Implied probability calculator
A price is a probability wearing a costume.
Type any one of them — a market price in cents, American odds, decimal odds, a fraction — and the other three fall out of it. They are the same number said four ways, and the whole reason prediction markets are easier to read than a sportsbook is that they say it the honest way: in cents.
stake returned plus profit, if it resolves your way—
What the conversion actually is
A contract that pays $1 if something happens and $0 if it does not is worth exactly the probability of it happening. Buy at 42¢ and you are saying “this is more likely than 42%”. That is the entire idea; the odds formats are packaging.
American odds hide it. −150 means stake $150 to win $100, which is a probability of 150/250 = 60%. +240 means stake $100 to win $240, which is 100/340 = 29.4%. Decimal odds are the cleanest of the three: the decimal is the total return per $1 staked, so the probability is just one divided by it.
One warning the conversions cannot give you: a single price converted on its own still contains whatever margin the venue charges. To get the number the market really believes, you need both sides — that is the no-vig calculator.
Questions
What is implied probability?
The probability a price implies, if the price is fair. A contract paying $1 that trades at 42 cents implies a 42% chance. On American odds of -150 it is 60%; on decimal odds of 2.38 it is 42%.
How do I convert American odds to probability?
For negative odds, probability = odds / (odds + 100) using the absolute value: -150 gives 150/250 = 60%. For positive odds, probability = 100 / (odds + 100): +240 gives 100/340 = 29.4%.
Does implied probability add up to 100%?
Across the two sides of a real market, no. It adds to more than 100%, and the excess is the venue's margin. Stripping it out is what the no-vig calculator does.