Let’s start with a question. Here’s a strategy:
- Win rate: 55%
- Risk-reward ratio: 1:1
- Risk per trade: 10% of the deposit
The expected value is positive. The strategy is profitable. Most traders would use it without hesitation. What is the probability that, with this strategy, you will eventually lose half your deposit? The answer: over 97%.
Welcome to the ruin problem – the math that almost no one talks about, but which explains why most traders lose money even with systems that work.
A “ruin ” isn’t always a zero balance
First, an important point: in trading, a “ruin” doesn’t necessarily mean a completely empty account. It means something different to everyone. For some, it’s losing 40% of their deposit, after which it becomes psychologically impossible to continue trading as before. For others, it’s a margin call from the broker. For a fund manager, it’s a drawdown that causes clients to withdraw their money. For a beginner, it’s losing an amount they can’t afford to lose again.
It doesn’t matter exactly where your limit lies. What matters is this: with enough trades and an incorrect position size, any strategy will eventually reach that limit with a probability approaching 100%. This isn’t pessimism – it’s mathematics.
An important table in trading
Most traders focus on profitability. But only a few consider the asymmetry of losses and recovery. And this is the foundation of it all.
| Lost | Need to earn to return |
| 10% | 11% |
| 25% | 33% |
| 50% | 100% |
| 75% | 300% |
| 90% | 900% |
Losing streaks aren’t bad luck – they’re normal
Here’s what most traders don’t understand about their strategies. With a 55% win rate, which is pretty good, mind you, a streak of five consecutive losses happens about once every 45 trades. This isn’t a disaster, nor is it a sign that the system has broken down. It’s a statistical norm that you simply have to ride out. A streak of eight consecutive losses occurs roughly once every 300 trades. It’s rare, but it happens. And if you’re risking 10% of your deposit per trade at that point, eight consecutive losses will leave you with 43% of your initial account balance (not 80%). A 57% loss – with a profitable strategy, in a typical statistical scenario.
This calculation is based on the principle of compound interest, but in reverse – negative compounding. When you lose money, each subsequent loss is calculated not from the initial amount, but from what remains in your account balance. Let’s break down the math behind this process. If your risk per trade is 10%, then after each loss, your capital is multiplied by 0.9 (i.e., 90% of the previous value remains).
Step-by-step calculation
The formula for determining the account balance after a series of losses looks like this:
where:
Sn – final amount;
S0 – initial deposit (let’s assume 1$ or 100%);
r – risk per trade (0.1);
n – number of consecutive losses (8).
Substituting the values, this amounts to approximately 43.05%.
Why does this happen? Many people mistakenly believe that eight losses of 10% each amount to a total loss of 80% (10 × 8). But that would only be true if you always risked a fixed percentage of your initial deposit. In trading, however, risk is usually dynamic. After the first loss, your account balance decreases, and 10% of the new balance is a smaller absolute amount. That is why you don’t lose everything at once, but your balance “melts away” very quickly. The main trap here isn’t how much you have left, but how much you need to earn afterward. To restore your account from 43% back to the original 100%, you’ll need to make a profit of over 132%, which is psychologically and mathematically much harder than simply letting that losing streak run its course.
The problem isn’t with the strategy. The problem is that the position size isn’t large enough to withstand normal losing streaks.
Three ways to ruin yourself
All three are common. You might recognize yourself in one of them.
1. “I have a profitable strategy.“
A trader uses a system with a 60% win rate. Everything goes well for six months. Then the market shifts – a strong trend emerges where the system was accustomed to a sideways market, or vice versa. A losing streak of twelve trades ensues. With a 5% risk per trade, this results in a 46% loss of the deposit. The trader’s confidence is shattered, and the system is abandoned.
What went wrong? The trader never calculated how many consecutive losses his strategy could sustain or what would happen to his account balance in that scenario. He knew the win rate, but he didn’t know the risk of ruin.
- “I need to increase my bet to recoup my losses.”
After a string of losses, a trader raises their risk from 2% to 5% to get their money back faster. The logic is clear, but the math is ruthless: it is precisely during a losing streak that the strategy is most likely to continue losing. Increasing the stake at this point isn’t a comeback; it’s accelerating your ruin. This approach has a name: Martingale thinking. It has destroyed more trading accounts than any bad strategy.
- “It’s practically a sure trade.”
The trader sees an obvious, perfect setup. He risks 20% of his deposit instead of the usual 2%. The trade works. Then another one just like it. The third one doesn’t. A single 20% loss of the deposit requires a 25% gain just to break even. Two such losses in a row – a 36% loss.
A single deviation from the norm can undo months of careful work. There are no “sure trades” in trading – only probability management.
The Kelly criterion
In 1956, mathematician John Kelly derived a formula for the optimal position size. It answers the question: given a strategy’s edge, what percentage of one’s capital should be risked in order to grow as quickly as possible without going broke?
The formula looks like this:
K = W − (1 − W) / R
Where W is your win rate, and R is the ratio of average profit to average loss.
Let’s take a specific example: a win rate of 55%, with a profit-to-loss ratio of 1.5 to 1.
K = 0.55 − (0.45 / 1.5) = 0.55 − 0.30 = 0.25
The full Kelly formula states: risk 25% of your capital per trade. This is mathematically optimal for growth, but psychologically unbearable and practically dangerous, because the volatility of your account will be enormous.
What do professionals do? They use a quarter or half of the Kelly number. In our example, that’s 6% to 12% per trade. Growth is slower, but ruin becomes mathematically unlikely.
Important: the Kelly formula only works if your numbers are accurate. If the win rate is calculated based on 20 trades, it’s unreliable. You need at least 100-200 trades for the statistics to start meaning anything.
There’s a method used by professional managers but rarely by retail traders. It’s called a Monte Carlo simulation.
The idea is simple. You take your statistics (win rate, average profit, average loss) and run 1,000 random sequences of these trades. Not just one scenario, but a thousand possible scenarios with the same parameters.
The result: you see not an average value, but a real range of outcomes. Including the top 5% and bottom 5% of scenarios.
When a trader sees that, with their “normal” strategy, the account goes down by 65% in 5% of simulations, this changes their attitude toward position sizing more than any explanation. Abstract risk becomes a concrete number.
You don’t need complex software for this. Excel with the RAND() function, basic Python, or ready-made online calculators – that’s all you need.
Two decisions to make before your first trade
1) A fixed percentage, not a fixed amount.
If you always risk the same dollar amount, you’re trading incorrectly from a mathematical standpoint. When your account grows, that fixed amount becomes a smaller percentage of your capital – you’re under-risking. When your account declines, that same amount becomes a larger percentage – you’re over-risking precisely when it’s most dangerous.
A fixed percentage solves this problem automatically. The position size decreases with losses and increases with gains. This is not only mathematically correct – it’s psychologically easier, because dollar-denominated losses become smaller during difficult periods.
2) Determine your stop-loss threshold now.
Two numbers you need to write down before you start trading:
- At what drawdown will you pause and review your system? For example, minus 20%.
- At what drawdown will you stop trading entirely? For example, minus 40%.
This isn’t pessimism or weakness. It’s the only way to make these decisions rationally, because when a real drawdown hits, you’ll be making them under the influence of panic, fear, and the desire to recoup your losses. And they’ll be bad decisions. Traders who don’t have predefined thresholds make the decision to stop at the worst possible point, when almost everything is already lost.
If you’ve already had a ruin
This is important because many people have been through this. A loss isn’t just a financial setback. It’s a lesson. It tells you that one of three assumptions was wrong:
First, the strategy is actually profitable. Second, the position size was appropriate. Third, there was enough data to draw conclusions. In most cases, the problem lies with the second or third. The strategy might have worked – it was killed by the bet size or an insufficient sample size. Before you write off the system, ask yourself honestly: Did you trade it mathematically correctly? If not, you simply don’t know if it actually works.
Final thoughts
A profitable strategy is a necessary condition for success in trading. But it is not sufficient.
The math of survival is simpler than it seems: losing streaks are inevitable, the asymmetry of recovery works against you, and position sizing determines not how much you will earn, but whether you will survive long enough for the strategy to start working.
Most traders spend 90% of their time looking for entry points and 10% managing position size. The math says this ratio needs to be reversed. Use the Kelly Criterion. Set a stop-loss threshold. It’s more boring than searching for the perfect setup. And it’s much more important.