Risk of ruin, read on an equity curve simulator

Risk of ruin is the probability that your account drops low enough to never recover. It isn't a mathematician's abstraction: it's the one thing that can end your trading career in a single stroke. An equity curve simulator makes it visible in seconds: a free Monte Carlo simulation of a few thousand runs on your own numbers is the cheapest scare you will ever get. Understanding what makes it explode, and how to keep it near zero, matters more than any strategy.

• Risk of ruin depends on three things: your win rate, your ratio, and above all your position size.
• Risking big doesn't double your risk of ruin, it makes it explode non-linearly.
• Even a winning system can ruin a trader who risks too much per trade.
• Survival comes before return: a blown account has a -100% return, permanently.

Many traders focus on return ('how much can I make') and ignore the question that decides everything: 'what's the probability I lose it all'. That's risk of ruin. And it has a fearsome property: as long as it isn't zero, a long enough losing streak will, statistically, eventually arrive.

The good news is it's almost entirely under your control. It doesn't depend on the market or on luck, but on three levers you set yourself. This guide explains the mechanics, why position size is the dominant lever, and how to keep your risk of ruin so low it becomes a non-issue.

What 'ruin' really means

Ruin isn't necessarily a zero account. It's a loss level you don't come back from, in practice. That is the first thing a risk of ruin calculator has to be told, because one that assumes ruin means a zero balance will always return a comfortingly small number. Losing 50% of your capital requires a 100% gain just to break even. Losing 70% requires a 233% gain. Past a certain threshold, the recovery effort becomes so huge that the trader gives up, or takes desperate risks that finish the account. Ruin is that point of psychological and mathematical no return.

This table is the deep reason defense comes before offense, and it is the output any Monte Carlo simulation calculator, free or paid, will hand you in a different shape. Big drawdowns aren't recovered linearly: they dig a hole whose climb costs a disproportionate effort. Avoiding the hole is a thousand times better than knowing how to get out of it.

In the formulas, 'ruin' means a capital level set in advance: zero in the classic gambler's problem, where the stake is a fixed amount, or a threshold you choose, half the account for instance. The distinction matters, because a trader who risks a fixed fraction of current capital can never land exactly on zero: in his chapter on the Kelly criterion, Edward Thorp notes that ruin in the technical sense then cannot occur, and redefines it as falling below a level as low as you like. The rest of this guide therefore states, for each figure, which loss level counts as ruin.

The three levers of risk of ruin

Mathematically, your risk of ruin depends on three variables: the probability of winning a trade (win rate), the relative size of your gains versus your losses (ratio), and the fraction of capital you risk each time (position size). The first two define your edge; the third defines your speed of destruction if things go wrong.

The crucial point: for a given edge, position size drives almost all of the risk of ruin. You can have a perfectly winning long-term system and still ruin yourself, simply because you risk too much per trade and a normal losing streak arrives before your positive expectancy has time to play out.

With leverage, that position size can exceed your capital, which makes the distinction between advertised leverage and risk per trade all the more useful: it is detailed in the guide to leverage in trading.

The risk of ruin formula

The simplest case has an exact formula, the gambler's ruin. The assumptions: each trade is a draw independent of the previous one, won with probability p and lost with probability q = 1 − p, the win and the loss are the same fixed stake, and ruin is capital at zero. If you start with k stakes of capital and p is above 0.5, the probability of ending ruined while playing indefinitely is (q ÷ p) to the power k; if p is 0.5 or below, it is 1: ruin is certain. That is the result proved in Karl Sigman's course notes on the gambler's ruin problem, at Columbia University, by conditioning on the first draw.

Read k as the inverse of your risk per trade: risking 10% of the starting capital on each trade means holding 10 stakes; 2% means 50. With 55% winning trades and a win equal to the loss, q ÷ p is 0.818, and the following table comes straight out of the formula, with no simulation.

When the average win is not equal to the average loss, the same method applies to a step larger than one unit: with a win of b times the loss, the probability of ruin becomes r to the power k, where r is the root between 0 and 1 of the equation p × r to the power (b + 1) − r + q = 0, solved numerically. With 40% winning trades and a win twice the loss, r is 0.823, and the probabilities are almost those of the table: 2.0% with 20 stakes, 14% with 10. What matters is neither the win rate alone nor the ratio alone, but their combination, then the number of stakes your risk per trade leaves you.

These figures assume independent draws and a fixed amount at risk. As soon as you risk a percentage of your current capital, size shrinks with the losses, zero is no longer reachable, and the Monte Carlo simulation further down takes over, with a chosen ruin threshold.

Why risking big is non-linear

Intuition says risking 2% instead of 1% doubles the risk. That's false, and dangerously optimistic. In the formula above, doubling the risk per trade halves k, and raising (q ÷ p) to the power k ÷ 2 amounts to taking the square root of the probability of ruin: going from 5% to 10% per trade moves ruin from 1.8% to 13%, and from 10% to 20%, from 13% to 37%. A square root turns a tiny number into one that counts. Losses also compound: each loss shrinks the capital the next one applies to, and big percentages dig exponentially deeper holes.

The exact figures depend on your edge, but the shape of the curve is always the same: flat and reassuring at the bottom, then shooting up. Edward Thorp shows it another way in the same chapter: betting a fixed fraction of capital, the probability of ever falling to half the starting capital is 1 in 2 with the full Kelly fraction and 1 in 8 with half that fraction, and he writes that overbetting is much more severely penalized than underbetting. Living on the flat part of the curve means risking fractions of a percent, not tens.

A winning system isn't enough

It's the most misunderstood paradox of trading: you can be right in the long run and go broke before you get there. Positive expectancy tells you what happens over thousands of trades; risk of ruin tells you whether you'll survive the few hundred between you and that long run. A real edge is worthless if a losing streak knocks you out before it can express itself.

That paradox is written in black and white in J. L. Kelly's 1956 paper, A New Interpretation of Information Rate: a gambler with an edge who bets his entire capital each time maximizes the expected value of his capital, and yet ends up broke with probability one if he continues indefinitely. The fraction that maximizes growth exists, but it is far smaller than expectancy alone suggests.

That's exactly why position size management isn't optional. It doesn't make your system a winner, but it guarantees you'll still be there when your winning system does its job. Survival is the precondition for performance.

The formula that turns that risk into lots, contracts or shares, with one worked example per market, is in the guide to calculating position size.

Position size, stop, daily limit and maximum drawdown form a single framework: it is summed up, block by block, in the guide to risk management in trading.

That calculation assumes losses of the planned size. When the market gaps through your stop, in what is called a black swan event, a single trade can cost several times the planned risk: one more reason to keep a margin.

How to keep your risk of ruin near zero

1. Risk a small fixed fraction per trade (0.5 to 1%), computed on your current capital.
2. Set yourself a maximum daily loss: beyond it, you stop, whatever your conviction.
3. Never double size to win it back; that's the behavior that turns a drawdown into ruin.
4. Watch your positions' correlation: three correlated trades are one big risk in disguise.
5. Measure your real risk afterward, to check your rules are held and not just displayed.

The myth of the protective big account

Many traders believe a bigger capital shields them from ruin. It's a dangerous illusion, because risk of ruin doesn't depend on your account's absolute size, but on the percentage you risk per trade. A trader with 100,000 risking 10% per position is no safer than a trader with 1,000 risking 10%: both travel the same destruction curve, just with different zeros. The number on your statement protects you from nothing; it's your risk discipline that protects you.

This confusion drives a precise, costly behavior: after growing their account, the trader feels invincible and relaxes their management, raising their percentages because they have 'room'. In reality, they've just reopened the door to the risk of ruin they had closed. The rule is the same at every capital level: it's the percentage risked, not the account amount, that decides your survival. A big badly-managed account blows up as fast as a small one, it just makes more noise falling.

The psychological point of no return

Risk of ruin isn't only mathematical, it has an equally real psychological dimension. Well before an account reaches zero, there's a threshold where the trader cracks: they lose faith in their system, start trading fear or revenge, and accelerate the fall themselves. This mental breaking point can arrive well before mathematical ruin, at a level specific to each person, and no general figure sets it.

That's why your real survival limit isn't the theoretical zero, but the loss level beyond which you stop trading rationally. Knowing that threshold, specific to you, and stopping well before reaching it, is part of managing risk of ruin as much as the percentage calculations. A trader who ruins themselves rarely does so all at once: they ruin themselves by first crossing their mental breaking point, then letting emotion finish the job.

Rebuilding after a big drawdown

If you've already suffered a deep drawdown, how you climb back determines whether you truly survive or sink again. The temptation to 'win it back fast' by raising risk is immense, but that's exactly what turns a recoverable drawdown into permanent ruin. The only healthy recovery is slow: reduce your size, return to ultra-prudent management, and rebuild the capital brick by brick, accepting it takes time.

This patience is counterintuitive when you're in the hole, because each day of slow recovery feels unbearable. But it's the only path that doesn't send you back to the bottom. Reducing your risk after a big drawdown isn't an admission of weakness, it's the decision that protects what's left and gives you a chance to come back. Digging faster to get out of the hole is the surest way to make it permanent.

A numeric example comparing two traders

Take a purely illustrative example to make the mechanics tangible. Trader A risks 1% of current capital per trade on a 20,000 account, so 200 on the first position. Trader B, with the exact same edge (same win rate, same win/loss ratio), risks 5%, so 1,000 on the first. Over a streak of eight consecutive losses, trader A ends at 18,455, a 7.7% loss that an 8.4% gain erases. Trader B ends at 13,268, a 33.7% loss that requires a 50.7% gain just to break even. And that streak is nothing exotic: with 55% winning trades drawn independently, the probability of meeting at least eight losses in a row is about 8% over a hundred trades, 37% over five hundred and 60% over a thousand.

The key point of this example: both traders have exactly the same edge, the same strategy, the same winning and losing trades in the same order. Only the position size differs, and yet their trajectories diverge radically. It wasn't the quality of the strategy that separated these two traders, it was purely their risk management. It's the clearest demonstration that risk of ruin is controlled independently of the ability to generate an edge.

Risk of ruin on a prop firm account

On a prop firm account, risk of ruin takes a particular shape, because 'ruin' isn't only a loss of capital, it's also losing the account itself the moment the maximum allowed loss is hit, well before losing most of the capital. At FTMO, for instance, the trading objectives page sets, for its 2-Step model, the maximum loss at 10% of the initial capital, a static limit computed on equity, open positions included, and the maximum daily loss at 5%; each firm publishes its own rules. An account is therefore 'ruined' in the sense of the challenge at -10%, a threshold that would pass for an ordinary rough patch on a personal account. This rule makes risk of ruin even more sensitive to position size than on a personal account.

Arithmetic sets the margin. With a 10% limit computed on the initial capital, ten 1% losses in a row hit it, and it takes twenty at 0.5%. Over two hundred trades at a 55% win rate with a win equal to the loss, a simulation of twenty thousand paths gives about 12% of accounts going under the limit when risking 1% per trade, about 1% when risking 0.5%, and almost none at 0.25%. Treating the firm's limit as a threshold to never approach, rather than a target to reach, is what keeps a funded account.

Risk of ruin and position correlation

The classic risk-of-ruin calculation often assumes trades independent of one another, but that isn't always the case. If you open several correlated positions at once, you aren't making several independent 1% bets, you're making one big bet disguised as several small ones. That invisible concentration pushes your real risk of ruin well beyond what your displayed per-trade percentage suggests, because a single piece of bad news can sink several positions at once instead of just one.

That's why mastering risk of ruin isn't just about choosing a good percentage per trade, it also requires watching how many of your open positions actually depend on the same market scenario. A trader who scrupulously respects their 1% per trade rule, but stacks five correlated positions, ends up with a risk of ruin much closer to that of a trader risking 5% on a single trade, without ever having consciously decided to.

What risk of ruin changes in your daily decisions

Once you've internalized risk of ruin as a priority, it concretely changes how you make every trading decision, not just your starting position size. Facing doubt about a setup, the question that should come first is no longer 'do I think I'm right?' but 'if I'm wrong, does the consequence stay inside my survival zone?'. That reframing, subtle as it looks, radically changes the kind of decisions you make in moments of uncertainty, because it shifts the center of gravity from prediction to protection.

In practice, that means accepting you'll miss opportunities that looked promising but whose required size to produce a meaningful gain would have exceeded your reasonable risk limit. Many traders find that frustrating at first, as if they were artificially capping their potential. But it's exactly the opposite: every opportunity passed up to stay inside a negligible risk-of-ruin zone is an opportunity to keep playing tomorrow, and trading is a game that only rewards those who stay at the table long enough to let their edge express itself over hundreds, then thousands, of trades.

Measuring it with Tradoshi

You can't manage a risk you don't measure. Tradoshi computes the percentage of capital truly risked on each trade (from your stop) and tracks your drawdown, so your risk of ruin stays a visible figure rather than a surprise.

• Real risk per trade: the engaged percentage is computed automatically, you see your rule breaches.
• Drawdown tracking: your maximum and current drawdown are displayed, your survival indicator.
• Drawdown mastery: an axis of the Oshi Score rates your ability to avoid digging big holes.
• Drift alerts: days where your risk climbs abnormally stand out in your stats.

Monte Carlo simulation

A Monte Carlo simulation replays the same series of trades thousands of times in a different order, or draws thousands of paths at random from your win rate and your ratio. The point is not the average, which does not move, but the spread: it shows the worst run your strategy can produce by chance alone. That number, rather than expectancy, is usually what decides whether you will hold on. An online Monte Carlo simulation is enough to see it.

The method comes from physics. In his 1987 account of the beginning of the Monte Carlo method, Nicholas Metropolis recalls that it was an old statistical sampling technique, revived at Los Alamos in 1947 to follow neutron diffusion, and that he named it after an uncle of Stanislaw Ulam who borrowed money to go gambling in Monte Carlo. Applied to your trades, it does nothing else: draw at random, many times, and count.

Here is what it gives on the system of the previous table, this time risking a fixed fraction of current capital, with ruin defined as losing half the account, over 500 trades and 20,000 randomly drawn paths:

The Kelly fraction for this system is 10%, the win rate minus the loss rate: that is where the median growth is strongest, and also where almost one path in two goes through a loss of half the account. Above it, the median itself falls below the starting capital. A Monte Carlo simulation tool costs nothing to try, and the free ones available online do the essential. What matters is not the model's sophistication but the honesty of the sample you feed it: a thousand draws on thirty biased trades produce one bias repeated a thousand times.

It says nothing about the market itself: unlike a Fibonacci retracement, which draws levels on a chart, it only replays your own results, in a different order.

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