with a real edge is entirely normal.
We checked this with 20,000 simulated runs: in about 16% of them the balance was negative after 1,000 bets, despite the positive EV. The table shows how the picture shifts with more bets (normal approximation, rounded):
| Bets | EV (units) | σ (units) | Chance of being down |
|---|---|---|---|
| 100 | +3 | 10.0 | about 38% |
| 500 | +15 | 22.3 | about 25% |
| 1,000 | +30 | 31.6 | about 15 to 17% |
| 5,000 | +150 | 70.7 | about 2% |
| 10,000 | +300 | 99.9 | about 0.1% |
Assumptions: independent bets, always odds of 2.00, true probability exactly 51.5%, a flat stake of one unit. In practice you do not know the true probability; if it is lower than you think, EV is smaller or negative.
How long losing runs can last
With a 51.5% hit rate you lose each bet with a 48.5% probability. The longest losing streak in n bets is roughly ln(n × p) ÷ ln(1 ÷ (1 − p)), here ln(515) ÷ ln(2.062) ≈ 8.6 losses in a row. In our simulation the median longest streak was 9 losses, and in 9 out of 10 runs it was 11 or fewer.
More important than the streak is the drawdown: the gap between your previous high and the low point that follows. The median largest drawdown was 26 units, and in 9 out of 10 runs it was at most about 44 units. At €10 a unit, a fall of €260 to €440 is not a sign that something is broken; it is ordinary for a 3% edge. Someone starting with €300 and €10 stakes can go bust in a perfectly normal phase. How to size stakes against your money is covered in Kelly criterion and bankroll.
Sure bets vs value bets: variance compared
With a sure bet you cover every outcome at different bookmakers. If all legs are accepted at the shown odds and stand, the result is almost the same whatever happens: a small margin, usually 1 to 2% of the total stake. The spread caused by the match result is then close to zero.
That does not make sure bets risk-free. The swings come from other sources:
- Price changes: the second price drops before you place it, and you cover at worse odds.
- Voided bets: a bookmaker voids a leg because of a palpable error, and the other side runs unhedged.
- Deductions: if a bookmaker passes on Austria's 5% betting fee, an arb can turn into a loss.
- Limits: a bookmaker accepts only part of the stake. More in bookmaker limits.
With value bets, by contrast, you carry the full variance from the example above. Value bets are not yet available in ArbVantage (coming soon); sure bets, free-bet conversion and middles are live.
How many bets you need
A rough rule: a result only becomes meaningful once EV is about twice the standard deviation. That gives n ≈ (2 × σ ÷ EV per bet)². For odds of 2.00 and +3% that is (2 × 0.9995 ÷ 0.03)² ≈ 4,400 bets. At +1% EV it is already about 40,000.
Nobody wants to wait that long. A faster signal is closing line value: whether you regularly get better odds than the closing price shows after a few hundred bets, because that figure varies far less than your balance.
The mental side: avoiding tilt
Variance is above all hard psychologically. After eight losses in a row, many people want to raise their stake to "win it back". That is exactly the road to bigger losses. What helps:
- Set stakes in advance, as a fixed amount or a small share of your bankroll, and do not change them during a run.
- Look at results in blocks of several hundred bets, not after every day.
- Plan breaks and set deposit limits with your bookmaker.
- Only use money you can afford to lose.
If betting stops feeling good, our responsible gambling page lists free, confidential help.
Frequently asked questions
How many bets does it take for expected value to show?
It depends on the edge and the odds. At odds of 2.00 and +3% EV you need roughly 4,400 bets before the result is about two standard deviations above zero. At +1% it is around 40,000. After 100 bets your balance says almost nothing.
Do sure bets have variance too?
Hardly any from the match result, if all legs are accepted at the shown odds and stand. Swings do come from price changes before the second leg, voided bets, passed-on betting fees and limits.
What is a normal downswing?
For 1,000 bets at odds of 2.00 with +3% EV, the largest fall from a previous high in our simulation had a median of 26 units, and in 9 out of 10 runs it was at most about 44 units. Nine losses in a row are common.
Does being down after 500 bets mean my bets are bad?
Not necessarily. At odds of 2.00 and +3% EV, roughly one in four runs is still negative after 500 bets. Whether you regularly beat the closing price tells you more.
Sources
- Edward O. Thorp: The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market
- J. L. Kelly Jr.: A New Interpretation of Information Rate, Bell System Technical Journal 35 (1956)
- Kaunitz, Zhong, Kreiner (2017): Beating the bookies with their own numbers, arXiv:1710.02824
As of October 2026. Calculations and simulation (20,000 runs of 1,000 bets each) by ArbVantage; results are model values, not a forecast.
Betting involves risk, sure bets included: odds change, bets get voided and accounts get limited. Only bet money you can afford to lose. Our responsible gambling page lists free help.
Not betting, legal or tax advice. 18+. As of October 2026. See our disclaimer.