Implied probability in one minute
Every price is a probability in disguise. One division converts it, and once you can do that in your head the whole board starts saying something readable.
A decimal price of 4.00 is the claim that something happens about a quarter
of the time. One divided by four is 0.25. That is the entire conversion, and
it is the single most useful thing anybody who looks at a betting board can
learn.
The three formats, one idea
Decimal is the easy one: divide 1 by the price. 2.50 is 40%, 1.50 is
66.7%, 10.00 is 10%.
Fractional is decimal with the stake removed, so add one before dividing.
3/1 is a decimal of 4.00, which is 25%.
American is two rules wearing one coat. A positive number is how much you win
from 100, so +150 is 100 divided by 250, which is 40%. A negative number is
how much you must stake to win 100, so -150 is 150 divided by 250, which is
60%.
They are three ways of writing the same sentence. The reason this product lets you pick one is that a reader in Ohio and a reader in Lyon read the same number differently, not that the numbers differ.
What to do with it
Once every price on a board is a percentage, the board becomes a forecast you can argue with. You can add the outcomes up and see the margin. You can compare one book's number to another's on the same footing. And you can put your own estimate next to it, which is the only way an edge can be identified at all.
What this does not tell you
The implied probability is not automatically an estimate of the true chance. It reflects the quoted price, including any margin and other pricing choices. On a three-way market the implied figures can sum to more than 100%. Estimating probabilities from that book is its own piece of arithmetic, and dividing every implied probability by the total is one allocation assumption, not a universally correct adjustment.
Common questions
How do I convert decimal odds to a probability?
Divide 1 by the decimal price. A price of 4.00 implies 1 divided by 4, which is 25%.
How do I convert American odds to a probability?
For a positive number, 100 divided by the number plus 100. For a negative number, the number divided by the number plus 100, ignoring the minus sign.
Does the implied probability equal the real probability?
Not necessarily. A quoted price can include the bookmaker's margin and other pricing choices, so implied probabilities in a conventional bookmaker market typically add up to more than 100%.