The Mathematics of Winning — Interactive Calculator
Can your trading plan survive its normal losing sequences?
Test position size, edge, and a defined trading horizon. The result estimates the chance of breaching a drawdown limit under explicit assumptions — not an unknowable promise about the future.
Your Trading Plan
The amount lost if a planned stop is filled. Include expected slippage.
Use realized results after commissions, spread, slippage, and partial exits.
“Ruin” is operational: the point where the plan should stop, not necessarily a literal $0 balance.
Fixed dollars keeps the entered loss constant. Re-size applies its starting percentage to current equity after every trade.
Compare Scenarios
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Chance of Breaching Drawdown Limit
Enter your numbers to test whether the plan can survive its normal loss distribution.
Exact finite-horizon path model
Position Size & Trade Math
Initial Risk / Equity
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Position risk as a percentage of starting equity.
Initial Risk Units
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Starting equity divided by the planned loss.
Losses To Limit
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Consecutive planned losses from the starting balance.
Expectancy / Trade
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Average result in R and starting dollars, conditional on the inputs.
Break-Even Win Rate
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Minimum net win rate at the entered net reward:risk.
Full-Kelly Diagnostic
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A highly estimate-sensitive growth diagnostic, never a sizing recommendation.
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Loss-Sequence Reality
Starting Loss Sequence
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Chance the next required number of trades are all losses.
Sequence In Horizon
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Chance that loss streak appears somewhere in the selected horizon.
Literal $0 In Horizon
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Depends on the selected sizing policy.
Execution Costs — An ES Illustration
A one-contract ES round trip may carry roughly −$17 in commissions plus one tick of spread in the course example. Actual costs vary by instrument, broker, order type, and slippage. Enter net performance statistics above so costs are not ignored.
Illustrative cost / trade$17.00
Trades / month100
Cost drag / month$1,700
Cost drag / year$20,400
$20,400
illustrative annual drag at this trade frequency, before slippage beyond the example
Position sizing belongs ahead of prediction.
A positive expectancy only matters if the account can survive enough trades for that distribution to emerge. "The Mathematics of Winning" walks through the full framework: position size, loss sequences, execution drag, and reward:risk.
