Stake sizing strategy

Kelly Criterion for Binary Options: Formula, Payout and Limits

A sizing concept for understanding stake limits, not a guarantee of outcome.

Education only: Strategy content does not provide trade instructions, market-direction recommendations, or profit claims. Test assumptions in a demo account, confirm broker rules, and stop when the setup fails.

Kelly Criterion for Binary Options: Formula, Payout and Limits visual

Stake sizing framework

How the strategy works

This is a bankroll-fraction model based on uncertain inputs, not a result-driven progression or a method for predicting price direction.

Kelly is useful as an educational concept because it shows how sensitive stake size is to assumed edge. In binary options, edge estimates are usually too uncertain for aggressive sizing.

01

Step 1

Kelly sizing calculates a stake fraction from an assumed edge and payout. In binary options, the edge estimate is usually the weakest input.

02

Step 2

At a 95% payout, the break-even win rate is about 51.28%. Full, half, and quarter Kelly produce very different stakes, and small samples can distort every version.

03

Step 3

Use Kelly as an educational calculation to see how sensitive stake size is to uncertain assumptions, not as proof of an edge.

Worked example

Use the example only as a planning model. It is not a market-direction recommendation, trade instruction, or profit claim.

95% payoutBreak-even win rate around 51.28%

SizingPrefer fractional examples for education

Input riskTreat unproven edge as zero

Demo validation

Demo testing checklist

The broker must show payout clearly because payout is part of the break-even and sizing math.

Use a paper worksheet or demo account to review the full stake path, payout, reset behavior, and cap breach. Do not treat the result as a threshold for funded trading.

01

Calculate break-even first

02

Stress-test win-rate error

03

Use fractional sizing only as a learning model

Market and expiry context

When the method can be observed—and when to stop

Market conditions and expiry must be written before a demo observation. They are test controls, not claims that a setup predicts direction.

Observe

Market conditions

A Kelly estimate requires a repeatable contract population with stable payout and a defensible probability estimate. Mixing assets, sessions, strategies, or market regimes makes the historical win rate an invalid input.

Skip

Do not test when

Treat the edge as unknown after payout changes, small samples, selection bias, strategy edits, or materially different volatility; an unknown or non-positive edge implies no Kelly stake.

Duration

Why expiry matters

The estimated win rate must come from the same expiry used in the calculation because duration changes both the setup and observed outcome distribution. Never transfer a result from one horizon to another.

Definitions used here

Key terms for this page

Open a definition when a broker uses the same label differently or leaves a condition unclear.

01

Expected value

The probability-weighted average net result under stated win, loss, refund, and payout assumptions. A high payout alone does not establish positive expected value.

02

Break-even win rate

The minimum win rate needed to offset losses at a stated payout. At an 80% payout it is about 55.56%.

03

Sample size

The number of eligible observations used to calculate a rate or performance statistic. Small samples produce less reliable estimates than larger, clearly defined samples.

04

Payout rate

The percentage return displayed for a contract before confirmation, subject to product and account conditions.

Calculated example

Work through the assumptions

Input

Net payout b = 0.80 and estimated win rate p = 0.58; q = 0.42

Math

Kelly fraction f = (b × p - q) / b = (0.80 × 0.58 - 0.42) / 0.80

Result

f = 0.055, or 5.5%; at p = 0.55 the result becomes negative

Study protocol

What to model before testing

Kelly sizing is only meaningful when the win probability and net payout are estimated from a defensible sample. Binary-option estimates are fragile because a small change in either input can move the suggested fraction sharply.

01

Record 1

Sample size, date range, rule, and observed payout

02

Record 2

Break-even rate versus the estimated win rate

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Record 3

Full, half, and quarter Kelly outputs alongside a hard cash cap

Review metrics

Measure the process, not the story

Confirm that the product is available for the intended user and that the exact operating entity and domain can be verified before any demo study. Define net payout b, assumed win probability p, and full-loss result -1 explicitly. The simple expected value per unit is b × p - (1 - p), and break-even is 1 / (1 + b).

01

Input uncertainty

Report the estimated win rate with sample size, selection rule, payout range, and a confidence interval rather than one point estimate.

02

Break-even margin

Compare the conservative probability bound, not only the sample mean, with 1 divided by 1 plus net payout.

03

Sensitivity

At an 80% payout, a one-percentage-point change in estimated win probability moves full Kelly by 2.25 percentage points.

04

Drawdown stress

Compare hypothetical full, half, and quarter fractions under loss clusters and retain a separate hard cash cap.

How to interpret the worksheet

With p = 58% and b = 80%, full Kelly is 5.5%, but a 58-of-100 sample has a wide approximate interval whose lower bound is below break-even. Treat the edge as zero when the conservative bound does not clear break-even or observations are selected, dependent, or live-unverified.

Sample

Publish the full denominator

Report planned, eligible, skipped, rejected, accepted, settled, missing, and excluded observations. Give every exclusion a reason fixed before its outcome was known.

Timing

Preserve the event chain

Use one timezone and keep submission, acceptance, entry reference, expiry, settlement, and screenshot times when the study depends on execution or duration.

Economics

Use actual payout and cash results

Show the payout distribution, full-loss or refund treatment, fees, stake path, cumulative exposure, and the same result path at a flat stake.

Uncertainty

Separate description from validation

Report missing data, rule changes, median and P95 where timing is measured, and confidence intervals for rates. A small demo batch does not establish an edge or a live-fund threshold.

Platform requirements

What this strategy needs from a broker

Kelly calculations require a clearly displayed payout. Unproven estimates of trading advantage remain unreliable inputs.

Check that the platform clearly shows the required contract, expiry, payout, order controls, and demo history before testing the method.

Payout guide Risk management strategy Glossary

Sources

Sources and assumptions

These references support definitions, payout math, uncertainty, and market context. They do not prove that a strategy is profitable.

01

CFTC

Binary Options Fraud resources: platform, solicitation, registration, and payout-risk context. This source does not validate a strategy.

Open source

02

Investor.gov

Binary Options Fraud: withdrawal, identity, software-manipulation, and return-claim warnings.

Open source

03

NIST

Binomial proportion confidence intervals explain why a small observed win rate is not a stable probability estimate.

Open source

Failure conditions

Avoid using guessed win rates, thin demo samples, or influencer results as the input for Kelly calculations.

Test

Calculate break-even win rate first

Test

Use fractional sizing only for education

Test