Odds Formats Explained: Decimal, Fractional, American and Implied Probability

Decimal, fractional and American odds are three ways of writing the same thing: how much a winning bet pays. Convert any of them into implied probability and you can compare a price with reality, and see the margin built into it. Once you know three short formulas, every format becomes readable at a glance.

Decimal odds: total return per $1

Decimal odds tell you how much comes back for each $1 staked, including the stake itself. They are common across Europe, Australia and Canada.

At decimal 2.50, a $10 bet returns $25 if it wins: your $10 back plus $15 profit. Profit is always (decimal − 1) × stake.

Decimal odds also give the fastest route to implied probability, the break-even win rate:

Decimal 2.00 is an even-money bet: double your stake back, implied 50%. Anything below 2.00 pays less than you risk; anything above pays more.

Fractional odds: profit per unit staked

Fractional odds, traditional in the UK and Ireland, show profit relative to stake. At 3/2 (said "three to two"), you win $3 for every $2 staked. A $10 bet at 3/2 wins $15 profit and returns $25 in total, exactly like decimal 2.50.

• Decimal = fraction + 1. 3/2 = 1.5, plus 1 = 2.50. 5/2 = 3.50. 2/5 = 1.40.
• Evens is 1/1, decimal 2.00.
• Odds-on means the fraction is less than 1, like 2/5 or 1/2: you win less than you stake.
• Implied probability = denominator ÷ (numerator + denominator). For 3/2: 2 ÷ 5 = 40%.

American odds: plus and minus

American (moneyline) odds use $100 as the reference point, and the sign tells you which way.

• Plus odds show the profit on a $100 stake. +150 means a $100 bet wins $150. A $20 bet at +150 wins $30 profit and returns $50.
• Minus odds show the stake needed to win $100. −200 means you risk $200 to win $100. A $20 bet at −200 wins $10 profit and returns $30.

Implied probability from American odds:

So +150 implies 100 ÷ 250 = 40%, and −200 implies 200 ÷ 300 = 66.7%. The common −110 implies 110 ÷ 210 = 52.38%.

Conversion table and formulas

To move between formats, go through decimal:

• American to decimal: +A becomes 1 + A ÷ 100. −A becomes 1 + 100 ÷ A.
• Decimal to American: if decimal is 2.00 or more, (decimal − 1) × 100 with a plus sign. If below 2.00, −100 ÷ (decimal − 1).
• Decimal to fractional: subtract 1 and write the result as a fraction. 2.50 − 1 = 1.5 = 3/2.

Watch the rounding. −110 is decimal 1.9091, often shown as 1.91. At 1.91 the implied probability is 52.36% instead of 52.38%, a small difference that matters when you are comparing thin margins. The free odds converter handles the arithmetic for any price.

Two worked conversions

A price of 7/4: decimal is 7 ÷ 4 + 1 = 2.75. American is (2.75 − 1) × 100 = +175. Implied probability is 4 ÷ (7 + 4) = 36.4%. A $20 bet wins $35.

A price of −250: decimal is 1 + 100 ÷ 250 = 1.40. Fractional is 0.40 = 2/5. Implied probability is 250 ÷ 350 = 71.4%. A $20 bet wins $8.

True odds vs. payout odds

The word odds does two jobs, and mixing them up causes real confusion.

True odds describe probability, written as failures to successes. A die roll of six has true odds of 5 to 1 against: five ways to miss, one way to hit, a 1 in 6 chance. Note that 5 to 1 against is not a 1 in 5 chance.

Payout odds describe what a bet pays. If a game paid 5 to 1 on a six, it would be perfectly fair. Pay 4 to 1 instead and the game keeps an edge.

Going the other way, fair decimal odds are simply 1 ÷ probability. An event with a 25% chance has fair odds of 4.00, which is 3/1 or +300. An event with a 60% chance has fair odds of 1.67, which is about −150. Any posted price shorter than the fair one contains a margin.

Casino payouts speak the same language

Casino payouts are just odds written as "X to 1". A European roulette straight-up bet pays 35 to 1, which is decimal 36.00 or American +3500.

The implied probability of 36.00 is 1 ÷ 36 = 2.78%. The true probability is 1 ÷ 37 = 2.70%. The price assumes the bet wins slightly more often than it really does, and that gap is the house edge:

Look out for "for" instead of "to". A payout of 35 to 1 returns $36 on a winning $1 bet. A payout of 35 for 1 returns $35 in total, which is really 34 to 1, because your stake is part of the $35. Pay tables that quote "for" make prizes look a unit bigger than they are.

Adding up implied probabilities: the overround

In a perfectly fair market, the implied probabilities of every possible outcome add up to exactly 100%. Real betting markets add up to more. The excess is called the overround, and it is the bookmaker's built-in margin.

A standard two-way line at −110 on both sides gives 52.38% + 52.38% = 104.76%. Both sides are priced as if they win more than half the time, which cannot be true.

Take a three-way market priced at decimal 2.40, 3.30 and 3.10. The implied probabilities are 41.67%, 30.30% and 32.26%, for a total of 104.23%.

To estimate fair probabilities, divide each one by the total. That gives about 39.98%, 29.07% and 30.95%, which add to 100% and correspond to fair decimal odds of roughly 2.50, 3.44 and 3.23. The difference between those and the posted prices is the margin. The sports betting math guide covers vig and overround in depth.

From odds to expected value

Once you have decimal odds and a probability, expected value is one line:

If a 2.50 price were attached to an event that truly happens 45% of the time, EV would be 0.45 × 2.50 − 1 = +$0.125 per $1. If the event truly happens 40% of the time, EV is exactly zero. Below 40%, it is negative.

The bottom line

Decimal odds show total return, fractional odds show profit per unit, and American odds pivot around $100. Convert any of them to implied probability with 1 ÷ decimal, and you can compare prices across formats instantly.

Implied probability is also how you see the margin. In a casino it is the gap between 1/36 and 1/37; in a betting market it is every percentage point above 100%. Understanding the price is not a reason to bet; it is how you see what a bet really costs.