Methods / 02

Put the edge under pressure.

A favourable estimate is the starting point. Account for fees, uncertain probabilities and the variance between an expectation and a realised result.

Interactive model / synthetic inputs

What survives the costs?

Sample scenarios
Position

Probability of a win, including trials that push.

Stake returned. Win and push together cannot exceed 100%.

Profit on a win, before commission. Excludes returned stake.

Fixed across all trials.

Costs, volume & stress
Costs, volume and stress

Identical terms and independent outcomes assumed.

Charged on wins, losses and pushes.

Charged only on the net win payout.

Moves win probability; push probability stays fixed.

Loss probability: 46.00%. Stress values are clipped to valid probabilities.

Net edge / stake
+1.91%
EV / trial
+1.91 units
Break-even win probability
51.01%
Expected total
+1,912.00 units
Total staked
100,000 units
Total standard deviation
3,016.84 units

The edge changes sign under stress

Probability stress EV per trial, units
Expected value across the probability stress rangeExpected value ranges from −5.81 to +9.64 units per trial. The following table gives the exact values.11.5-7.748.00%56.00%Win probability

● Base case— Net EV┄ Zero EV

Probability stress scenarios
ScenarioWinEV / trial
Lower probability48.00%−5.81 u
Base case52.00%+1.91 u
Higher probability56.00%+9.64 u

A sensitivity test, not a confidence interval. More volume scales expected value; it does not guarantee a profit. Standard deviation assumes independent trials and fixed probabilities. Shared risks and changing conditions can produce materially different outcomes.

Calculation & assumptions

EV = stake × (p × b × (1 − c) − (1 − p − q) − f)

p is win probability; q is push probability; b is the net payout multiple; c is commission on win profit; f is cost per unit staked. Percentages are converted to fractions. Break-even solves EV = 0 with push probability fixed. If no valid win probability covers the costs, the result is “Not reachable”.

Total expected value = EV × trials. Total standard deviation = stake × √(trials × per-unit outcome variance). A win earns b × (1 − c) − f; a push loses f; a loss loses 1 + f. Total staked is turnover, not the capital required.

Illustrative mathematics only. These are not client results, calibrated forecasts, a bankroll recommendation or a claim about an achievable edge. No input is stored or sent anywhere.

What survives the review

Data integrity
Reconcile timestamps, duplicated events, missing outcomes and the information available at the decision time.
Out-of-sample tests
Use later periods and held-out records. Report the gap between fitting the model and applying it.
Execution
Include fees, settlement rules, latency and capacity. A theoretical price is not an available fill.
Stop conditions
Define loss limits, stale-input rules and the change in assumptions that requires a new review.

Follow the calculation.

The sample research note carries one set of assumptions through to expected value and turnover.

Read the sample paper