Betting odds explained: American, decimal and fractional

Betting odds do two jobs at once. They tell you how much a winning bet pays, and they tell you what probability the bookmaker is assigning to the outcome, with its margin added on top. Once you can read both, you can compare books, spot an expensive market and work out what a price really implies.

This guide explains American, decimal and fractional odds, how to convert between them, how to calculate implied probability and how to find the bookmaker's margin. Every example is worked through with real numbers.

What are the three types of betting odds?

The same price can be written three ways. Canadian books usually show American or decimal odds and let you switch in your account settings. Fractional odds are mostly a British convention, but you will still see them on horse racing and some futures. Canadian horse racing itself is not priced at fixed odds: bets go into pari-mutuel pools, as our guide to horse betting in Ontario and Canada explains.

Each row is one price. Only the notation changes.

How do American odds work?

American odds are built around $100.

• A plus sign shows how much profit a $100 bet makes. At +150, $100 wins $150.
• A minus sign shows how much you must stake to make $100 profit. At -150, you stake $150 to win $100.

For any stake, the formulas are:

• Positive odds: profit = stake x (odds / 100)
• Negative odds: profit = stake x (100 / odds without the minus sign)

So $40 at +125 makes $50 profit, and $40 at -125 makes $32 profit. In both cases you also get your $40 back.

The sign tells you who the favourite is. A minus price means the book thinks that side is more likely than not to win; a plus price means it thinks the opposite. A price of +100 is an even-money bet.

How do decimal odds work?

Decimal odds show the total return for every $1 staked, including the stake. They are the easiest format for calculations.

• Total return = stake x decimal odds
• Profit = stake x (decimal odds - 1)

A $25 bet at 2.40 returns $60, which is $35 profit plus your $25. A $25 bet at 1.40 returns $35, or $10 profit.

Decimal odds are also the format that makes parlays simple, because you multiply the legs together. We cover that in our guide to parlays and same game parlays. Our parlay calculator multiplies the legs for you and shows the payout on your stake.

How do fractional odds work?

Fractional odds show profit relative to stake. At 5/2 you win $5 for every $2 staked. At 1/4 you win $1 for every $4 staked.

• Profit = stake x (first number / second number)
• Decimal equivalent = (first number / second number) + 1

So 7/4 is 2.75 in decimal, and a $20 bet at 7/4 makes $35 profit.

How do you convert odds between formats?

Use decimal as the bridge. Convert whatever you have into decimal, then into the format you want.

And back again:

Books round their prices, so a conversion can be a cent or two off what the screen shows in the other format. That is normal. To skip the arithmetic, type any price into our odds converter and it shows the other two formats and the implied probability.

What is implied probability in betting?

Implied probability is the chance of an outcome that a price represents. It is the most useful number you can pull out of a line, because it lets you compare a book's view with your own.

• Decimal: implied probability = 1 / decimal odds
• Negative American: odds / (odds + 100), using the number without the sign
• Positive American: 100 / (odds + 100)

If you think a team wins 45% of the time and the book offers +150 (40%), the price is higher than your estimate says it should be. If the book offers +100 (50%), it is lower. That comparison is the whole idea behind finding value, with one large caveat: your 45% is an estimate, and most bettors overrate their own estimates.

What is the bookmaker margin (vig)?

Add up the implied probabilities on every outcome in a market and the total is always more than 100%. The extra is the bookmaker's margin, also called the vig, juice or overround. It is how a book earns money regardless of who wins, in the same way the house edge works in a casino. For a worked casino example, our bitcoin dice guide shows how to read the house edge straight from a game's win chance and multiplier.

Two-way market

A hockey total priced at -110 on both sides:

• Over: 110 / 210 = 52.38%
• Under: 110 / 210 = 52.38%
• Total: 104.76%

The margin as a share of money staked is 1 - (1 / 1.0476) = 4.55%. On average, for every $100 bet across both sides at those prices, the book expects to keep about $4.55.

Three-way market

A soccer match or an NHL 60-minute line has three outcomes. Suppose the prices are 2.10, 4.20 and 3.10:

• 1 / 2.10 = 47.62%
• 1 / 4.20 = 23.81%
• 1 / 3.10 = 32.26%
• Total: 103.69%, a margin of about 3.6%

Margins vary a lot. Main lines on major leagues are usually the tightest. Player props, futures and less popular leagues usually carry more.

How do you remove the vig to find fair odds?

To estimate what the book thinks the true probabilities are, divide each implied probability by the total.

Take a moneyline of -150 and +130:

1. Implied: 60.0% and 43.48%. Total: 103.48%.
2. Fair probabilities: 60.0 / 103.48 = 57.98%, and 43.48 / 103.48 = 42.02%.
3. Fair decimal odds: 1 / 0.5798 = 1.725 and 1 / 0.4202 = 2.38.
4. In American odds: about -138 and +138.

So the fair line is roughly -138 / +138, and the book's line is -150 / +130. The gap on each side is what you pay for the bet. This simple method spreads the margin evenly; in practice books often load more of it onto the longer price, so treat the result as an estimate. Our no-vig calculator runs the same steps for two-way and three-way markets. For a full walk-through of the market itself, including two-way and three-way lines and how overtime settles, see our guide to what a money line is in betting.

Why do betting odds change before a game?

Opening prices are the book's first estimate. They move for three main reasons:

• New information. A starting goalie or quarterback is confirmed, a key player is ruled out, or the weather turns.
• Money. If one side takes far more action than the book wants, it shortens that price and lengthens the other to balance its risk.
• Other books. Prices across the market tend to converge, so a move at one large book is often followed elsewhere.

When a favourite goes from -130 to -150, its implied probability rises from 56.5% to 60.0%. If you had already bet at -130, your price is better than the closing one. Bettors call the final pre-game price the closing line, and consistently beating it is widely seen as a sign of good judgement, although no single result proves anything either way.

Once a game starts, prices move with every goal and penalty; our live betting guide covers how in-play odds and cash out work.

Why should you compare odds between books?

Because the same outcome can carry a different price at different books, and small differences add up. Betting $50 at 1.91 instead of 1.87 is only $2 more on a winning bet, but over hundreds of bets it is a meaningful share of your results. Checking the implied probability total on a market also tells you how expensive a book is in general.

When you shortlist books from our best betting sites in Canada ranking, add up the implied probabilities on the markets you bet most and see which book charges least. Several of the books we review show both decimal and American odds, so pick whichever you find easier and stick to it.

Worked example: reading a full line

A book lists an NHL game:

Here is what you can read from it.

1. Who is favoured. The home team, because its moneyline has the minus sign. The favourite always takes the -1.5 side of the puck line.
2. What a bet pays. $30 on the home moneyline makes $20 profit. $30 on the away moneyline makes $39. $30 on home -1.5 makes $49.50.
3. What the book thinks. On the moneyline, 60.0% and 43.5%, which de-vigs to roughly 58% and 42%.
4. What each market costs. The moneyline totals 103.5%, a margin of about 3.4%. The puck line totals 37.7% + 66.7% = 104.4%, a margin of about 4.2%. In this example, the puck line is the more expensive market of the two.

If a line ever looks impossible, such as the underdog giving goals, it is either a misread or an error. Books reserve the right to void bets placed at obvious pricing errors. Our NHL betting guide explains how puck lines are set and settled.

Responsible gambling

Understanding odds does not change the fact that the margin means most bettors lose over time. Decide what you can afford before you start, use the deposit limits and time-outs your book offers, and stop if you find yourself chasing losses.

Help is free and confidential. ConnexOntario: 1 866 531-2600. Jeu: aide et référence (Quebec): 1 800 461-0140. For other provinces and for self-exclusion options, see our responsible gambling page.