Converting Fractional Betting Odds into Implied Probabilities

Summary

The document explains how to convert fractional betting odds into implied probabilities. For odds stated as a to b, it gives the conversion b divided by the sum of a and b. Applying that formula to the quoted odds yields implied chances of 0.652 for remain and 0.333 for leave. Their sum falls short of one, and the difference is described as the bookmaker’s margin, or the cost embedded in betting on both outcomes.

A second answer gives different odds and calculations, illustrating why the quoted prices and timing matter. It also points out that odds alone do not reveal the number of bets or the venue’s full profit margin. The document is a brief worked example rather than a general treatment of probability estimation; its numerical conclusions depend on the specific odds cited, and the two answers are not reconciled.

Key ideas

• Fractional odds of a to b imply a probability of b divided by a plus b.
• The implied probabilities from opposite outcomes can sum to less than one because of the bookmaker’s margin.
• Odds-based probabilities depend on the prices available at the time they are quoted.
• The odds alone do not reveal betting volume or fully characterize the venue’s margin.

Tags

# Brexit implied probability


# Brexit implied probability












It is possible to bet on the Brexit e.g. on this page:

https://sports.ladbrokes.com/en-gb/betting/politics/british/eu-referendum/uk-european-referendum/220800266/

The quotes are 8/15 for remain, and 8/4 for leave.

Can someone derive the implied probabilities for remain/leave?

## Answer by nbbo2 (score 4, accepted)

https://quant.stackexchange.com/a/27657

The general formula for conversion of "a to b" odds to a probability is $p=\frac{b}{a+b}$

http://www.calculatorsoup.com/calculators/games/odds.php

So 8/15 remain implies remain with probability 0.652

8/4 for leave implies leave with probability 0.333

The amount 1-0.652-0.333 = 0.0145 represents the bid-ask spread or loss that you suffer (and the other side collects) for making both bets.

## Answer by LazyCat (score -1)

https://quant.stackexchange.com/a/27656

It's 6/4 to leave right now. Hence, the implied probabilities are 6/10 = 0.6 to leave and 8/23 to stay. So it's about 2/3 to leave, 1/3 to stay. You can't do much better, since you don't know number of bets and the profit margin for the venue.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.