KEY TAKEAWAYS

• Decimal fair odds are 1 divided by the probability, so a 40% chance is 2.50.
• American fair odds are positive below 50% and negative above 50%, so 40% is +150 and 60% is -150.
• Fair odds are a break-even price, not a prediction that the bet will win.
• A sportsbook price longer than your fair odds only matters if your estimate is reliable.
• Fair odds ignore the sportsbook’s margin, so real prices are almost always shorter.

To convert a probability into betting odds, you turn the percentage chance of an outcome into the price at which a bet on it would break even. For decimal odds, divide 1 by the probability: a 40% chance becomes 1 ÷ 0.40 = 2.50. For American odds, a probability below 50% becomes +(100 × (1 − p) ÷ p), so 40% is +150, and a probability above 50% becomes −(100 × p ÷ (1 − p)), so 60% is −150. The result is the fair price, often called fair odds: the price at which a bet has neither a long-run edge nor a long-run cost if the probability is exactly right. This is the reverse of the calculation in the guide to what implied probability means in sports betting, which starts from a price and works out the percentage. Going from probability to price lets a bettor put a number on an opinion and compare it with what a sportsbook actually offers. This guide shows each formula, explains what it means in practical terms, walks through a full worked example, and covers the limits: estimates are uncertain, and real sportsbook prices include a margin that fair odds leave out.

Probability vs. Odds: What Each Number Measures

A probability is a number between 0 and 1 (or 0% and 100%) that describes how likely an outcome is. If a team is estimated to win 4 times in every 10 comparable games, its probability is 0.40, or 40%. A probability never describes a payout, and it never promises what will happen in a single game.

Odds, in the betting sense, are a price. They describe how much a winning bet pays relative to the stake, and they come in several formats. American odds, such as +150 or −150, are standard at U.S. sportsbooks. Decimal odds, such as 2.50, show the total return per unit staked. The articles on how to read American odds and on how decimal odds work cover each format in detail.

The difference between odds and probability is a common source of confusion. In everyday language, “odds” sometimes means a ratio of the chance of an outcome not happening to the chance of it happening, such as “3 to 2 against” for a 40% outcome. In a sportsbook, odds are the price quoted for a bet, and the probability is hidden inside that price. The two are linked by a fixed formula, so either one can be converted into the other without losing information, provided the price carries no margin.

That last condition is the important one. A fair price is the price you would get if nobody earned a margin on the bet. A sportsbook adds that margin, so its quoted price for any outcome is normally a little shorter than the fair price. Converting a probability to fair odds therefore produces a reference point, not an expected quote. It tells you where a break-even price sits, which is the number you need before you can judge whether any offered price is attractive.

How to Convert Probability Into Odds Step by Step

Start by writing the probability as a decimal between 0 and 1. A 40% chance is p = 0.40, and a 60% chance is p = 0.60. The formulas below only work when p is strictly between 0 and 1, because an outcome that is impossible or certain has no meaningful price. Convert the percentage to a decimal first, then apply whichever format you need.

Step 1: Decimal odds

The decimal formula is the simplest: decimal odds = 1 ÷ p. In practical terms, if a bet wins with probability p, a winning return of 1 ÷ p per unit staked makes the average outcome exactly break even. At p = 0.40, the fair decimal price is 1 ÷ 0.40 = 2.50, so a $100 stake would return $250 including the stake on a win, which is a $150 profit.

Step 2: American odds

American odds depend on which side of 50% the probability falls. For p below 0.50 (an underdog), American odds = +(100 × (1 − p) ÷ p). For p above 0.50 (a favorite), American odds = −(100 × p ÷ (1 − p)). At p = 0.50 the price is +100, which is the same as −100. The formula for underdogs says that the profit on a $100 stake equals the ratio of losing to winning chances times $100. The formula for favorites says that the stake needed to win $100 equals the ratio of winning to losing chances times $100.

Step 3: Fractional and “odds against” form

Fractional odds are the ratio (1 − p) ÷ p. A 40% outcome gives 0.60 ÷ 0.40 = 1.5, which is 3/2 (“3 to 2 against”), and a 25% outcome gives 0.75 ÷ 0.25 = 3, which is 3/1. This ratio is the same quantity as decimal odds minus 1, so fractional odds are simply the profit per unit staked.

All three formats can be checked against each other. A decimal price of 2.50 converts to American odds of (2.50 − 1) × 100 = +150, and a decimal price below 2.00 converts to American odds of −100 ÷ (decimal − 1). The step-by-step method for moving between formats is covered in the guide to converting betting odds between formats; this article focuses on where the starting number comes from.

Worked Example: Turning 40% and 60% Into Fair Odds

Suppose a bettor estimates that Team A has a 40% chance of winning a game and that Team B has a 60% chance. These numbers are hypothetical and are not current sportsbook prices. The table applies the formulas to these two estimates and to several other common probabilities, with American odds rounded to the nearest whole number and decimal odds rounded to two places.

Probability Decimal odds (1 ÷ p) American odds Fractional (odds against)
10% 10.00 +900 9/1
25% 4.00 +300 3/1
40% 2.50 +150 3/2
50% 2.00 +100 1/1
60% 1.67 −150 2/3
75% 1.33 −300 1/3
90% 1.11 −900 1/9

For Team A at 40%, the decimal price is 1 ÷ 0.40 = 2.50 and the American price is 100 × 0.60 ÷ 0.40 = +150. A $100 stake would return $250 on a win, a $150 profit, and lose $100 otherwise. The long-run average is 0.40 × $150 − 0.60 × $100 = $0, which is why +150 is the fair price for a 40% chance.

For Team B at 60%, the decimal price is 1 ÷ 0.60 = 1.67 (1.6667 unrounded) and the American price is −(100 × 0.60 ÷ 0.40) = −150. A bettor would stake $150 to win $100. The average is 0.60 × $100 − 0.40 × $150 = $0, so −150 is the fair price for a 60% chance. Notice the symmetry: the two fair prices are mirror images, which is expected because the two probabilities add up to 100%.

How to Read the Gap Between Fair Odds and a Price

Once you have fair odds, you can compare them with a price a sportsbook offers. Suppose the Team A estimate of 40% gives fair odds of +150, and a sportsbook hypothetically lists Team A at +170. At +170, the break-even probability is 100 ÷ (170 + 100) = 37.04%. The offered price implies a lower probability than the 40% estimate, so the price is longer than the fair odds. If the estimate were exactly right, a $100 bet would have an expected value of 0.40 × $170 − 0.60 × $100 = +$8.00.

If the sportsbook instead listed Team A at +130, the break-even probability would be 100 ÷ 230 = 43.48%, which is higher than 40%. The same calculation gives 0.40 × $130 − 0.60 × $100 = −$8.00. Here the price is shorter than the fair odds, and a bettor who trusts the 40% estimate would see the bet as costing money on average. Comparing a probability with a break-even percentage is the same decision rule whether you do it in odds or in percentages.

The same logic works for favorites. With a 60% estimate and fair odds of −150, a hypothetical price of −135 has a break-even probability of 135 ÷ 235 = 57.45%, which is below 60%. A $100 stake at −135 profits $74.07 on a win, so the expected value is 0.60 × $74.07 − 0.40 × $100 = +$4.44. At −165, the break-even is 165 ÷ 265 = 62.26%, and the expected value is 0.60 × $60.61 − 0.40 × $100 = −$3.64. The sign of the expected value flips with the price, but it is never a certainty: a positive expected value describes an average over many equivalent bets, not what happens on one.

Common Mistakes When Converting Probability

The most frequent error is treating a point estimate as exact. A 40% estimate is a judgment, and a model or a bettor could easily be off by several points. At 36%, the fair odds are +178 (100 × 0.64 ÷ 0.36 = 177.78, rounded). At 44%, they are +127 (100 × 0.56 ÷ 0.44 = 127.27, rounded). That range is wide enough that a +170 price is attractive at 44%, close to break-even at 40%, and slightly negative at 36%, where its expected value is 0.36 × $170 − 0.64 × $100 = −$2.80.

A second mistake is confusing the odds ratio with the probability. A 3/2 “odds against” ratio is not 3 out of 2 or 60%; it corresponds to a 40% chance. A third is using the wrong formula for the side of 50%: applying the underdog formula to a 60% probability produces a nonsense positive price. A fourth is forgetting that fair odds describe an average, so a correct 60% estimate still loses 4 games in 10 on average, and long losing runs happen even when the estimate is right.

Finally, rounding can mislead. Converting +178 back to a probability gives 100 ÷ 278 = 35.97%, not exactly 36%. Small rounding differences are normal, but rounding early compounds across steps, so keep unrounded values until the final display. And no calculation here removes the need for responsible staking: a bet with a positive expected value on paper can still lose, and money needed for essentials should never be put at risk.

Why Sportsbook Prices Rarely Match Fair Odds

Real sportsbook prices include a margin, usually called the vig or juice, so they are normally shorter than fair odds. Take a hypothetical game where both sides are exactly 50% likely. The fair price for each side is +100, but a sportsbook might list both at −110. At −110, the break-even probability is 110 ÷ 210 = 52.38% per side, and the two sides sum to 104.76%. A bettor on either side has an expected value of 0.50 × $90.91 − 0.50 × $100 = −$4.55 per $100 staked. This is the price of the margin, even when the probability is perfectly known.

This is why a fair-odds calculation must be applied carefully. To judge whether a price is attractive, a bettor needs the price compared against an estimate, but also against the market’s own margin-free view, which the guide to calculating no-vig odds and true probability explains. Fair odds from your own estimate and no-vig odds from the market are two separate reference points, and comparing them is more informative than looking at either alone.

In practice, fair odds work best as a sanity check and a way to clarify thinking. They help a reader see what a price assumes, translate a percentage forecast into a number that can be compared across sportsbooks, and recognize when a stated probability and a stated price disagree. They do not predict outcomes, and they do not guarantee profit.

Fair odds sit between several ideas covered elsewhere on this blog. If you need the opposite direction, the implied probability guide linked above shows how a price becomes a percentage. If a price is already in one format and you need another, the odds-format conversion guide covers the equivalences. To see how a price translates into a record a bettor needs, read about the break-even win rate in sports betting. A sensible next step is to practice converting a few probabilities by hand; then compare each result with a real price and ask what that price assumes about the outcome.

Frequently Asked Questions

How do you calculate probability in betting?

For a simple event, divide the number of favorable outcomes by the total number of equally likely outcomes. One chance in four is 0.25, or 25%. Most sports probabilities are estimates from models or judgment rather than exact counts, so they carry uncertainty.

How do I convert probability to a percentage?

Multiply the decimal probability by 100. A probability of 0.40 is 40%. To go the other way, divide the percentage by 100, so 40% becomes 0.40. Use the decimal form in odds formulas, because they expect a value between 0 and 1.

What is +200 implied probability?

At +200, the implied probability is 100 ÷ (200 + 100) = 33.33%. That is the break-even win rate for the price. Going the other way, a true 33.33% chance has fair odds of +200 (3.00 in decimal), before any sportsbook margin.

What is the difference between odds and probability?

Probability measures how likely an outcome is, from 0 to 1. Odds describe a price or a ratio. A 40% probability is 3-to-2 against as a ratio, 2.50 in decimal odds and +150 in American odds. Betting prices also include a margin that probability does not.

Why is the sportsbook’s price shorter than my fair odds?

A sportsbook builds a margin into its prices, so each side is shorter than its fair price. A true 50% outcome might be listed at -110 instead of +100. Your estimate may also differ from the sportsbook’s, and either one can be wrong.

Do fair odds guarantee a profit if a price is longer?

No. A longer price than your fair odds only shows a positive expected value if your probability estimate is correct, and expected value is a long-run average. Individual bets still lose often, and a small estimate error can erase the apparent edge.