American odds
American odds are anchored on $100:
- Plus (+150): profit on a $100 stake. +150 wins $150.
- Minus (−120): stake needed to profit $100. −120 risks $120 to win $100.
+100 and −100 are both even money. No valid American price sits between them, which is why magnitudes below 100 are not real prices (the odds converter rejects them).
Decimal odds: the version to do math with
Decimal odds are the total return per 1 unit staked, including the stake. They make every formula in this academy one line long.
decimal(+X) = X/100 + 1 // +150 → 2.50 decimal(−X) = 100/X + 1 // −120 → 1.8333 profit per unit = decimal − 1 implied probability = 1 / decimal
| American | Decimal | Fractional | Implied |
|---|---|---|---|
| +300 | 4.000 | 3/1 | 25.0% |
| +150 | 2.500 | 3/2 | 40.0% |
| +100 | 2.000 | 1/1 | 50.0% |
| −110 | 1.909 | 91/100 | 52.4% |
| −150 | 1.667 | 67/100 | 60.0% |
| −250 | 1.400 | 2/5 | 71.4% |
Converting back
decimal ≥ 2.00 → American = +(decimal − 1) × 100 decimal < 2.00 → American = −100 / (decimal − 1)
- Decimal 1.80 is below 2.00, so the American price is negative.
- −100 / (1.80 − 1) = −100 / 0.80 = −125.
Answer: 1.80 = −125, implying 55.6%.
Limitations
Books round displayed prices. A −110 shown on screen may be −109.5 or −110.4 internally, so tiny differences in converted numbers are normal.