Behind the counter, "american odds to decimal" 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 one.
Betting odds implied probability is the chance a price suggests, before any judgement about whether it is right. For decimal odds it is one divided by the price. To convert American odds to a percentage, a positive number gives one hundred divided by the number plus one hundred, and a negative number gives the number, without its sign, divided by itself plus one hundred. A price of +150 implies forty per cent, and a price of -200 implies close to sixty seven.
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.
Are betting odds accurate? As forecasts, closing prices are well calibrated: outcomes priced at a fifty per cent chance happen close to half the time across many events. As prices, they are deliberately a little short of fair. Betting odds are different in different countries mostly in notation and in margin: decimal, fractional and American formats show the same chance, while books serving smaller markets tend to add a wider cut.
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.
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.
The book shortens the side taking most stakes and lengthens the other, so it is never heavily exposed to a single result.
News such as injuries, lineups or weather moves them, and so does money, with stakes from sharp bettors shifting prices faster than casual ones.
A trading team or a model estimates the chance of each outcome from form, ratings and past results before any margin is added.