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.
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
- Implied probability vs actual probability — a near-equivalent wording where 'actual probability' is another term for true probability
Related terms
Odds & probability
Implied probability
Explains how to convert odds into a probability estimate.
Odds & probability
American odds to implied probability
Shows the formula for converting American odds into implied probability.
Odds & probability
Probability vs possibility
Distinguishes between a quantifiable chance and a binary yes/no potential.
Odds & probability
Odds vs probability
Explains the difference between odds ratios and probability percentages.
Odds & probability
Likelihood vs probability
Clarifies the statistical distinction between likelihood and probability.
Odds & probability
Straight flush probability
Covers the true probability of being dealt a straight flush in poker.
Sources
- Player Props: Understanding the Math Behind the Lines wizardofodds.com Supports the explanation of bookmaker margin and fair odds sum.
- 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.