Start with the estimate
Suppose a bookie offers a hypothetical 2.10 and a model estimates a 50% chance. The model is making a judgement about how often the selection would win, not reporting a fact about the next game.
To see the effect, work with a $1 stake. Decimal odds include that original dollar.
This applies the probability-weighted expectation described by OpenStax to the possible win and loss. The probability assumption remains an input, not an observed result.
Expected profit = estimated probability × decimal odds − 1
Suppose, purely as an example, that a selection has an estimated 50% chance and is offered at 2.10:
- A win returns $2.10, including the $1 stake.
- The assumed average return is 0.50 × $2.10 = $1.05.
- Subtracting the $1 stake gives an expected profit of $0.05, or 5% of the stake.
That is an average under the assumption, not a payment you collect on each bet. If the actual chance were 45%, the same 2.10 offer would have an expected loss of 5.5% per stake.
Test the probability assumption
Keep the illustrative price fixed at 2.10 and change only the assumed chance. The table uses a hypothetical $20 stake and excludes fees and commission.
| Assumed chance | Expected profit per $1 | Expected profit on $20 |
|---|---|---|
| 45% | 0.45 × 2.10 − 1 = −$0.055 | −$1.10 |
| 50% | 0.50 × 2.10 − 1 = $0.05 | $1.00 |
| 55% | 0.55 × 2.10 − 1 = $0.155 | $3.10 |
These are averages implied by an assumption. In each individual case a winning bet returns $42 including the stake, while a losing bet returns $0. The table does not estimate anyone's actual chance. An estimate that is five percentage points too high can reverse the conclusion.
At 2.10, the break-even probability is approximately 47.62% before costs. An actual probability above that would imply positive EV; a probability below it would imply negative EV. Establishing that probability is the difficult part.
What does a fair-price estimate tell you?
A bookie’s price is the offer. A fair-price estimate is what a model thinks that chance should cost without bookmaker margin. Those are different kinds of number.
The estimate might use market prices, sporting data and modelling assumptions. Calling it fair does not make it correct. You should be able to see what went into it and when those inputs were checked.
Removing margin from a market requires a method. The estimate can be affected by market depth, stale quotes, participant availability, line identity and which outcomes are actually offered. A number labelled fair is only as useful as its evidence and assumptions.
Two-way and three-way markets need different treatment. A model must also compare the exact line and settlement class. Whole-number lines that can push are not interchangeable with adjacent half-number lines.
Why can positive-EV bets lose?
Even a correctly estimated advantage does not determine the next result. Several losing bets can occur in a row, while a weak process can have a winning run.
Increasing a stake after a loss does not improve the probability or price. Bankroll limits and variance remain relevant regardless of what an EV estimate says.
What evidence should you inspect?
Before accepting a value label, ask three things: what is the exact bet, where did the estimated chance come from, and is the quoted offer still available on those terms? Then check fees, commission and the intended stake. Those details belong beside the green percentage.
For retrospective analysis, use records captured at the relevant time. Closing line value can provide context, but it also has limitations and is not proof of profitability.
Where BetBible fits
The public calculators explain entered prices. A free account opens Odds, Stats, Racing and free BetBot. +EV is part of membership and supplies model-based analysis, not guaranteed outcomes.
Start with line shopping if you want to understand how the offered price changes the calculation. Read arbitrage betting for the different problem of covering all outcomes.