Four ways of writing the same price
American, decimal, and fractional odds are not three kinds of bet. They are three notations for one thing: the price of a bet. US sportsbooks post American odds (+150 means $100 of stake wins $150 of profit; -200 means it takes $200 of stake to win $100). The UK tradition is fractional (3/2 reads "3 of profit for every 2 staked"). Europe, Australia, and nearly every betting exchange use decimal, which is simply the total returned per $1 staked, stake included. Same wager, same payout, three outfits.
The fourth format is the one the other three are hiding: implied probability. Divide 1 by the decimal odds and you get the win chance at which the price would be exactly fair. That number is the universal translator. You cannot easily compare +150 against 8/13, but you can always compare 40% against 61.9%, and once everything is a probability you can also see what the bookmaker added on top (more on that below). For textbook probability questions (dice, cards, and/or combinations, repeated tries), our probability calculator is the right tool; this page is about reading prices.
The formulas
Here A is the American number, decimal is the total return per $1 staked, and the fractional form expresses the profit per $1 as a ratio. One quirk worth knowing: American odds between -100 and +100 do not exist. The scale jumps straight from -100 to +100, and both of those are the same price, even money, where a win doubles your money. When the exact fractional conversion is ugly (decimal 1.91 works out to 91/100), we show the nearest clean fraction (10/11) and say so, because a tidy label should never quietly change the price.
Worked example
+150 with a $50 stake. Decimal odds: 1 + 150 ÷ 100 = 2.50. Implied probability: 1 ÷ 2.50 = 40%. Fractional: 2.50 − 1 = 1.50 of profit per $1, which is exactly 3/2. The $50 stake returns 50 × 2.50 = $125.00 if the bet wins: your $50.00 back plus $75.00 of profit. If it loses, the $50 is gone, and no format changes that part.
The vig: the price is not a probability
Here is the part most odds converters skip. Take the most common price in American sports betting, -110 on both sides of a point spread. Each side implies 52.38%, and 52.38 + 52.38 = 104.76%. Real chances sum to exactly 100, so the extra 4.76 points is the overround: the bookmaker's fee, baked directly into the prices. Scale both sides back down to 100 and the fair no-vig chance is 50% each, fair odds of +100. The book's hold on a balanced market works out to 4.54% of every dollar wagered, and a typical two-way market holds 4 to 5 percent. That fee is collected whether you win or lose, because you paid it the moment you accepted the price.
This is why the two-sided fields exist on this page. One price alone looks like a probability; two prices together reveal the fee. The sportsbook's number is not its honest opinion of the chance, it is that opinion plus a margin, and the sum over 100 IS the margin. Once you see it, prices read differently: a line that looks generous is often just a line whose fee you have not computed yet.
One honest paragraph before you go, in the same spirit as our loot drop calculator's "nothing is due" rule: this page is for understanding prices, not beating them. Because the fee is baked into every posted price, the expected value of a bet at those odds is negative by construction unless you genuinely know something the market does not, and the market is very good at knowing things. Treat betting as entertainment with a known cover charge (the vig you can now calculate), and if it has stopped feeling like entertainment money, that is worth a conversation with someone you trust, not another conversion.