Answered with numbers you can check — including ours.
For decimal odds the implied probability is 1 divided by the odds. Odds of 2.00 imply 50%, 4.00 imply 25%, 1.25 imply 80%.
For fractional odds of a/b the implied probability is b / (a + b), so 3/1 implies 25%. For positive American odds the formula is 100 / (odds + 100); for negative American odds it is odds / (odds + 100), using the absolute value.
The important step almost everyone skips: those implied probabilities do not sum to 100%. Across a three-way football market they typically sum to 104-108%. The excess is the bookmaker's margin, also called the overround or the vig, and it is how the book makes money.
To get the market's genuine view, divide each implied probability by the total. If the three outcomes imply 45%, 30% and 30% - summing to 105% - the de-margined probabilities are 42.9%, 28.6% and 28.6%. Compare your model against those, not the raw numbers, or you will see phantom value in every market.
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