In one sentence
Risk of ruin is the chance that your betting bank hits zero, or a level you cannot continue from, given your edge, your stake size and the odds you bet at.
How it works
Even with a real edge, results arrive in a random order. If your stakes are large relative to your bank, an early bad run can finish you before the good results arrive. Risk of ruin puts a number on that danger.
Think of the bank as a walker on a cliff path. The edge is a gentle slope away from the edge; the randomness is a wobble. A small bank or big stakes puts the walker close to the cliff, where one wobble is enough.
Two facts matter most. With no edge, or a negative one, ruin is certain eventually at flat stakes. With a positive edge, ruin risk falls very fast as the bank grows in units of stake.
The maths
For even-money bets at flat stakes, the classic gambler's ruin result gives:
For any odds, a good approximation is:
- p is the win probability and q = 1 − p.
- U is your bank measured in stakes (bank ÷ stake).
- μ is the expected profit per bet in units of stake, after commission.
- σ² is the variance of the result of one bet, in units of stake squared.
In plain English: ruin risk falls exponentially as your edge and your bank in units rise, and rises as the bets get more volatile.
Worked betting example
You have a £500 bank, stake £20 a bet (25 units) and back Over 2.5 goals at evens (2.00) with a true win rate of 52%, an illustrative edge. The first sums leave out commission.
- Edge per bet: 0.52 − 0.48 = 0.04 units, or £0.80.
- Exact risk of ruin: (0.48 ÷ 0.52) to the power 25 = 13.5%.
- Approximation: variance ≈ 0.998, so exp(−2 × 0.04 × 25 ÷ 0.998) = 13.5%.
- A simulation of 20,000 banks over 5,000 bets gave 13.9% ruined, close to the formula.
Now change the bank, keeping £20 stakes:
| Bank | Units | Risk of ruin |
|---|---|---|
| £250 | 12.5 | 36.8% |
| £500 | 25 | 13.5% |
| £1,000 | 50 | 1.8% |
Doubling the bank from £500 to £1,000 cuts the risk by a factor of more than seven.
Add 2% commission and a win pays 0.98 units instead of 1, so the edge shrinks from 0.04 to 0.030 units per bet. With the same £500 bank, risk of ruin rises from 13.5% to about 22%, and a simulation over 5,000 bets gives 21%. With no edge at all, 72% of simulated banks were wiped out within 5,000 bets, and the rest would follow eventually.
Where it's good
- Choosing a stake size before starting a new strategy.
- Deciding how big a bank you need for a given edge and stake.
- Showing clearly why a small edge plus commission plus big stakes is dangerous.
- Setting stop-loss or review levels, for example "risk of losing half the bank" instead of all of it.
Limitations and pitfalls
- Every formula depends on the true edge, which you only estimate. Overstating it makes ruin look far less likely than it is.
- The simple formulas assume flat stakes and independent bets with similar odds. Mixed odds, correlated bets and changing stakes need simulation.
- Percentage staking makes literal ruin impossible in theory, but you can still lose 90% of the bank; ask for the risk of a large drawdown instead.
- Betfair minimum stakes mean a shrinking bank eventually cannot place bets, a practical form of ruin.
- Long-odds betting has much higher variance, so ruin risk is far higher for the same edge.
- The number ignores life: most people stop or change strategy long before literal ruin.
How to build it
- Use the formulas in a spreadsheet for quick checks.
- For realistic cases, run a Monte Carlo simulation in numpy with your actual odds distribution, commission and staking rule.
- Test several edge assumptions, including a pessimistic one.
- Practical tip: a common target is a risk of ruin under 1%. At evens that needs about 58 stakes with a 4% edge and about 115 with a 2% edge, and far more at longer odds.
Related methods
- Fixed stakes – the staking plan the classic formula assumes.
- Kelly criterion – percentage staking that avoids literal ruin.
- Drawdown analysis – the softer version of ruin that matters in practice.
- Brownian motion and random walks – the maths behind the approximation.
- Monte Carlo simulation – the tool for realistic cases.