Odds to Probability
Convert betting odds into an implied probability.
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Example
Odds of 3:1 against (o=1/3): p = 0.25
How it works
This formula turns odds written as "o to 1" into the chance of an event happening, expressed as a proportion between 0 and 1. It works because odds compare the number of favorable outcomes to the number of unfavorable outcomes: if the odds are o to 1, then there are o favorable parts out of a total of 1 + o parts. Dividing favorable parts by total parts gives the probability p = o/(1 + o).
When to use it
Use this when betting odds, risk ratios, or chance statements are given in odds form and you need the equivalent probability. It is common in gambling, statistics, forecasting, and decision-making when comparing chances across different events.
Worked example, step by step
Suppose an event has odds of 4:1 in favor, so o = 4. Use the formula: p = o / (1 + o) Substitute the value: p = 4 / (1 + 4) Simplify: p = 4 / 5 Convert to decimal: p = 0.8 So the implied probability is 0.8, or 80%.
Common mistakes to avoid
- Using odds in the wrong direction, such as treating 1:4 against as o = 4 instead of o = 1/4
- Forgetting that o must be the odds as a ratio to 1, not a percentage
- Stopping at the fraction and not converting it to a probability or percent when needed
Did You Know?
Bookmakers' implied probabilities always sum to over 100% — the excess is their built-in margin.
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