american-decimal-conversion draft

Bidirectional conversion between American odds and decimal odds

Tags
odds conversion fundamentals
Vocabulary
american_odds
Sportsbook-style odds; positive (e.g. +150) means win $150 on $100 stake, negative (e.g. -120) means stake $120 to win $100. Mimir's canonical even-money form is -100.
decimal_odds
Total payout (stake + winnings) per $1 stake; e.g. 2.50 means $2.50 returned for every $1 bet.
even_money
A bet whose payout equals its stake — win $1 on $1 wagered, with implied probability 50%. Decimal 2.00; American +100 or -100 (Mimir uses -100 as canonical).

American and decimal are two notations for the same underlying probability claim. American is sportsbook-native in the US; decimal is sportsbook-native in Europe and the UK and is the easier format for arithmetic. Converting between them is a deterministic, lossless transform.

Worked example

American +150 → decimal: 1 + (150 / 100) = 2.50. American −120 → decimal: 1 + (100 / 120) ≈ 1.833. Decimal 2.50 → American: positive branch since decimal ≥ 2.0 → (2.50 − 1) × 100 = +150. Decimal 1.833 → American: negative branch since decimal < 2.0 → −100 / (1.833 − 1) ≈ −120.

Gotchas

Open questions

Cross-references