🔢 Betting Math — Odds Formats, Probability & Expected Value
Understanding betting mathematics is crucial for anyone who wants to treat betting as more than entertainment.
Odds Formats
Decimal Odds
The default in Europe, Australia, and Canada.
- Decimal odds of 2.00 mean you receive $2 for every $1 staked (including your stake).
- Your profit = Stake × (Odds - 1)
- Example: $100 at 2.50 → Profit = $100 × 1.50 = $150, Return = $250
American Odds
The default in the US.
- Positive (+150): Bet $100 to win $150 profit
- Negative (-200): Bet $200 to win $100 profit
- Converting: American > 0 → Decimal = (American/100) + 1; American < 0 → Decimal = (100/|American|) + 1
Fractional Odds
Common in the UK and horse racing.
- 3/1 means you win $3 for every $1 staked
- 5/2 means you win $5 for every $2 staked
- Converting to decimal: (numerator/denominator) + 1
Implied Probability
Every set of odds implies a probability:
Implied Probability = 1 / Decimal Odds
| Odds | Implied Probability |
|---|---|
| 1.50 | 66.7% |
| 2.00 | 50.0% |
| 3.00 | 33.3% |
| 5.00 | 20.0% |
| 10.00 | 10.0% |
When a bookmaker offers 2.00 on a coin flip (which should be 50%), the 0% margin seems fair. But they typically offer 1.90, implying 52.6% — that 2.6% is their margin (vig).
Expected Value (EV)
EV = (Probability of Winning × Amount Won) - (Probability of Losing × Amount Lost)
Example: Betting $100 at odds of 2.50 on an event you believe has a 45% chance:
- EV = (0.45 × $150) - (0.55 × $100) = $67.50 - $55.00 = +$12.50
- This is a +EV bet — you expect to profit $12.50 per $100 bet over time.
The Vig (Bookmaker's Margin)
The bookmaker builds in a margin by offering odds that imply more than 100% total probability.
Two-way market:
- Team A: 1.85 (implied 54.05%)
- Team B: 1.85 (implied 54.05%)
- Total: 108.1% → 8.1% vig
To find the true probability, remove the vig:
- True probability of Team A = 54.05% / 108.1% = 50%
Use our odds converter calculator to quickly switch between formats and see implied probabilities.