Put as "american odds formula", 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 the same.
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.
Decimal odds are the simplest format for reading a price. The number is the whole return for one unit, stake included, so 2.50 returns two and a half units and the profit is 1.50. The decimal odds formula is just payout equals stake times odds, simple enough to need no calculator. Evens in decimal odds is 2.00, where the profit matches the stake. Decimal odds can never be negative or fall below 1.00, because the return always includes the stake, and most sports betting quotes its prices this way.
No. Converting between decimal, fractional and American notation changes only how the number looks; the probability and the margin stay identical.
A figure such as minus 200 shows the stake needed to win one hundred, which is why a favourite always carries a negative number.
Seeing the same number as decimal and as American or fractional catches misreadings, since any format can express the price and its chance.
A figure such as +150 shows the profit on a stake of one hundred, and a positive number marks the underdog in the market.