Odds to probability converter
Odds are a ratio and probability is a fraction of the whole. Every betting format is a rearrangement of the same number.
%
Odds against, to 1
3.000 00
- Odds on, to 1
- 0.333 33
- Decimal odds
- 4.000 00
- American odds
- 300.0
- One in how many
- 4.0000
- Log-odds
- -1.098 612
Show the working
- Probability = 25
- p = 25 / 100 = 0.25
- Odds against, to 1 = (1 - 0.25) / 0.25 = 3
- Odds on, to 1 = 0.25 / (1 - 0.25) = 0.333 333
- Decimal odds = 1 / 0.25 = 4
- American odds = 0.25 >= 0.5 ? -100*0.25/(1-0.25) : 100*(1-0.25)/0.25 = 300
- Log-odds = ln(0.25/(1-0.25)) = -1.098 61
- One in how many = 1 / 0.25 = 4
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- odds against = (1 - p) / p
- decimal odds = 1 / p
- American odds = -100p/(1-p) for favourites, 100(1-p)/p for underdogs
- logit = ln(p / (1 - p))
Bookmakers price above the true probability; the excess across all outcomes is the overround.