Risk of ruin in trading: the number that matters

Every risk of ruin calculator asks for your win rate and your risk per trade, then tells you the odds of losing your whole account. The number is usually tiny, and it is answering a question you will never face. Nobody rides an account to zero with their rules intact. You stop at 20% down, or 30%, or the prop firm stops you at 10%.

The question worth answering is narrower: at the risk you take today, what is the chance you ever hit the drawdown you would quit at? That number is rarely tiny, and it moves far faster with position size than intuition suggests.

Why the textbook formula misleads you#

The formula repeated on most risk of ruin pages is:

risk of ruin = ((1 − win rate) / win rate) ^ units of capital

It comes from gambling, where every bet wins or loses the same amount. Trading does not work like that, and the formula breaks visibly the moment you feed it a normal trading profile.

Take a strategy that wins 45% of the time, with +2R winners and −1R losers. It makes money: the average trade is worth +0.35R. But the base of the formula is 0.55 / 0.45 = 1.22. Raise a number above 1 to any power and you get something above 1, which the formula reads as certain ruin. The payoff size is simply not in the equation.

The variants that do add payoff size still define ruin as a zero balance, usually with fixed-dollar bets. If you risk a fixed percentage of your current balance, your size shrinks as the account shrinks, and you never literally reach zero. The model answers a question about someone else's sizing.

Define ruin as your quit line#

Replace "zero" with the drawdown at which you would stop trading the strategy. That might be:

• the level where you would lose confidence and abandon the system,
• the maximum loss on a prop-firm evaluation,
• the point where the money stops being money you can afford to lose.

Write it down as a percentage of your starting balance. Everything below uses 20% as the example quit line, but the arithmetic works for any number.

Then turn that percentage into risk units. If you risk a fixed fraction of the account on each trade, each loss is taken from a slightly smaller balance, so the distance to your quit line is approximately:

risk units to quit line ≈ ln(1 / (1 − quit line)) / risk per trade

At 2% risk and a 20% quit line: ln(1 / 0.8) = 0.2231, and 0.2231 / 0.02 = 11.16 units. That is the continuous approximation used below. Ten straight losses at 2% leave you at 0.98¹⁰ = 81.7% of the starting balance. Eleven leave you at 80.1%, still a hair above the line. Twelve full losses are required to fall below 80%.

That number, the count of losing units between you and your quit line, is the most important figure in this post. Everything else is a question of how likely your strategy is to lose that many units net, at any point, before the edge pulls you away from the line.

To estimate the odds of reaching it, you need three inputs, and you have already met two of them if you read how many trades before you know a strategy works:

• Mean R: your average result per trade, in R-multiples.
• Variance of R: how widely individual outcomes scatter around that average (the standard deviation, squared).
• Risk units to your quit line, from the step above.

For a strategy with a positive edge, a good approximation of the probability of ever hitting your quit line is:

risk of ruin ≈ e ^ −( 2 × mean R × risk units / variance of R )

The shape is what matters. The edge and the distance to the line sit on top of the fraction; the scatter sits underneath. And the whole thing is in an exponent, so small changes in risk per trade produce large changes in the result.

Worked example: 1% versus 2% risk#

Same strategy as before: 45% win rate, +2R winners, −1R losers.

Mean R:

(0.45 × 2) + (0.55 × −1) = 0.90 − 0.55 = 0.35R

Variance of R, the average of the squared outcomes minus the square of the mean:

(0.45 × 4) + (0.55 × 1) = 1.80 + 0.55 = 2.35
2.35 − (0.35 × 0.35) = 2.35 − 0.1225 = 2.2275

At 2% risk per trade, with a 20% quit line, you have 11.16 risk units:

exponent = 2 × 0.35 × 11.16 / 2.2275 = 7.81 / 2.2275 = 3.51
risk of ruin ≈ e^−3.51 ≈ 0.030, about 3%

At 1% risk per trade, the distance doubles to 22.31 units:

exponent = 2 × 0.35 × 22.31 / 2.2275 = 15.62 / 2.2275 = 7.01
risk of ruin ≈ e^−7.01 ≈ 0.0009, about 0.09%

Halving your risk did not halve the danger. It cut it by a factor of more than thirty, because the distance to the line sits in the exponent. The reverse holds too: the step from 1% to 2% feels like a modest increase in aggression, and it is a roughly thirtyfold increase in the chance of hitting your quit line.

I ran this on SMC, the same book as in how many trades before you know a strategy works. That post used mean +0.18R and a standard deviation of 2.15R on 312 trades. The live sample is now 317 trades: mean +0.16R, standard deviation 2.13R, variance 4.55. Same shape — a ~25% win rate with winners around +3.5R. I would stop trading it at 20% down. Recent SMC trades are sized at 1%; for most of the sample the usual size was 2%.

At 1% risk, 22.31 units to the line:

exponent = 2 × 0.16 × 22.31 / 4.55 = 7.14 / 4.55 = 1.57
risk of ruin ≈ e^−1.57 ≈ 0.21, about 21%

At 2% it is about 45%. Halving risk did not cut the danger by thirty here. SMC is the thin-edge column in the table below, not the +0.35R example, so the distance in the exponent has less to work with. The ceiling that keeps a 1% chance of hitting the 20% line is about 0.35% per trade. I am still at 1%. The number did not change how much I risk. It told me the 1% I already moved to is still the loose choice.

The same math across risk levels#

The approximation is close for strong edges and small risk, and it turns optimistic for thin edges at larger size. The table below is a simulation instead: 20,000 simulated accounts per cell, fixed-fractional sizing, binary +R / −1R outcomes, 3,000 trades each, and a 20% quit line measured from the starting balance. You can check the pattern yourself with the Monte Carlo simulator.

Both columns are profitable strategies. At 1% risk the thin-edge column already has a one-in-sixteen chance of hitting the quit line. At 2% it is more than one in four. Traders in the second column who size like traders in the first column are the ones who "had an edge and still blew the account". Both parts of that sentence are true.

Your win rate is an estimate, and the error is large#

Every number above assumes you know your win rate. You do not. You measured it from a sample, and small samples are loose.

Say you have logged 60 trades and won 45% of them. The standard error of that win rate is:

√(0.45 × 0.55 / 60) = √0.004125 = 0.064

That is 6.4 percentage points. A true win rate of 39% is entirely consistent with what you observed, one standard error below it.

Rerun the strategy at 39% with the same +2R / −1R payoff. Mean R drops from 0.35R to 0.17R: (0.39 × 2) − 0.61 = 0.17. In simulation, the chance of hitting a 20% quit line at 2% risk goes from 2.5% to 18%. The strategy did not change. The only difference is how optimistic your read of 60 trades was.

This is the practical reason to size from a pessimistic estimate of your edge, not your measured one. The measured number feels true. The pessimistic one has to be survivable.

FIB is the one. The first 30 trades, April to August 2025, won 53% with a mean of +0.47R and a variance of R of 2.07. I was risking 2%. Plug those numbers into the formula and the chance of hitting a 20% quit line is about 0.6% — small enough that 2% feels conservative.

At 60 trades the win rate was 43%, the mean was +0.18R, and the variance of R was 1.94. The standard error of that win rate is 6.4 percentage points, the same figure as the worked example above. One standard error below the measured rate is 37%.

The book settled at 98 trades: 36% winners, mean +0.007R, variance of R 1.86. That is not a mild haircut. It is the pessimistic number. At 2% risk the formula now reads about 92%. The strategy did not change. The sample got honest.

Would 2% have survived the real number? On this particular path, a constant 2% never printed 20% down from the starting balance — the first 30 trades built a 31% cushion, and giving it all back still left the account roughly flat. From the peak it was a 34% hole. The 2% I was using at trade 30 was sized for a 0.6% risk of ruin that was never real. I kept taking FIB through a 58-trade September at 28% winners and −0.29R a trade. I did not cut size. I just stopped, eventually.

Turning it around: how much should you risk?#

Rearrange the approximation and you can start from the risk of ruin you are willing to accept and solve for position size:

risk per trade ≈ 2 × mean R × ln(1 / (1 − quit line)) / (variance of R × ln(1 / acceptable risk of ruin))

With a 20% quit line and a 1% acceptable chance of hitting it, ln(1 / 0.8) = 0.2231 and ln(1 / 0.01) = 4.605:

This is where the 1% rule sits in context. It is a reasonable default for someone who has no data. Once you do have data, it can be too loose for a thin edge and more conservative than needed for a strong, well-measured one. Remember the approximation runs optimistic for thin edges, so treat these figures as ceilings, not targets.

Once you have a risk percentage, the position sizing calculator turns it into a position size from your balance and stop distance. That step needs to be the same calculation every time.

My quit line is 20%. I did not derive it from this formula, and I did not write it down before I needed it. I picked it after the fact because it is where I would actually stop trading a setup — not zero, and not the 10% a prop firm would have stopped me at.

The last time I blew an account I was not at 1%. January 2026: 46 trades, −9.9R, median risk 8%, average 13%. At 8% per trade, three losses cross 20%. I took forty-six. I did not stop at 20%. Compounded on the sizes I logged, the month finished around 6% of where it started. The next month the median was 1%, and that is still what I use.

The formula in this section would have told me 8% was a quit line with a three-trade fuse. I did not run it. I used a smaller number after the account was gone.

What this calculation does not tell you#

• It measures from your current balance, not from your peak. A trailing drawdown, where the limit follows your highest balance, is stricter. Given enough time, a strategy with normal variance will eventually have some 20% dip from some peak. If you trade an evaluation with a trailing rule, read the firm's rules precisely; the prop firm use case covers how to journal those trades.
• It assumes independent trades. Three correlated positions on the same catalyst behave like one large position. Your real risk units are fewer than your trade count suggests.
• It assumes a loss is −1R. Gaps, slippage, and moved stops produce losses larger than 1R, and each one moves you closer to the line than the model expects. If your journal shows losers regularly worse than −1R, use your recorded R-multiples, not the textbook ones.
• It assumes a stationary edge. The formula knows your past sample. It does not know whether the market regime that produced it still holds.
• It does not include daily loss limits or time limits. An evaluation that ends after 30 days, or that fails you on a single bad day, is a different problem with a shorter fuse.

What to do with this#

Write down your quit line as a percentage. Pull your recorded R-multiples for one strategy and calculate the mean and the variance. Put them through the formula at the risk you currently take, then again at a win rate five or six points lower than the one you measured.

If the second number is one you would not accept, the fix is not a better setup or more screen time. It is a smaller risk percentage, applied the same way on every trade. Of the three inputs, your edge is uncertain and your quit line is fixed by your circumstances. Position size is the only one you set yourself before each trade.