Put as "decimal odds vs american odds", the numbers start with notation. Betting odds come in three formats that say the same thing in different ways. Decimal odds show the total return per unit staked, American odds show a win on a hundred or the stake needed to win a hundred, and fractional odds show profit against stake. What changes between them is the notation; the price and the margin inside it stay exactly the same.
Decimal odds vs American odds is a question of habit more than value. Both describe the same probability and the same margin, so neither format pays more. The case for why decimal odds are better is practical: the return is visible at once, comparing two prices needs no sign rules, and multiplying the legs of a combination bet works directly. American odds suit anyone who thinks in wins per hundred, and fractional odds still appear at the racing counter.
Every format can be turned back into a chance. Decimal odds give it as one divided by the price, so 4.00 suggests twenty five per cent, and American and fractional odds convert through the same path. Summing those chances across every outcome of an event gives more than one hundred per cent, and the excess is the margin. Learning any of the three formats matters less than seeing that margin, since it sits inside every price in whatever notation.
Convert every outcome of an event into an implied chance and add them up; the amount above one hundred per cent is the book's margin.
Seeing the same number as decimal and as American or fractional catches misreadings, since any format can express the price and its chance.
One over the price: 4.00 points to twenty five per cent, and fractional or American prices convert through the same route.
Fractional odds set profit against stake, so 5/2 pays five units of profit for every two staked, with the stake returned on top.
A figure such as +150 shows the profit on a stake of one hundred, and a positive number marks the underdog in the market.