Risk of Ruin in Betting: What Are the Chances I Go Bust, Even With an Edge?

The question

"I've got a real edge. Surely I can't go bust?"

You can, and plenty of bettors with genuine edges have. Risk of ruin in betting is the chance that a normal run of bad luck empties your bank before your edge has time to show, and the stake you choose controls it far more than the edge does.

The idea in one sentence

Your edge pushes your bank up on average, luck pushes it around, and the risk of ruin is the chance luck pushes it to zero first, which depends mostly on how many stakes deep your bank is.

The picture

Picture your bank as a walker on a path with a cliff edge behind them. Every bet is a step: a big step forward when you win, a small step back when you lose. The edge means the steps drift forward on average. The luck means they wander.

Start close to the cliff (a bank of only a few stakes) and a short wander backwards is enough to go over.
Start far from the cliff (a bank of many stakes) and the drift carries you away before the wandering can catch you.

Here's a bettor with a genuine +5% edge at odds of 3.0 (a 35% win rate), 2% commission, staking the same amount every time. The only thing that changes is the stake as a share of the starting bank.

Stake per bet	Bank in stakes	Ever lose half the bank	Ever go bust	Go bust within 1,000 bets
5%	20	69%	48%	42%
2%	50	40%	16%	8.5%
1%	100	16%	2.6%	0.3%

Same edge, same bets. At 5% stakes it's close to a coin toss whether the bank survives. At 1% it's about a one-in-forty chance, ever.

Try it · Risk of ruin

Edge before commission (ROI)+5.0%

Stake as % of starting bank2%

Average decimal odds

Starting bank (£)

Commission

Horizon for the "within" figures

Ever lose half the bank

40.1%

Ever go bust

16.1%

Within 1,000 bets: halved 32.2%, bust 8.82% (4,000 simulated bankrolls)

Stake as % of starting bank

Win rate 35.0%Per £1 after commission +3.60pr = 0.03653Quick version 0.03612

Your bank is 50 stakes deep (£20.00 a bet). For a 1% risk of ruin you'd need about 127 stakes (£2540 at this stake size).

Assumes level stakes and independent bets. The top two figures are for betting forever; the “within” figures come from a quick simulation.

Worked Betfair example

You back at an average of 3.0 in Match Odds and Over/Under markets. Your true win rate is 35%, a +5% edge before commission. Bank £1,000, level stakes of £20 (2% of the starting bank). (Illustrative figures; checked against 20,000 simulated bankrolls.)

Profit per £1 bet after commission. A win pays 2 × 0.98 = £1.96. Expected profit: 0.35 × 1.96 − 0.65 = +£0.036 per £1, or +3.6%.
How much each bet swings. The standard deviation of one £1 bet is √(0.35 × 1.96² + 0.65 − 0.036²) ≈ £1.41. The swing is 40 times the edge.
Your bank in stakes. £1,000 ÷ £20 = 50 stakes.
The ruin rate r. Solve 0.35 × e^(−1.96r) + 0.65 × e^r = 1. The answer is r ≈ 0.0365. (The shortcut 2 × edge ÷ variance = 2 × 0.036 ÷ 1.993 ≈ 0.0361 gets you almost the same.)
Chance of ever going bust. e^(−0.0365 × 50) ≈ 16%. Our simulation gave 16.0%.
Chance of ever losing half the bank. e^(−0.0365 × 25) ≈ 40%.
The fix: drop to £10 stakes. Now the bank is 100 stakes deep and the risk of ruin is e^(−0.0365 × 100) ≈ 2.6%. You've given up half your profit per bet and cut the chance of going bust by a factor of six.

Verdict: at £20 stakes, a real edge still has a one-in-six chance of going bust. That isn't the edge failing; it's the stake being too big for the bank.

How big a bank do you need?

Flip the formula round. For a 1% risk of ruin with this edge, you need about ln(100) ÷ 0.0365 ≈ 126 stakes in the bank. For 5%, about 82 stakes. Longer odds or a thinner edge need more.

The formula

Risk of ruin for level stakes

P(\text{ruin}) \approx e^{-r B}

B is your bank measured in stakes (bank ÷ stake).
r is the ruin rate, set by your edge and your odds (below).
e is the constant 2.718…

In plain English: every extra stake in the bank multiplies the risk by the same factor, e^(−r). Double the bank in stakes and the risk is squared. That's why a smaller stake is so powerful.

Finding r exactly

p\,e^{-r w} + q\,e^{r} = 1

p is your win rate and q = 1 − p.
w is what a £1 win pays after commission: (odds − 1) × (1 − commission).

In plain English: r is the one number that balances the pull of the wins against the pull of the losses. A calculator solves it in a blink; the tool above does.

The quick version

r \approx \frac{2\mu}{\sigma^{2}}

μ (mu) is your expected profit per £1 staked, after commission.
σ² (sigma squared) is the variance of one £1 bet.

In plain English: a bigger edge or a smaller swing makes ruin less likely. With no edge, μ is zero or below, r is zero, and ruin is certain given enough time.

Proportional staking

If you stake a fixed percentage of your current bank, as Kelly does, you shrink your stakes as you lose and never literally hit zero. The risk that matters then is a deep fall, such as losing half. That's covered in Lesson 6.2 and Lesson 6.4.

Try it

Enter a 5% edge, odds 3.0, 2% commission and a 2% stake, and check you get about 16% for going bust and 40% for losing half. Then halve the stake to 1% and watch both figures fall far faster than the stake did.

Common mistakes

Thinking an edge makes you safe. A +5% edge at 5% stakes is close to a coin toss to survive. The edge sets the direction; the stake sets the danger.
Measuring your bank in pounds. £1,000 means nothing on its own. £1,000 in £50 stakes is 20 stakes deep; in £10 stakes it's 100.
Using a bigger edge than you really have. Risk of ruin is very sensitive to μ. If your +5% is really +2%, the numbers are much worse. Plan with a cautious edge.
Ignoring odds. At longer odds each bet swings more, so the same edge needs a deeper bank.
Forgetting correlated bets. Several bets on the same match can all lose together, which is one bigger bet in disguise.

Why real edges are thinner than they look on paper: why good models still lose money.