# Expected value of a bet: from odds and your own estimate to a result

> Educational calculator: enter a stake, decimal odds and your own probability estimate to see implied probability, break-even and expected value, with open formulas.

Source: https://bookiechecklist.com/ev-calculator/
Updated: 2026-11-13

Expected value (EV) is the average result of a bet if your own probability estimate were right: stake × (probability × decimal odds − 1). At odds of 2.00 and an estimate of 45%, an A$20 stake has an EV of −A$2.00. Your estimate is an opinion, not a fact, and a positive figure on paper does not predict any single result.

## Calculate

Enter a stake in A$, decimal odds of 1.01 or more, and your own estimate of the chance as a percentage. The tool shows the implied probability, the break-even point and the expected value.

Use Calculate to run it and Reset to clear it. Results are illustrative, not a price.

If the tool does not load, the formulas and the six worked examples below work without it.

**Where this stands:** the tool runs in the browser; the static table below repeats its logic.

## The formulas

- Implied probability q = 1 ÷ O, where O is the decimal odds.
- Expected value EV = S × (p × O − 1), where S is the stake and p is your estimate as a fraction.
- Break-even probability = q. At p equal to q, EV is zero.
- Market margin = (sum of 1 ÷ O for every outcome) − 1.

The inputs are a stake S, odds O of at least 1.01, and an estimate p from 0 to 100%. These are definitions and are rechecked once a year.

**Where this stands:** four formulas, all stated in full and checkable by hand.

## Six worked examples

**Expected value · illustrative arithmetic, not prices or advice · checked 2026-11-13**

| Stake | Odds | Your estimate | Implied probability | Expected value |
|---|---|---|---|---|
| A$20 | 2.00 | 45% | 50.00% | −A$2.00 |
| A$25 | 3.50 | 30% | 28.57% | +A$1.25 |
| A$50 | 1.60 | 60% | 62.50% | −A$2.00 |
| A$15 | 6.00 | 15% | 16.67% | −A$1.50 |
| A$40 | 2.20 | 50% | 45.45% | +A$4.00 |
| A$100 | 1.25 | 75% | 80.00% | −A$6.25 |

Working for the first row: 20 × (0.45 × 2.00 − 1) = 20 × (−0.10) = −2.00.

**Where this stands:** two of the six examples are positive, and only because the invented estimate beats break-even.

## Reading the result

A positive EV says your estimate is above the break-even chance. It does not say the estimate is right. Market prices already carry a margin: prices of 1.85 and 2.05 imply 54.05% and 48.78%, a total of 102.83%, so the margin is 2.83%.

Learn more in [implied probability](https://bookiechecklist.com/implied-probability/) and [the overround page](https://bookiechecklist.com/bookmaker-margin-overround/). For the evidence on long-run results, see [can you win consistently betting online?](https://bookiechecklist.com/can-you-win-consistently-betting-online/) and [are bookmaker odds fair?](https://bookiechecklist.com/are-bookmaker-odds-fair/).

**Where this stands:** EV compares your estimate with the price; it says nothing about a single bet.

## What this tool does not do

It does not suggest bets, rank prices or forecast results. It does not store what you enter. Set limits before you play: [set a deposit limit](https://bookiechecklist.com/set-a-deposit-limit/), and [register with BetStop](https://bookiechecklist.com/register-with-betstop/) if you want to exclude yourself. Other help is on [the responsible gambling page](https://bookiechecklist.com/responsible-gambling/).

**Where this stands:** the tool teaches arithmetic and makes no recommendation.

## 18+ only. Gamble responsibly.

18+ only. Gambling can be harmful. Need help? Call [Gambling Help Online](https://gamblinghelponline.org.au) on 1800 858 858 (free, 24/7) or visit gamblinghelponline.org.au.

To exclude yourself from licensed Australian online and phone wagering providers, register with [BetStop](https://www.betstop.gov.au) at betstop.gov.au. We are not a bookmaker and do not take bets.

**Where this stands:** free help and exclusion routes exist and are named above.

## FAQ

**What is expected value?**

It is the average result of a bet if your own probability estimate were right: stake × (probability × odds − 1). It is not the result of any single bet.

**What does a negative expected value mean?**

On your estimate, the bet loses money on average. At odds of 2.00 and an estimate of 45%, an A$20 stake has an expected value of −A$2.00.

**Does a positive figure mean I will win?**

No. It shows only that your estimate beats the break-even chance. Any single bet still wins or loses outright, and your estimate is an opinion, not a fact.

**What odds can I enter?**

Decimal odds of 1.01 or more. Anything lower returns the message: Enter odds of 1.01 or more.

**How is the market margin worked out?**

Add 1 ÷ odds for every outcome in the market and subtract 1. For prices of 1.85 and 2.05 that gives 0.5405 + 0.4878 − 1 = 2.83%.