Decimal Odds, Probability and Expected Value
Work through expected value, probability sensitivity, commission, overround and quote timing.
Price, probability & uncertainty
Find out what your edge depends on.
A price is observable; the true chance is not. Learn the calculation, then change its assumptions. This workshop separates returns, break-even probability, model uncertainty and bookmaker margin.
- 01Calculate returns
- 02Stress-test the estimate
- 03Inspect a market
- 04Check timing
18+ learning material. Every case study, price and probability in these workshops is fictional unless explicitly labelled otherwise. These exercises do not place bets, reserve account funds, or establish that a strategy is profitable. Set affordable time and money limits; taking no bet is a valid decision.
Interactive expected-value calculator
What does £10 at 2.10 actually mean?
- Gross return if won
- £21.00
- Net profit if won
- £11.00
- Break-even after fee
- 47.62%
- Estimated net EV
- £1.55
| Piece of the calculation | Your inputs | Meaning |
|---|---|---|
| Win contribution | 55.0% × £11.00 | Probability-weighted net win, after the entered fee. |
| Loss contribution | 45.0% × £10.00 | Probability-weighted stake lost. |
| Net EV | £1.55 | Win contribution minus loss contribution, not a promised result. |
| Fair odds from estimate | 1.818 | No-fee price corresponding to the entered probability. |
What if the probability is five points wrong?
| Assumption | Chance | Estimated EV per £1 | Estimated EV on your stake |
|---|---|---|---|
| Lower estimate | 50.0% | 5.00p | £0.50 |
| Entered estimate | 55.0% | 15.50p | £1.55 |
| Higher estimate | 60.0% | 26.00p | £2.60 |
Commission here applies to the winning profit of one isolated ordinary bet. Exchanges often charge on net market winnings, with account-specific rates and other conditions; this is not a full exchange account calculation. Pushes, partial wins, taxes, promotions and builder repricing are outside this binary EV model.
Read the source: Smarkets: probability-weighted expected value ↗
Bookmaker margin workshop
Why the three probabilities add to more than 100%.
Home, draw and away are mutually exclusive and exhaustive for a normal-time result market. Convert all three prices, not only the one you prefer. The excess of their summed implied probabilities above 100% is the overround. It is a pricing characteristic, not a guarantee of the operator’s realised profit.
- Implied probability sum
- 104.81%
- Excess over 100%
- 4.81 pp
- Market outcomes
- 3
- Normalisation rule
- Proportional
| Outcome | Raw implied chance | Proportionally normalised |
|---|---|---|
| Home | 47.62% | 45.43% |
| Draw | 29.41% | 28.06% |
| Away | 27.78% | 26.50% |
Read the source: Smarkets: implied probability and market overround ↗
A timestamped decision
A good-looking comparison can still be unusable.
| Record | Fictional time | What you can conclude |
|---|---|---|
| Research estimate recorded | 14:00 UTC · home win 52% | This was the estimate before the quote, if the record is authentic and unchanged. |
| Price snapshot | 14:15 UTC · home win 2.00 | A quote was observed at this time; it was not necessarily available to you later. |
| Confirmed line-up change | 14:30 UTC | The 14:00 probability may now be stale. |
| Kickoff | 15:00 UTC | A 15:10 comparison is historical, not a current pre-match opportunity. |
Match the exact fixture, kickoff, market, line, selection and period. A 2.00 price for a home win cannot be compared with the probability of home-or-draw. An Over 2.0 price is not interchangeable with Over 2.5 because a two-goal score settles differently.