The Trading Expectancy Simulator runs 1,000 randomized trade sequences using your win rate, average R:R, and position size, then plots the full distribution of equity curve outcomes — revealing the drawdowns and ruin probabilities that the static expectancy formula conceals. A positive expectancy is necessary but not sufficient; this simulator shows whether your position sizing survives the inevitable variance.
How to Use
| Input | What to Enter | Example |
|---|---|---|
| Win Rate | Historical percentage of winning trades | 55% |
| Average Win (R) | Average winner as a multiple of your risk unit | 2R |
| Average Loss (R) | Average loser as a multiple of risk (usually 1R) | 1R |
| Risk Per Trade | Account percentage risked per trade | 1% |
| Starting Account Size | Total capital at simulation start | $25,000 |
| Number of Trades | Trades per simulated sequence | 200 |
The simulator returns a median equity curve, 10th/90th percentile bands, a max drawdown histogram, and a ruin probability percentage. Use the 10th percentile outcome — not the median — as your planning scenario when setting position sizes.
Formula Explained
Expectancy = (Win% × Avg Win in R) – (Loss% × Avg Loss in R)
Longest Losing Streak ≈ log(n) / log(1 / Win Rate)
Expectancy tells you the average R gained per trade. A 55% win rate with 2:1 R:R yields (0.55 × 2) – (0.45 × 1) = +0.65R per trade. Positive expectancy confirms the edge exists, but it reveals nothing about the sequence of those wins and losses — and sequence is everything for drawdown.
The losing streak formula gives the expected worst consecutive loss run over n trades. At a 50% win rate over 100 trades: log(100) / log(1/0.5) = 2 / 0.301 ≈ 7 consecutive losses. This streak will appear in virtually every 100-trade sample, not because the system is broken, but because that is what 50% win rate variance produces. At a 40% win rate over 200 trades, extend that expectation to roughly 10 in a row.
Position size is where Monte Carlo simulation changes behavior. The expectancy calculator produces one number — average R per trade. But tripling position size does not triple drawdown; it multiplies tail risk nonlinearly. At 2% risk per trade the simulation looks manageable. At 3% risk with the same edge, the ruin probability can be 15 times higher. The formula does not show this. The distribution does.
Example Calculations
Scenario 1: Conservative Sizing at 1% Risk
- Account: $25,000
- Win Rate: 55%, R:R: 2:1
- Risk Per Trade: 1% ($250 per trade)
- Trades Simulated: 200
- Result: Median ending balance approximately $57,500 (+130%); 10th percentile simulation shows a 22% peak-to-trough drawdown ($5,500) at some point during the sequence; 3.2% of simulations hit a 40%+ drawdown; ruin probability (50% account loss defined as ruin) = 0.4%
At 1% risk, the 10th percentile planning drawdown is approximately $5,500. That is a loss most traders can hold through psychologically without abandoning the system.
Scenario 2: Aggressive Sizing at 3% Risk, Same Edge
- Account: $25,000
- Win Rate: 55%, R:R: 2:1
- Risk Per Trade: 3% ($750 per trade)
- Trades Simulated: 200
- Result: Median ending balance approximately $180,000; ruin probability rises to 6.1% — a 15x increase in tail risk for a 3x increase in position size
The median outcome looks dramatically better, but 6.1 out of every 100 simulation runs end in account destruction. Full Kelly at this win rate and R:R works out to 32.5% of account per trade; half-Kelly lands at 16.25%. Neither is remotely practical — the Kelly criterion calculator confirms the theoretical optimum, and Monte Carlo shows exactly why practitioners cap at 25% of Kelly or less.
Scenario 3: Prop Firm Candidate on Topstep $50K Combine
- Account: $50,000
- Win Rate: 50%, R:R: 2:1
- Risk Per Trade: 0.5% ($250 per trade)
- Trades Simulated: 100
- Result: 5th percentile simulated drawdown stays within the $3,000 trailing max drawdown limit; ruin probability under 0.5%
Topstep’s 6% trailing max drawdown is an absolute hard limit. Running the simulator before trading the Combine reveals the maximum risk-per-trade that keeps the worst 5% of simulated outcomes inside that boundary. For most win rates between 45–55%, that ceiling sits at 0.5–0.75% per trade.
When to Use the Monte Carlo Simulator
- Before going live with a new strategy: Verify that positive expectancy translates to survivable drawdowns at your planned position size, not just a favorable average
- Before entering a prop firm evaluation: Determine the maximum risk-per-trade that keeps the 5th percentile simulated outcome within the firm’s hard drawdown limit
- After a significant drawdown: Distinguish between normal variance and genuine system failure — if the actual drawdown falls within the simulated distribution, the edge likely still exists
- When adjusting position size: Quantify exactly how much tail risk increases with each incremental increase in risk percentage before making the change
- When reviewing risk of ruin analytically: Cross-validate the closed-form ruin probability against Monte Carlo results to confirm both calculations agree
Related Tools
- Expectancy Calculator — Calculate static expectancy R-value first to confirm positive edge before running the full Monte Carlo simulation
- Risk of Ruin Calculator — Compute ruin probability analytically, then compare against Monte Carlo results to validate both approaches
- Kelly Criterion Calculator — Determine mathematically optimal position sizing, then stress-test it with Monte Carlo to evaluate tail-risk implications at fractional-Kelly levels
- Drawdown Calculator — Calculate the account recovery percentage required for any drawdown level identified in the Monte Carlo percentile bands
Frequently Asked Questions
What is Monte Carlo simulation in trading?
Monte Carlo simulation runs thousands of randomized trade sequences using your historical win rate and R:R ratio, producing a distribution of possible outcomes rather than a single average. This reveals worst-case drawdowns and ruin probabilities that the static expectancy formula cannot show — specifically, the full range of equity paths a positive-expectancy system produces due to random sequencing alone.
How do you calculate trading expectancy?
Trading expectancy equals (Win Rate × Average Win in R) minus (Loss Rate × Average Loss in R). A system with a 55% win rate and 2:1 R:R produces expectancy of (0.55 × 2) – (0.45 × 1) = +0.65R per trade. A 2:1 R:R system only needs a 34% win rate to break even before commissions — most traders significantly overestimate the win rate required to be profitable.
How many losing trades in a row should I expect?
The expected longest losing streak over n trades is approximately log(n) / log(1 / Win Rate). At a 50% win rate over 100 trades, expect roughly 7 consecutive losses. At a 45% win rate over 200 trades, the expected worst streak extends to approximately 10. Planning position sizes around this formula prevents panic-quitting a working system during normal variance.
What is the minimum win rate needed with a 2:1 risk/reward ratio?
A 2:1 R:R system breaks even at approximately 34% win rate before commissions, solving Win Rate × 2 = (1 – Win Rate) × 1 to get Win Rate = 33.3%. Commissions and slippage push the practical break-even closer to 36–38% in most futures and equity markets. Research by Brad Barber and Terrance Odean found 70–80% of retail day traders lose money net of fees — a break-even threshold this low suggests most losses stem from position sizing and discipline failures, not insufficient win rates.
How do prop firm drawdown limits affect position sizing?
Prop firm hard drawdown limits directly cap the maximum allowable risk per trade. Topstep’s $50K Combine carries a $3,000 trailing max drawdown (6%). To keep the 5th percentile Monte Carlo outcome within that limit at a 50% win rate and 2:1 R:R, risk per trade must stay at or below approximately 0.5%. Running the simulator before funding reveals the exact ceiling specific to your win rate and R:R combination — a number no static formula can provide.
