A strategy can have positive expected value if its true outcome probabilities justify the offered payouts after costs. Demonstrating that condition is harder than writing the formula: a model estimate is not the true probability, and a short winning record does not prove it.
This article gives hypothetical arithmetic and an evidence checklist. The former “97% of bettors lose / 3% win” figures and claimed survey of hundreds of profitable bettors were not supported by a cited study and are removed.
Use the actual payout
For a binary bet with decimal payout d and true win probability p, the expected net return per dollar staked is:
Expected ROI = p × d − 1
Gross break-even win probability = 1 / d
Decimal odds include the returned stake. At −110, d = 1 + 100 / 110 = 1.90909 and the gross break-even rate is 52.38095%. The assumption of a 50% true win chance gives 0.50 × 1.90909 − 1 = −4.54545% expected stake return. At a 55% true chance it is +5%, before additional costs.
The 2.38-percentage-point gap between a 50% chance and the break-even rate is a different unit from the 4.55% expected stake loss. An overround or no-vig estimate is also not a direct realized-return measurement.
For a $1 exchange contract bought at cost c, gross expected profit per share is p − c, while gross ROI on acquisition cost is (p − c) / c. Include the actual applicable fees and execution costs. A model estimate in place of p gives a conditional estimate, not verified edge.
Calibration helps inspect probabilities
A reliability curve compares stated probabilities with observed frequencies on a defined population. ECE summarizes binned discrepancies and depends on bin definitions and sample composition. It is not a local error bound, and no universal ECE cutoff proves a paid probability source is worth buying or will beat the market.
Inspect held-out predictions, their timestamps, outcome labels and baseline comparisons. Evaluate the subset you intend to trade separately: selection can change calibration. A calibrated model can agree with market prices and still have no gross trading edge.
Sizing cannot repair negative expectation
For a simplified binary bet, Kelly’s fraction is (p × b − (1 − p)) / b, where b = d − 1 is net profit per dollar staked, not the decimal payout d. Its log-growth result assumes a specified probability and payoff distribution.
Fractional Kelly reduces exposure under those same inputs. It neither validates an uncertain probability nor guarantees avoidance of ruin. Concurrent and correlated positions require a portfolio analysis. See the formula and limits for checked contract examples.
More observations help only with a valid design
A fixed number such as 1,000 bets does not certify a strategy. Uncertainty depends on payouts, probabilities, dependence, selection and regime changes. Repeated trades in the same game may not be independent. Report the traded population and any threshold selected after seeing outcomes.
Separate training, calibration and evaluation periods. Preserve losses, rejected orders, missing-data exclusions and cost assumptions. A ledger can make results inspectable; verified execution identifiers add a different kind of evidence. Neither should be presented as more complete than it is.
Selling early is a different payoff policy
If a contract bought at 40c is actually sold at 55c, gross profit is 15c per share, or 37.5% of acquisition cost, before fees. The quoted 55c bid and sufficient size are needed; a midpoint or last trade does not guarantee that exit.
Exiting and holding to settlement have different payoff distributions. An early sale can reduce some outcome exposure, but it can also introduce costs and forego later gains. It is not a universal route to higher expected profit. Compare predeclared policies on the same population with executable-price assumptions.
Evidence to ask for
Ask for dated predictions, exact offered or filled prices, settlement rules, evaluation scope, costs and uncertainty. Review model quality separately from strategy returns. Inspect the public results and CLV evidence under their stated coverage and provenance limits; pregame CLV is a market-relative diagnostic, while a near-terminal in-play close may already contain the outcome.
The condition for positive expectation is useful arithmetic. Whether a real strategy satisfies it remains an empirical question.