Gambling terms, explained straight

Odds, Probability & Bankroll

Implied probability vs true probability

Implied probability is the chance of an outcome derived from betting odds, while true probability is the actual likelihood of that outcome occurring; the difference represents the bookmaker's margin.

Conversion formula
For decimal odds D, implied probability P = 1/D.
Fair odds sum
For fair odds, implied probabilities would sum to exactly 100%.
American odds
Positive odds: 100/(Odds+100); negative odds: |Odds|/(|Odds|+100).21

Key points

  • Bookmaker odds encode an implied probability that includes a margin, so it usually differs from the true probability.1
  • The gap between implied and true probability is where the bookmaker's edge lies.1
  • For fractional odds a-b, implied probability is b/(a+b).21

Where this term is used

Not the same as

Sources

  1. Player Props: Understanding the Math Behind the Lines wizardofodds.com Supports the explanation of bookmaker margin and fair odds sum.
  2. Mathematics of bookmaking en.wikipedia.org Supports the conversion formulas for fractional and American odds.

Sources are drawn from regulators, universities and published research, and each one is labelled with what it actually is — a preprint is not called a paper. Bookmaker and affiliate pages are never cited here, because a page that sells betting is not a neutral authority on it.