Decoding "decimal odds to american odds" starts 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.
Converting between the formats takes one step each. Fractional to decimal odds means dividing the fraction and adding one, so 5/2 becomes 3.50. American odds to decimal works the same way: a positive number is divided by one hundred and one is added, and for a negative number one hundred is divided by the number, ignoring its sign, before adding one. Decimal odds to American odds reverses the path: above 2.00, subtract one and multiply by one hundred.
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.
A figure such as +150 shows the profit on a stake of one hundred, and a positive number marks the underdog in the market.
Seeing the same number as decimal and as American or fractional catches misreadings, since any format can express the price and its chance.
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 minus 200 shows the stake needed to win one hundred, which is why a favourite always carries a negative number.
One over the price: 4.00 points to twenty five per cent, and fractional or American prices convert through the same route.
The whole return for one unit staked, stake included, so a price of 2.50 returns two and a half units, of which 1.50 is profit.