Behind the counter, "betting odds implied probability" traces back to an estimate. Every price a bookmaker offers begins as an estimate of probability and ends as a number with a margin added. The estimate comes from data, models and traders; the margin comes from the business. Knowing how the two are combined explains why prices move, why they differ between books, and why the chances they imply never add up to exactly a whole.
Why do betting odds change between the opening price and the start? News moves them: an injury, a lineup, a change in the weather. Money moves them too, since a book shifts the price where stakes pile up. Sharp bettors, whose stakes carry information, move prices faster than casual ones. By the start, a price usually reflects everything the market knows, which is why the closing price is the best single estimate a book offers.
Do betting odds add up to one? The implied probabilities of every outcome in a market would, if the prices were fair. In practice they add up to more, often one hundred and four or one hundred and five per cent on a two way market and more on markets with many outcomes. That excess is the overround, the book's margin, and it is the reason a bettor backing every outcome loses money for certain.
Mostly in notation and margin: decimal, fractional and American formats express the same chance, while books serving smaller markets often take a wider cut.
For a positive price, divide one hundred by the number plus one hundred; for a negative one, divide the number, sign removed, by itself plus one hundred.
By the start, the closing price has absorbed everything the market knows, so across many events it forecasts outcomes better than the opening one.
Divide one by the decimal price: odds of 2.00 imply a fifty per cent chance, and odds of 4.00 imply twenty five per cent.
The amount by which implied chances across all outcomes exceed one hundred per cent, often around four or five per cent on a two way market.
The book shrinks every price slightly below fair, so the return on a winning bet is a little smaller than the true chance deserves.