Gambling terms, explained straight

Odds, Probability & Bankroll

Implied probability vs actual probability

Implied probability is the likelihood of an outcome suggested by quoted odds, while actual probability is the real-world chance of that outcome occurring.

Formula for implied probability (fractional odds a–b)
P = b / (a + b)1
Formula for implied probability (positive American odds)
P = 100 / (Odds + 100)1
Formula for implied probability (negative American odds)
P = |Odds| / (|Odds| + 100)1

Key points

  • Implied probability is derived from odds using a conversion formula; actual probability is the real-world likelihood independent of the market.12
  • A gap between the two figures can indicate pricing error, bookmaker margin, or other market effects, not a change in the event itself.2
  • The comparison is used in sports betting, betting exchanges, and finance to assess whether odds offer value relative to the true chance.13

Where this term is used

Not the same as

Sources

  1. Mathematics of bookmaking en.wikipedia.org Provides the definition of implied probability and the conversion formulas for fractional and American odds.
  2. Player Props: Understanding the Math Behind the Lines wizardofodds.com Explains how the gap between implied and actual probability reflects pricing error or margin.
  3. Dynamic Scoring: Probabilistic Model Selection Based ... - PMC pmc.ncbi.nlm.nih.gov Supports the application of this comparison in sports betting and finance contexts.

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.