Behind the counter, "decimal odds to american odds" 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 about sixty seven.
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.
By the start, the closing price has absorbed everything the market knows, so across many events it forecasts outcomes better than the opening one.
The book shortens the side taking most stakes and lengthens the other, so it is never heavily exposed to a single result.
Mostly in notation and margin: decimal, fractional and American formats express the same chance, while books serving smaller markets often take a wider cut.
News such as injuries, lineups or weather moves them, and so does money, with stakes from sharp bettors shifting prices faster than casual ones.
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.
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.