Calculate probability, odds ratios, and betting odds with step-by-step solutions
Odds represent the likelihood of an event occurring compared to it not occurring. They are commonly used in probability theory, statistics, and betting. Odds can be expressed in different formats including fractional, decimal, and American odds.
Expressed as a fraction (e.g., 3/1)
Profit = Stake × (numerator/denominator)
Expressed as a decimal (e.g., 4.00)
Total Return = Stake × Decimal Odds
Expressed with + or - (e.g., +300, -150)
+ = underdog, - = favorite
Odds = p / (1 - p)
Where p = probability of success
p = odds / (1 + odds)
Where odds = odds ratio
The odds ratio compares the odds of an event occurring in one group to the odds of it occurring in another group:
OR = (a/b) / (c/d) = (a×d) / (b×c)
Where a, b, c, d are the frequencies in a 2×2 contingency table.
Probability = 0.25 (25%)
Odds = 0.25 / (1 - 0.25) = 0.25 / 0.75 = 1/3
Fractional odds: 1/3
Decimal odds: 1.33
Odds = 2/1
Probability = 2 / (1 + 2) = 2/3 = 0.667
Probability = 66.7%
| Format | Example | Probability | Profit on $100 |
|---|---|---|---|
| Fractional | 3/1 | 25% | $300 |
| Decimal | 4.00 | 25% | $300 |
| American | +300 | 25% | $300 |