Like-for-like comparison
| Decimal odds | Profit on 10 units | Raw break-even probability | Wins needed to cover one loss at equal stakes |
|---|---|---|---|
| 1.25 | 2.50 | 80.00% | 4 wins |
| 1.50 | 5.00 | 66.67% | 2 wins |
| 2.00 | 10.00 | 50.00% | 1 win |
| 4.00 | 30.00 | 25.00% | 1 win covers 3 losses |
| 10.00 | 90.00 | 10.00% | 1 win covers 9 losses |
The table describes equal-stake payoffs before costs. It does not show expected value.
Same expected value, different pattern
Suppose one price is 1.50 with estimated probability 70%:
EV = 0.70 x 1.50 - 1 = 0.05 units per unit.
Suppose another is 5.00 with estimated probability 21%:
EV = 0.21 x 5.00 - 1 = 0.05 units per unit.
Both have the same estimated EV under the inputs, but the 5.00 outcome is expected to win less often and produce a more uneven sequence of results. OpenStax defines expected value and variance.
Estimation error matters
A small probability error can change either estimate. At 1.50, reducing p from 70% to 65% changes EV to 0.65 x 1.50 - 1 = -0.025. At 5.00, reducing p from 21% to 18% changes EV to 0.18 x 5.00 - 1 = -0.10. Probability models should be evaluated; calibration guidance describes one relevant check.
Compare sensitivity to probability error
The same absolute probability error can have different payoff consequences. At decimal 1.25, break-even probability is 80%. If the real chance were estimated at 78%, EV would be 0.78 x 1.25 - 1 = -0.025 units per unit. At decimal 10.00, break-even is 10%; an estimate of 8% gives EV of 0.08 x 10 - 1 = -0.20. Both estimates miss break-even by two percentage points, but the EV effect differs because the payoff differs.
Long prices also produce wins less frequently under a coherent estimate, so short samples can look especially uneven. Short prices can produce long winning sequences while one loss removes several small profits. Neither pattern establishes quality without comparing accepted prices with evaluated probabilities.
Decision table
| Question | Why it matters |
|---|---|
| What is the raw break-even probability? | Establishes the quoted threshold |
| Where did the model probability come from? | Determines whether EV is evidence-based |
| How sensitive is EV to a plausible probability change? | Exposes fragile conclusions |
| Is the stake rule independent of the price label? | Prevents short odds being treated as automatically safe |
| Are settlement and costs identical? | Keeps the comparison like for like |
Use short and long as descriptive price labels, not strategy categories or confidence scores. Always retain the exact accepted price in the decision record.
Related resources
Read even money for the midpoint or price and probability matrix for a decision record.
Continue learning
- Next guide: Starting Price vs Fixed Odds
- Related guide: Fair Odds vs Bookmaker Odds
- Definition: Odds-On
Assumptions and limitations
Examples assume binary fixed-odds payoffs, equal stakes and no margin removal, commission or limits. "Short" and "long" are relative labels. Neither price range is recommended, and realised sequences can differ materially from expectation.
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