Betting odds tell you what a winning ticket pays and how often it must win to break even. Start there, before deciding whether you like the selection. A likely winner can still be a poor purchase when the payout is too small.
The calculation you need is break-even probability = 1 ÷ decimal odds. American and fractional odds express the same payout in different formats. This guide walks through the conversions, separates profit from total return, and shows which information the number alone cannot give you.
Read the selection, line and price separately
A betting slip contains more than an odds quote. The selection says what you are backing. The line sets a condition, such as a scoring margin or a player-stat threshold. The price determines the payout if that condition wins. Changing the line changes the bet; changing the price changes what the same bet pays.
A minus sign can appear in both the point spread and the American price. Those signs do different jobs. A negative spread gives the selected team a scoring handicap. Negative American odds describe the amount risked relative to the reference profit. Read each number with its label rather than treating the entire slip as shorthand for a favorite.
Before comparing prices, check the event, market, selection, line and settlement terms. Full-game and regulation-only markets are not interchangeable. Neither are player props with different thresholds. The NFL spreads guide covers the scoring condition; this page deals with the price attached to it.
A sourced price in three formats
The table below uses historical quotes from the Smarkets implied-probability guide. Its example is the 2016 Australian Open final between Novak Djokovic and Andy Murray. These are the guide's recorded teaching prices, not current offers, recommended bets or a record of our results. The probability row is recalculated from the prices rather than copied from the guide's rounded display.
| Format | Novak Djokovic | Andy Murray |
|---|---|---|
| American | -500 | +450 |
| Decimal | 1.20 | 5.50 |
| Fractional | 1/5 | 9/2 |
| Break-even | 83.33% | 18.18% |
Read down a player's column to see the same price in different formats. The favorite's negative American price, short decimal price and small fractional return all describe the same transaction. The underdog's positive price and larger return describe another. Switching the display format does not improve either price.
American odds: what the plus and minus mean
American odds use a reference amount of 100. With a positive quote, the number describes profit for that reference stake. With a negative quote, the absolute number describes the stake required for the reference profit. This is a notation convention, not an instruction to stake that amount.
In the historical table, +450 expresses profit of 450 relative to a stake of 100. The -500 quote expresses a stake of 500 relative to profit of 100. The reference amounts let you read the ratio quickly. Your own accepted stake scales that ratio; it does not change the odds.
Let A be positive American odds and M the absolute value of negative American odds. The decimal conversions are 1 + A / 100 and 1 + 100 / M, respectively. Applying those definitions gives 1 + 450 / 100 = 5.50 and 1 + 100 / 500 = 1.20.
Be careful with the direction of comparison. For the same winning outcome, a larger positive quote pays more. Among negative quotes, the one closer to zero pays more relative to the same stake. Converting both prices to decimal avoids relying on that verbal rule when signs differ.
Decimal odds include the returned stake
Decimal odds state the total return per amount staked on a winning ticket. Write the relationship as total return = stake × decimal odds. Profit excludes the returned stake, so profit = stake × (decimal odds - 1). Mixing up those quantities makes a payout look larger than it is.
The historical decimal price of 1.20 returns the original stake plus profit equal to 0.20 times that stake. The 5.50 price returns the original stake plus profit equal to 4.50 times the stake. These multipliers follow from the quoted prices; they do not describe how frequently either player would win.
For a losing ordinary cash back bet, the stake is lost. A void or refunded push is a separate settlement, not a win at decimal odds. An exchange commission, a bonus-credit rule or another fee can also change what reaches your balance. Read the ticket's terms before treating the displayed decimal price as your final cash return.
Fractional odds show profit relative to stake
For fractional odds written a/b, the numerator describes profit and the denominator describes stake. Divide the numerator by the denominator to obtain profit per amount staked, then add the returned stake: decimal odds = 1 + a/b.
That makes the historical 1/5 quote equivalent to 1.20 decimal and 9/2 equivalent to 5.50. A fraction below one is not a losing payout. It means the profit portion is smaller than the stake returned with it. A fraction above one means the profit portion is larger.
Use a calculator rather than rounding the fraction before converting it. Intermediate rounding can make equivalent quotes appear different. Keep the full value while comparing, then round the displayed percentage consistently. The accepted price on the actual ticket remains the record that matters.
Calculate the break-even probability
For an ordinary back bet that either wins or loses, with no additional fee, the break-even probability is q = 1 / d, where d is decimal odds. Multiplying by 100 expresses the result as a percentage. This is a payout threshold, not a verified forecast of the event.
For the historical favorite quote, 100 / 1.20 = 83.33% when rounded for display. For the underdog quote, 100 / 5.50 = 18.18%. A smaller payout requires a higher winning frequency to break even. A larger payout can break even at a lower winning frequency, but it can still be overpriced.
You can obtain the same result without converting formats first. For positive American odds use q = 100 / (A + 100). For negative odds use q = M / (M + 100). For fractional odds use q = b / (a + b). Here q is a proportion; multiply it by 100 only when displaying a percentage.
The assumption about settlement matters. With a refunded push, the familiar threshold applies to the win rate among decisions that are wins or losses. It is not automatically the required unconditional chance of a win across wins, losses and pushes. If settlement can split a stake, void only part of a ticket or charge additional costs, model those outcomes explicitly.
Do not mistake a no-vig estimate for your ticket's threshold
The opposing historical quotes sum to 101.52% implied probability when calculated at full precision and then rounded. That is not evidence that the match has more than a complete set of outcomes. It shows that raw price-implied probabilities need not add to a probability distribution.
Add only mutually exclusive selections that cover the same market. A team to win and that team to cover a spread are not opposite outcomes; both might win. Neither does a mix of full-game and first-half quotes form a complete board. Keep unrounded probabilities for the addition: rounding each displayed row first can produce a slightly different total. The purpose is to measure the posted set of prices, not to make an arbitrary collection of percentages add to one.
A proportional no-vig calculation divides each raw implied probability by the total. It produces a market-relative estimate whose values add to one. That is useful for comparisons, but the assumptions behind the normalization do not become a fact about the players' true chances.
Most importantly, your payout has not changed. To assess the ticket you can actually buy, compare a defensible probability estimate with the raw break-even threshold of the offered price, adjusted for relevant costs. Do not replace that threshold with a lower no-vig number and declare value. That would remove the margin from your spreadsheet without removing it from the ticket.
The vig, overround and hold guide works through the complete-market calculation and explains why overround is not the same percentage as actual sportsbook revenue.
A bigger payout is not automatically a better bet
When the event, selection, threshold and settlement are identical, the higher decimal price offers a larger winning return. That is a price comparison. When any of those conditions changes, the payout alone cannot rank the choices. A harder scoring condition may pay more because it wins less often.
The same distinction applies to predictions. A model can disagree with a market because it found useful information, but also because it uses stale inputs, answers a different question or has not been calibrated. An odds converter cannot tell those explanations apart. It translates a price; it does not validate a probability estimate.
Avoid subtracting margin twice. If you compare a model probability directly with the offered price's break-even rate, the price already reflects the payout being offered. An extra generic deduction for the same margin would be a second adjustment. Separate real additional costs, such as commission, from the margin already embedded in the quote.
Check the quote before using the answer
Confirm the format before typing a number into a converter. A decimal quote must represent total return, not profit alone. A fractional quote needs both parts. An American quote needs the correct sign. A blank, suspended or malformed price is not a request to substitute a familiar default.
Then confirm that the quote is still available and that its market matches the ticket. Do not compare a historical screenshot with a current price and describe the difference as an available opportunity. Nor should a price restricted by account eligibility or promotion terms silently become the general price in a guide.
Keep fees separate until you know how they are charged. A fee on net winnings, a commission on a settled exchange market and a fee on stake have different effects. The fee-free formulas on this page deliberately do not assume an operator's current commission schedule.
Keep a record that you can understand later
Save the accepted event, market, selection, line, odds, stake and time together. Preserve whether the market includes overtime and the settlement rule relevant to a push or void. Record the result separately from the pre-bet estimate so the outcome cannot silently rewrite what you believed beforehand.
The bet-tracking guide explains that record. The closing-line-value guide covers comparing an accepted price with a later close. Neither a good close nor an isolated win proves that a probability estimate is reliable.
The useful stopping point is clear: know what must happen, what the ticket returns and what chance the price requires. When a quote or rule is unclear, leave the decision unresolved. Understanding the notation is a reason to make fewer avoidable mistakes, not a reason to place more bets.
Where these numbers come from
The historical prices come from the named table in the Smarkets conversion guide. Format conversions, return multipliers and displayed probabilities are deterministic calculations from those prices. The Smarkets odds definitions distinguish total return from profit. No current market, model accuracy, sportsbook profit or betting recommendation is asserted here.
Breakeven win rate at recorded American prices
Breakeven probability is calculated only from American prices that were actually captured in the odds-history table.
Expected value from graded outcomes
Expected-value cells render only when a verified source binds observed win outcomes to the price paid for the same bets.
