I keep running into traders who obsess over their win rate and never do the one calculation that would actually tell them whether they survive. They will spend a month tuning entry conditions to nudge their hit rate from 52 to 54 percent, and then risk an amount per trade that guarantees a blown account the first time variance does what variance does. The math that matters here is not glamorous. It is a coin-flip counting exercise and a formula older than most of the assets people trade. But it settles arguments fast, and it changes how you size positions once you actually see the numbers.
Start with the part almost nobody internalizes. A losing streak is not a sign that something broke. It is the expected behavior of a random-ish process, and you can predict roughly how long a streak to expect just from your win rate and your trade count. Run the numbers once and the panic that comes with five reds in a row mostly evaporates, because you already knew it was coming.
Why a coin-flip trader hits a seven-loss streak
Take a trader who wins 50 percent of the time. Every trade is roughly a coin flip. The chance of losing any single trade is one half. The chance of losing seven in a row starting on a given trade is one half to the seventh power, which is one in 128. That sounds rare enough to ignore. It is not, and the reason is that you are not taking one shot at it. You are taking hundreds.
Over 200 trades you have around 194 different starting points where a seven-loss run could begin. When an event with a one in 128 chance gets 194 attempts, you should expect it to show up. Not might. Should. The rough expected number of seven-loss streaks across 200 coin-flip trades sits comfortably above one, which means a run that feels like a catastrophe is really just the house showing you the fine print. If your win rate is below 50 percent, the expected streak gets longer. At 40 percent you should plan for eight or nine reds in a row somewhere in a few hundred trades, and you should plan for it to arrive at the worst possible time, because it usually does.
The quick rule of thumb I use in my head is that the longest losing streak you should expect over N trades is roughly the base-2 logarithm of N, adjusted for how far your loss rate sits from a coin flip. For a couple hundred coin-flip trades that lands right around seven. You do not need to memorize the derivation. You need to accept that seven reds is normal and build for it instead of being surprised by it.
The formula that decides whether you survive
Knowing a streak is coming is only half of it. The other half is whether the streak ends your account. That is what risk of ruin measures. It is the probability that your equity draws down to a level you cannot recover from, given your edge and how much you put at stake each trade.
For a simplified even-money case where wins and losses are the same size, there is a clean version. Risk of ruin equals ((1 minus edge) divided by (1 plus edge)) raised to the power of the number of losing units your account can absorb. Edge here is your win rate minus your loss rate, so a 55 percent win rate gives an edge of 0.10. The exponent is how many full risk-units of capital you are holding. If you risk 1 percent per trade, you have 100 units. If you risk 5 percent, you have 20.
That exponent is the whole game. Two traders can run the identical strategy with the identical edge, and the only difference between them is the size of the number they type into the risk field. One types 1 and effectively never goes broke. The other types 5 and carries a real, countable probability of ruin over a long enough run. Same signals. Same win rate. Completely different survival odds. This is why I get tired of the strategy-quality conversation. Strategy quality sets your edge, and edge matters, but position size sets your exponent, and the exponent is what compounds against you.
Numbers you can check your own account against
Here is the shape of it, using the even-money formula so you can sanity-check your setup. These are rounded and meant to build intuition, not to be quoted to the decimal.
- 55 percent win rate, 1 percent risk per trade: risk of ruin is effectively negligible, small enough to round toward zero over any realistic number of trades.
- 55 percent win rate, 5 percent risk per trade: risk of ruin climbs into the low single-digit percent range. Survivable, but no longer something to wave off.
- 55 percent win rate, 10 percent risk per trade: risk of ruin jumps to a genuinely uncomfortable level, roughly one in eight or worse. Same edge, far more dangerous.
- 50 percent win rate, any risk above a few percent: with zero real edge, ruin over a long enough run trends toward certainty. Size only delays it.
The pattern is the point. Holding your edge fixed, every increase in per-trade risk raises your ruin probability faster than it raises your growth. Doubling your risk does not double your danger, it does something worse, because the exponent shrinks and the base gets raised to a smaller power. Halving your risk buys you a disproportionate amount of safety. This is the trade almost nobody makes voluntarily, because smaller size feels like leaving money on the table right up until the streak that would have ended you passes by harmlessly instead.
The workflow I actually run
When I am evaluating whether a strategy is deployable, the sizing check comes before I care much about the returns. The steps are boring and they take about ten minutes.
- Estimate the realistic win rate and average win-to-loss ratio from a decent sample, ideally a few hundred trades, not thirty. Small samples lie about win rate in both directions.
- Compute the expected longest losing streak for the number of trades you plan to take in a year. If that streak would draw your account down past your personal pain threshold at your current risk level, the size is wrong regardless of the backtest.
- Plug your win rate and risk-per-trade into the risk-of-ruin formula and look at the exponent. If risking a smaller percentage moves ruin from noticeable to negligible, take the smaller percentage. It almost always does.
- Assume the worst streak lands during your largest drawdown and your worst emotional state, because in practice the two correlate. Size for that scenario, not the average one.
The failure mode I see most often is a trader who backtests a real edge, sizes it aggressively because the equity curve looks beautiful, hits the seven-loss streak that was always in the cards, and quits the strategy at the exact bottom. The edge was fine. The math around the edge was never run. A survivable version of the same strategy at a quarter of the size would have ridden straight through the streak and been up on the far side.
None of this requires better forecasting. It requires accepting that the streak is coming, that your win rate does not save you from it, and that the one number standing between a rough month and a dead account is the percentage you risk per trade. Run your own figures through the formula before you size the next position, and let the exponent talk you into being smaller than your confidence wants you to be.