Risk of Ruin and Losing Streak Math
The probability of blowing up your account given your sizing, why 7-loss streaks are statistically guaranteed, and how to size to survive streaks you're going to have.
Two things every trader should know before taking a live trade: the probability that the strategy will produce a 7-loss streak in the next 100 trades, and the probability that their current sizing will blow up the account even if the strategy is profitable. Both are computable. Both are counterintuitive. Most retail traders don't know them - which is why they're shocked by "normal" streaks and accidentally size themselves into ruin on strategies that are mathematically winning. This lesson covers streak math (how often N losses in a row happens), risk of ruin formulas (the probability of blowing up given sizing and edge), and the sizing rules that result from taking these numbers seriously.
Streak math: what's "normal"?
Losing streaks are the most emotionally triggering part of trading. They're also the most predictable. For any strategy with a given win rate, the probability of an N-loss streak over K trades can be calculated exactly.
The formula (simplified)
For a win rate p_win (e.g., 0.5 for 50%), the probability of at least one streak of N consecutive losses over K trades approximates:
P ≈ 1 − (1 − p_loss^N)^(K − N + 1)
Simplified approximation - exact formula is more complex but this captures the magnitude. Works well for p_loss > 0.3 and moderate K.
where p_loss = 1 − p_win.
Translation: as you take more trades, the probability of any given streak occurring approaches certainty. There's no "getting lucky" out of streaks - they're baked into the statistics of any random process with imperfect accuracy.
The table every trader should memorize
Given win rate, the probability of seeing at least one streak of N losses over K trades:
| Win rate | 100 trades, 5-loss streak | 100 trades, 7-loss streak | 200 trades, 7-loss streak |
|---|---|---|---|
| 60% | 14% | 2% | 4% |
| 55% | 26% | 5% | 10% |
| 50% | 42% | 10% | 19% |
| 45% | 63% | 20% | 37% |
| 40% | 80% | 35% | 57% |
| 35% | 91% | 53% | 78% |
| 30% | 97% | 71% | 92% |
How to read this: a 40% WR strategy has a 57% chance of a 7-loss streak in 200 trades. Over a full year of active trading (300-500 trades), that probability approaches certainty.
Worse, you'll probably see it more than once. A 35% WR strategy over 500 trades will see multiple 7-loss streaks.
Why streaks feel impossible
Human pattern recognition is biased to see causation in random outcomes. After 3 losses, the brain starts constructing a narrative: "something is wrong." After 5, it's sure: "the strategy is broken." After 7, it's frantic: "I need to do something." Each of these feelings is happening at a moment where, mathematically, nothing has changed. The dice just keep rolling.
The trader who sizes up to "catch up," widens stops to "give the trade room," or switches strategies after 7 straight losses is responding to statistical normality as if it were strategy failure. The resulting behavior is what actually blows up the account.
Risk of ruin - the formula that should terrify you
Risk of ruin (RoR) = the probability your account goes to zero (or some specified floor) given your sizing, edge, and the number of trades played.
The general formula (Vince, 1990):
RoR ≈ ((1 − A) ÷ (1 + A))^C
A = advantage ratio, p = WR, q = loss rate, u = fraction of account lost on a loss, w = fraction won on a win. Assumes binary outcomes; real trades are continuous but this approximation is close.
Where:
- A (advantage) = (p × w − q × u) ÷ (average risk per trade)
- C (capital units) = account / per-trade risk $
Don't worry about computing it by hand. What matters is the shape of the relationship.
Risk of ruin table - the one you'll actually use
Holding a realistic 40% WR / 2:1 RRReward-to-riskDistance to target ÷ distance to stop. Minimum workable setups are typically 2:1 or better.Read in glossary → strategy (expectancy +0.2R per trade), the probability of blowing up varies dramatically with per-trade size:
| Per-trade risk | Risk of ruin (eventual) |
|---|---|
| 0.5% | < 0.001% |
| 1% | ~0.01% |
| 2% | ~1% |
| 3% | ~5% |
| 5% | ~12% |
| 10% | ~35% |
| 20% | ~70% |
| 25% (full Kelly) | ~90% (of some drawdownDrawdownPeak-to-trough decline in account equity. Resets only at new equity peaks. Recovery math is asymmetric.Read in glossary →, not total ruin) |
Key observations:
- Doubling the per-trade risk doesn't double the RoR - it increases it by 5-10×.
- Below 2% per trade, RoR is effectively zero for a strategy with positive edge.
- Above 5% per trade, RoR climbs fast even on winning strategies.
- Above 10% per trade, you have roughly a 1-in-3 chance of wiping out a positive-edge account.
This is why the 1% rule1% ruleStandard risk policy: never risk more than 1% of account equity on a single trade. The single most protective rule in trading.Read in glossary → exists. It's not arbitrary. It's the sizing at which positive-expectancyExpectancyExpected R-multiple per trade: (WinRate × AvgWinR) − (LossRate × AvgLossR). Positive = edge. Negative = bleed.Read in glossary → strategies essentially cannot blow up.
Risk of ruin for negative-expectancy strategies
If your strategy has negative expectancy (avg loss > avg win × win rate), RoR is 100% given infinite time. You will blow up. It's a matter of when, not if.
This is what gambling at casinos is. The house edge is 1-5% depending on the game. No matter how much you win short-term, playing long enough guarantees you lose everything. Many retail traders unknowingly run negative-expectancy strategies (due to widened stops or over-trading with fees), then wonder why their accounts bleed down over months even with occasional big wins.
The variance trap
Here's a pattern that fools many traders:
A strategy has small positive expectancy (+0.1R per trade). Over 100 trades, expected gain is +10R.
But the standard deviation of 100-trade outcomes might be 25R. So a "normal" outcome is anywhere from -15R to +35R. That's enormous variance - 40% of traders running the strategy over 100 trades will be negative purely from randomness.
Those traders will conclude the strategy doesn't work. They'll switch. The strategy is fine. They just didn't have enough sample size to see expectancy assert itself against variance.
The rule that follows from this
Don't judge a strategy on < 100 trades. Below 100, you're mostly seeing variance, not signal.
Even 100 trades is marginal for high-variance strategies. If you're running a low-WR, high-RR system (like 30% WR / 4:1 RR), expect your first 50-100 trades to feel terrible even if the edge is real. The big winners that carry the strategy are rare - miss them and you're dead in the water.
Monte Carlo - simulating your strategy's distribution
For traders who want to go deeper: Monte Carlo simulation runs thousands of hypothetical trade sequences using your win rate and RR-multipleThe dollar amount risked on a trade. Every outcome is measured in R: a 2R winner made twice the risked amount.Read in glossary →-distribution. The result is a distribution of possible equity curves.
What a Monte Carlo reveals
- Expected final equity (the median) - your realistic outcome.
- 5th percentile - the "bad luck" outcome. If you're not OK with this, you're sized too big.
- 95th percentile - the "good luck" outcome. Don't plan around this.
- Maximum drawdown distribution - shows worst-case drawdowns you'd reasonably expect.
A simulated example
50% WR, 2:1 RR, 1% risk per trade, 500 trades, starting $10,000:
| Percentile | Final equity | Max drawdown along the way |
|---|---|---|
| 5th (bad luck) | $11,200 | 22% |
| 25th | $14,800 | 15% |
| 50th (median) | $18,500 | 12% |
| 75th | $22,500 | 10% |
| 95th (good luck) | $29,000 | 7% |
Read this carefully:
- Even the bottom 5% outcome is positive - you likely won't go negative over 500 trades on a positive-edge strategy with 1% sizing.
- Even the best 5% outcome has 7% max drawdown - drawdowns are unavoidable.
- Median drawdown is 12% - plan for this emotionally. Don't be surprised by it.
Tools like RiskSimulator, Edgewonk, or a simple Python/R script can generate these for your own tracked data. Worth doing before scaling size.
Rules derived from this math
1. Compute your worst-plausible streak before starting
For your strategy's WR, estimate the longest streak you might face in a year. If you can't mentally survive that streak, pick a different strategy.
2. Size small enough that streak + drawdown math doesn't break you
Work backwards from the streak. If you can expect a 7-loss streak at 40% WR:
- 7 losses × 1% = 7% drawdown (survivable, boring)
- 7 losses × 3% = 21% drawdown (emotionally brutal, likely breaks most traders)
- 7 losses × 5% = 35% drawdown (career-threatening)
3. Respect sample size
Until you have 100+ tracked trades, your "results" are variance not signal. Don't evaluate, don't change anything major, just keep executing and tracking.
4. If RoR > 1%, you're sized wrong
If your sizing gives above 1% chance of account ruin, you're trading to blow up on a long enough timeline. Reduce size until RoR is negligible, regardless of how that feels relative to expected returns.
Streak math, in plain English
- A 50% WR strategy will produce a 5-loss streak about 4 out of 10 times over 100 trades. Almost certain over 200 trades.
- A 40% WR strategy will produce a 7-loss streak in more than half of all 200-trade windows.
- A 30% WR strategy will produce a 10-loss streak in most 500-trade windows.
These are not edge cases. They are the central case.
Every professional trader has survived their worst streak. Most blown-up retail traders didn't, because they were sized too large to survive the streaks their strategies guaranteed them.
Common questions
If I can compute my edge, why not size bigger? Because your estimated edge is not your true edge. Estimation error plus variance means you need a marginMarginBorrowed capital used to increase position size. Amplifies both gains and losses proportionally.Read in glossary → of safety. The 1% rule is that margin. You give up half your expected return in exchange for 100× lower risk of ruin.
How do I actually compute risk of ruin for my strategy? Three ways, in rising order of complexity: (1) look up a table based on your WR + per-trade risk %, (2) use a Monte Carlo tool (many free online), (3) run a full simulation in Python/R with your actual R distribution.
What's a "safe" long losing streak? None. Longer streaks are always possible. The question isn't what's safe - it's what's bounded. A 7-loss streak at 1% = 7% drawdown. That's bounded. A 7-loss streak at 5% = 35% drawdown. That's unbounded in practice because it breaks you psychologically before math recovers.
Can I use streak math to know when to stop? Partly. If your streak far exceeds statistical norms (e.g., 12-loss streak on a 50% WR strategy - probability < 0.1% over 100 trades), something has changed. Either variance was wild, or the strategy broke. Worth investigating journal data.
Key takeaways
- Long losing streaks are not edge cases. They're mathematical guarantees for any imperfect-accuracy strategy over enough trades.
- A 40% WR strategy produces a 7-loss streak in >50% of 200-trade windows. Plan for it.
- Risk of ruin climbs nonlinearly with per-trade size. 1% → basically zero. 5% → ~12%. 10% → ~35%.
- Below 1% sizing, positive-expectancy strategies essentially cannot blow up.
- Above 2% sizing, the tradeoff between faster compounding and higher ruin risk becomes material.
- Don't judge a strategy on fewer than 100 trades. Variance dominates below that sample size.
- Monte Carlo simulation turns "what could happen" into distributions. Use it before scaling size.
- The worst mistake: a real edge, killed by oversizing into statistically-normal streaks.
Up next: Trading Psychology - the three killers (revenge tradingRevenge tradingTaking impulsive trades immediately after a loss to 'get it back'. The single most destructive pattern in retail trading.Read in glossary →, FOMO, overtrading), the pattern-recognize-and-escape framework, and the mental routines that turn disciplined math into actual behavior.
Related lessons
Risk Management Foundations
Why risk comes before setup, the three layers of risk policy (per-trade, daily, weekly, max drawdown), and the mindset shift that separates career traders from accounts that blow up.
Position Sizing Deep Dive
The formula you will use on every trade - across stocks, futures, options, and forex. ATR-based sizing, correct scale-ins, and why the stop always comes before the size.
Stop Placement Masterclass
Four stop types - structural, ATR, time, percentage - when each works, when each fails, and the exact rules for moving a stop to break-even without sabotaging your edge.