Risk of ruin explained: the maths of losing streaks and position size

Risk of ruin is the probability that a trader's account falls to a level from which they cannot or will not carry on, usually defined as a fixed drawdown such as 50%, rather than literally zero. It depends on three things: your edge (win rate and the size of wins against losses), how much you risk per trade, and how many trades you take. Of those, risk per trade is the one you control completely, and it has by far the largest effect.

This guide works through the classic formula, why it only partly applies to trading, what losing streaks really look like, and how much of an account a streak removes at different risk levels. Every number below was calculated, not estimated, and every scenario is illustrative.

What "ruin" means for a trader

In gambling maths, ruin means the bankroll reaches zero and the player can no longer bet. For a trader that definition is too narrow. Very few people keep trading the same way until the last pound or euro has gone. Long before that, one of these happens:

• The account is too small to open the minimum position size at a sensible risk.
• The trader loses confidence in the method and abandons it, often at the worst moment.
• The losses become emotionally unbearable and decisions deteriorate, as the guide to trading psychology describes.
• A personal limit is reached: "if I am down 30%, I stop".

So a practical definition is: risk of ruin is the probability of hitting a chosen drawdown threshold before reaching a chosen goal, or within a chosen number of trades. Common thresholds are 20%, 30% and 50%. Pick one before you start, because the answer changes completely depending on where you draw the line. The guide to drawdown and recovery explains why deep drawdowns are so hard to climb out of: a 50% loss needs a 100% gain to get back to where you began.

The classic risk of ruin formula

The best-known formula comes from probability theory's "gambler's ruin" problem. It assumes:

1. Every bet is even money: you win one unit or lose one unit.
2. Your probability of winning, p, is known and stays the same on every bet.
3. You stake a fixed one unit each time, whatever the size of your bankroll.
4. Bets are independent of each other.
5. You keep playing indefinitely, or until you are ruined.

Define the edge as the probability of winning minus the probability of losing (p − q, where q = 1 − p). If you start with N units, the probability of eventually losing all of them is:

Risk of ruin = ((1 − edge) ÷ (1 + edge)) to the power N

Because (1 − edge) ÷ (1 + edge) simplifies to q ÷ p, this is the same as (q ÷ p) to the power N. If the edge is zero or negative, the risk of ruin under these assumptions is 100%: play long enough and you will lose everything.

Worked example with the classic formula

These figures are illustrative and assume the conditions above.

• Win rate 55%, so q ÷ p = 0.45 ÷ 0.55 ≈ 0.818.
• With 10 units (risking 10% of the starting account per bet): 0.818 to the power 10 ≈ 13.4%.
• With 20 units (5% per bet): ≈ 1.8%.
• With 50 units (2% per bet): ≈ 0.004%.

Now drop the win rate to 51%, so q ÷ p ≈ 0.961:

• 10 units: ≈ 67.0%.
• 20 units: ≈ 44.9%.
• 50 units: ≈ 13.5%.
• 100 units (1% per bet): ≈ 1.8%.

Two lessons stand out. First, the number of units you can afford to lose matters enormously: halving the stake doubles the units, which squares the risk of ruin, so at a 55% win rate 13.4% becomes about 1.8%. Second, a thin edge needs a lot of units behind it. A 51% win rate on even-money bets is a real advantage, yet with 20 units the formula still gives roughly a 45% chance of losing the lot.

Why the classic formula does not fit trading well

The formula is a useful intuition pump, but every one of its assumptions breaks in trading:

• Wins and losses are not equal. Most strategies aim for wins larger or smaller than losses, as the risk-reward ratio guide explains. A 40% strategy that wins 2R and loses 1R is nothing like a 40% coin flip. There are extensions of the formula for uneven payoffs, but they become complicated quickly and still rely on the other assumptions.
• Your win rate is not known. You only have an estimate from a backtest or a journal, and that estimate has a wide margin of error unless the sample is large. It can also drift as market conditions change.
• Stakes are not fixed. Most traders risk a percentage of current equity, so stakes shrink after losses and grow after wins.
• Trades are not always independent. Correlated positions, such as being long EUR/USD and GBP/USD at the same time, can lose together.
• Real results include gaps, slippage and costs, so a 1R loss is sometimes 1.3R.

Treat the classic number as a lower bound on the danger, not a precise figure.

Fixed-fractional sizing never reaches zero, and that is not the point

If you always risk a fixed percentage of your current balance, mathematically you can never reach exactly zero. After a 1% loss you have 99% of the account, and the next 1% is 1% of that smaller figure. Each loss is slightly smaller in money terms than the one before. This is the logic behind the position sizing method most educators teach, and it is a real protection.

It does not make you immune to ruin in the practical sense. The account can still fall to a level that is useless. Here is how many consecutive losses (or, more realistically, how many net losses in a bad patch) it takes to hit two common thresholds:

• 0.5% risk per trade: 45 losses to reach a 20% drawdown; 139 to reach 50%.
• 1% risk per trade: 23 losses to reach 20%; 69 to reach 50%.
• 2% risk per trade: 12 losses to reach 20%; 35 to reach 50%.
• 5% risk per trade: 5 losses to reach 20%; 14 to reach 50%.

The calculation is the number of losses n where (1 − risk) to the power n first falls below 1 minus the threshold. At 1% risk, 0.99 to the power 69 ≈ 0.4998, so 69 net losses halve the account. At 5% risk it takes only 14.

There is also a mechanical floor. Brokers have minimum trade sizes, commonly 0.01 lots in forex. A small account at a tight risk percentage can reach the point where the minimum lot already exceeds the intended risk, and the position size calculator will then round the size down to zero. That is ruin in the practical sense, even with money still in the account.

Losing streaks: the numbers people underestimate

Most traders think about streaks badly. A 40% win rate sounds respectable, so ten losses in a row sounds near impossible. The probability that any particular run of ten trades are all losers is:

0.6 to the power 10 ≈ 0.0060, or about 0.6%

That is roughly 1 in 165. It is the right answer to a narrow question: "what are the chances the next ten trades all lose?" It is the wrong answer to the question that matters: "what are the chances I will suffer a ten-loss streak at some point?"

Over a long series there are many overlapping runs of ten, and each one is another chance for the streak to appear. Worked out exactly (by tracking the probability of every possible current streak length trade by trade, not by simulation), the chance of seeing at least one streak of ten or more losses at a 40% win rate is approximately:

• 10% over 50 trades
• 20% over 100 trades
• 45% over 250 trades
• 70% over 500 trades
• 92% over 1,000 trades

For a 50% win rate, a ten-loss streak is rarer but far from impossible: about 4% over 100 trades, 22% over 500 trades and 39% over 1,000.

Shorter streaks are close to certain. At a 40% win rate, the probability of at least one run of five losses is about 98% over 100 trades, and at least one run of eight losses is about 49% over 100 trades and 97% over 500.

The practical point: if you trade a lower win-rate strategy for a year or two, a streak of ten or more losses is not bad luck to be explained away. It is the expected outcome, and your sizing should survive it comfortably. Note that these figures assume trades are independent and the win rate is exactly as stated. If the true win rate is lower than your estimate, or losses cluster in certain market conditions, real streaks will be longer.

What a ten-loss streak does to the account

Here is the same ten-loss streak at four levels of risk per trade, using fixed-fractional sizing. The drawdown is 1 minus (1 − risk) to the power 10. The gain needed to recover is calculated from the reduced balance.

• 0.5% per trade: 0.995 to the power 10 ≈ 0.9511, a drawdown of about 4.9%. Recovery needs a gain of about 5.1%.
• 1% per trade: 0.99 to the power 10 ≈ 0.9044, a drawdown of about 9.6%. Recovery needs about 10.6%.
• 2% per trade: 0.98 to the power 10 ≈ 0.8171, a drawdown of about 18.3%. Recovery needs about 22.4%.
• 5% per trade: 0.95 to the power 10 ≈ 0.5987, a drawdown of about 40.1%. Recovery needs about 67.0%.

Notice how the relationship is not linear. Going from 1% to 2% roughly doubles the drawdown, but going from 2% to 5% more than doubles it again and triples the gain needed to recover. At 5% per trade, a streak that a 40% strategy has about a 70% chance of meeting within 500 trades leaves you needing two-thirds more just to get back to your starting balance.

These figures also understate the real damage, because an account rarely falls in one clean streak. A typical bad patch is several losses, a small win, more losses, and the drawdown measured from the peak can be deeper than any single streak suggests.

Expectancy: the other half of the equation

Sizing controls how fast a strategy can hurt you. Expectancy determines whether, in the long run, it is likely to help you at all. Expectancy per trade is:

Expectancy = (win rate × average win) − (loss rate × average loss)

It is easiest to measure in R, where 1R is the amount risked on a trade.

Worked example

These are illustrative numbers.

• Win rate 40%, average win 2R, average loss 1R.
• Expectancy = (0.40 × 2) − (0.60 × 1) = 0.80 − 0.60 = +0.20R per trade.

At 1% risk per trade, +0.20R is about +0.2% of the account per trade on average, before compounding. Over 100 trades that is an expected +20R. But the average hides a wide spread of outcomes, and the streak figures above all still apply.

Now suppose costs and slippage mean the average win is really 1.8R and the average loss 1.1R. Expectancy becomes (0.40 × 1.8) − (0.60 × 1.1) = 0.72 − 0.66 = +0.06R. A strategy that looked comfortably positive is now thin, and a slightly lower true win rate would make it negative. At 1:2 the break-even win rate is one in three, about 33.3%, before costs.

With zero or negative expectancy, no sizing method prevents ruin over a long enough run. Small risk per trade only slows it down. This is the core reason the guide to why most retail CFD traders lose focuses on costs and the absence of a tested edge: most retail CFD accounts lose money, and good position sizing cannot fix a strategy that loses on average.

Monte Carlo simulation in plain words

Because no tidy formula covers uneven payoffs, percentage sizing and a finite number of trades, traders use Monte Carlo simulation. The idea is simple:

1. Describe the strategy with its win rate and average win and loss in R.
2. Let a computer "play" a long sequence of trades, deciding each one at random with the right probabilities and updating the balance at your chosen risk per trade.
3. Record the worst drawdown and the final balance.
4. Repeat thousands of times and count how often the drawdown crossed your ruin threshold.

The result is not a forecast. It is a picture of the range of outcomes the stated assumptions allow, which is usually much wider than people expect.

An illustrative simulation

We ran 10,000 simulated sequences of 500 trades for a strategy with a 40% win rate, 2R wins and 1R losses (expectancy +0.2R), with fixed-fractional sizing and no costs. The approximate share of runs that suffered a peak-to-trough drawdown of at least 20%, 30% and 50% at some point:

• 0.5% risk per trade: about 0.1% hit 20%; essentially none hit 30% or 50%. Median worst drawdown about 8%.
• 1% risk per trade: about 19% hit 20%; about 1% hit 30%; essentially none hit 50%. Median worst drawdown about 15%.
• 2% risk per trade: about 95% hit 20%; about 45% hit 30%; about 2% hit 50%. Median worst drawdown about 29%.
• 5% risk per trade: every run hit 30%; about 84% hit 50%. Median worst drawdown about 61%.

This is a strategy with a genuine positive edge, and at 5% per trade most runs still went through a halving of the account. At 2%, nearly half the runs saw a 30% drawdown, which is the kind of decline that makes many traders abandon a working method.

The same simulation with a 30% win rate at 2R (expectancy −0.1R per trade) shows the other side. Even at 0.5% risk, about 42% of runs hit a 30% drawdown, and roughly 95% finished the 500 trades below their starting balance. At 1% risk, about half the runs hit a 50% drawdown. Smaller size bought time, not safety.

You can run your own version in a spreadsheet with a random number column, or with the Monte Carlo features in some backtesting software. Use the most pessimistic realistic inputs, not your best month.

How much to risk per trade

There is no single correct figure, and The PIP Report does not recommend one. The maths does point to some principles:

• Start from your ruin threshold, not your return target. Decide the drawdown you would treat as a stop for the strategy, then choose a risk per trade at which a long losing streak stays well inside it.
• Assume your edge is smaller than your data suggests. Small samples flatter. If you have fewer than a few hundred trades in your trading journal, the true win rate could easily be several percentage points lower.
• Count correlated positions as one risk. Three trades at 1% that all depend on the US dollar can behave like one 3% trade.
• Include costs and slippage in R. The spreads and commissions guide covers what each trade really costs.
• Lower risk lowers growth too. That trade-off is real. The guide to realistic trading returns and compounding shows how quickly the arithmetic of high monthly targets forces risk upwards, and the compounding calculator lets you test different growth rates. To run your own win rate, payoff and risk per trade through thousands of simulated trade sequences, use the risk of ruin calculator.

Common mistakes

• Quoting the probability of the next streak instead of any streak. A 0.6% chance on the next ten trades becomes a likely event over a few hundred.
• Using the classic formula on a strategy with uneven wins and losses. The number it gives is not meaningful for a 1:2 or 1:3 strategy.
• Treating a backtest win rate as fact. Overfitting inflates results, as explained in how to backtest a strategy. Simulate with a lower win rate as well.
• Raising risk after losses to "win it back". This is the fastest route to ruin, because it increases size precisely when the account is smallest and the trader is under most pressure.
• Ignoring leverage and margin. A position that fits the risk budget can still be closed by a margin call if the account is thin, as covered in leverage and margin.
• Defining ruin only as zero. The account you can no longer trade properly, or the method you abandon after a drawdown, is the ruin that actually happens.

Frequently asked questions

What is a good risk of ruin?

There is no universal figure, because it depends on the drawdown you define as ruin and the number of trades you consider. What matters is that you decide the threshold in advance, test it with realistic inputs including a lower win rate than your best estimate, and size so that the probability of reaching it is small enough that you would be comfortable if it happened.

What is the risk of ruin formula?

For even-money bets with a fixed stake and a known win rate, the probability of losing all N units is ((1 − edge) ÷ (1 + edge)) to the power N, where the edge is the win probability minus the loss probability. It does not handle uneven wins and losses, percentage-based sizing or a finite number of trades, so traders usually rely on Monte Carlo simulation instead.

How likely is a losing streak of 10 trades?

At a 40% win rate, the chance that a specific run of ten trades all lose is 0.6 to the power 10, about 0.6%. The chance of seeing at least one such streak somewhere in 500 trades is about 70%, and in 1,000 trades about 92%. At a 50% win rate the figures are about 22% over 500 trades and 39% over 1,000.

Does risking 1% per trade mean I can lose 100 trades before ruin?

No. With fixed-fractional sizing each loss is 1% of the remaining balance, so 100 consecutive losses would leave about 37% of the account rather than zero. But practical ruin comes much sooner: 23 net losses produce a 20% drawdown and 69 produce a 50% drawdown at 1% risk.

Can a strategy with a positive edge still be ruined?

Yes. A strategy with positive expectancy can still hit a deep drawdown if risk per trade is too high. In the illustrative simulation above, a strategy with +0.2R expectancy risked at 5% per trade hit a 50% drawdown in about 84% of runs. Positive expectancy says what tends to happen on average over many trades; position size decides whether you survive the path there.

How do I calculate my own risk of ruin?

Collect at least a few hundred trades from your journal or a careful backtest, work out the win rate and the average win and loss in R after costs, then run a Monte Carlo simulation at your intended risk per trade and count how often the drawdown crosses your threshold. Repeat with a slightly worse win rate to see how sensitive the result is.