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12 min read · updated September 26, 2026

How betting odds work

What −150 and +130 actually mean, how every price hides a win probability, why the two sides of a game add up to more than 100%, how to take the cut back out, and how the site's price check turns all of it into one plain verdict.

The short version

A betting price is a win probability in disguise. −150 means the book thinks a team wins about 60% of the time; +130 means about 43%. Add the two sides of a game together and you get more than 100%, and the extra is the cut, the book's built-in margin. Take the cut out and what's left is the market's honest forecast. Compare a price to your own forecast and you know whether it's cheap, fair or expensive. That's all odds are. The rest of this article is the arithmetic, a few worked examples, and how the site does the arithmetic for you.

Why prices, not percents

The number you set for every game on this site is a percent: "the home team wins 62% of the time." A sportsbook says the same kind of thing, but in a different language. It doesn't tell you the chance; it tells you what it will pay. The two are the same idea from opposite ends. If something happens often, it pays little when it does. If it rarely happens, it pays a lot.

Once you can translate between a price and a percent, a sportsbook's board stops being a wall of plus and minus signs and becomes a list of forecasts you can argue with. That translation is what this article teaches.

American odds

In the U.S., prices are usually quoted as American odds, a number with a sign in front.

• A minus number is a favorite. It's how much you'd risk to win $100. At −150, you risk $150 to win $100.
• A plus number is an underdog. It's how much you'd win on a $100 bet. At +130, you risk $100 to win $130.
• +100 (sometimes written "even") is a coin flip: risk $100 to win $100.

The minus side feels backwards at first, because a bigger number means a surer thing: −300 is a heavier favorite than −150. It helps to read the minus sign as "you have to put up this much."

From a price to a probability

Here's the one formula for American odds:

−N  →  N / (N + 100)
+N  →  100 / (N + 100)

It comes straight from the payouts. At −150 you put up $150 to get back $250 in total, so the price is fair if you win 150 out of every 250 times: 150 / 250 = 60%. At +130 you put up $100 to get back $230, so it's fair if you win 100 out of every 230 times: 100 / 230 = 43.5%.

That percent is called the implied probability: the chance the price is charging you for. Some common prices:

Notice that there are no odds between −100 and +100. Both of those mean 50%, and the numbers grow outward from there in each direction: −200 is 66.7%, +200 is 33.3%. A pair of prices like that, mirror images with no cut, adds up to exactly 100%.

Decimal odds

Much of the world uses decimal odds: the total you get back for each dollar staked, your dollar included. At 2.50, a $1 bet returns $2.50 if it wins, $1.50 of it profit.

Decimal odds are the easiest to turn into a probability:

probability = 1 / decimal

So 2.50 is 1 / 2.5 = 40%, and 1.667 is 1 / 1.667 = 60%. To get decimal from American, add the payout per dollar to the dollar itself: −150 pays $100 on $150, which is 0.667 per dollar, so 1.667; +130 pays $130 on $100, which is 1.30 per dollar, so 2.30. The table above has both.

Decimal odds are also what you multiply when you string bets together, which is the subject of the parlays article. You may also run into British fractional odds like 3/2, which means win $3 for every $2 staked: that's 1 + 3/2 = 2.50 in decimal, or 40%.

Going the other way, from a probability to American odds, is useful when you want to know what a fair price would be:

p above 50%  →  −100 × p / (1 − p)
p at or below 50%  →  +100 × (1 − p) / p

We'll use that in a moment.

Why the two sides add to more than 100%

Here's a real-looking pair of prices for one game:

• Home −135: 135 / 235 = 57.4%
• Away +115: 100 / 215 = 46.5%

One team or the other has to win, so the true chances must add up to exactly 100%. These add to 57.4 + 46.5 = 103.9%. The extra 3.9% is the book's margin. On this site we call it the cut. You'll also hear it called the vig (short for vigorish), the juice or the hold; they all mean the same thing here.

The cut is how a sportsbook makes money no matter who wins. Take the classic line, −110 on both sides. Each side implies 110 / 210 = 52.4%, so together they make 104.8%, a cut of 4.8%. Suppose the book takes $110 on each side, $220 in all. Whichever side wins gets back its $110 plus $100 in winnings, $210. The book keeps $220 − $210 = $10, which is 10 / 220 = 4.5% of everything bet. (The 4.8% and the 4.5% are the same cut measured two ways: one as the extra above 100%, the other as a share of the money.)

From the bettor's side it looks like this. A 50/50 game at −110 returns 1.909 per dollar when it wins. Half the time you get 1.909 back, half the time nothing, so on average you get 0.5 × 1.909 = 0.955 back per dollar, and lose about 4.5¢ on every dollar you bet. You're paying 52.4% for something that happens 50% of the time.

That small gap is the whole business. It's also why most bettors lose over time: to break even you don't just have to be right more than half the time, you have to be right often enough to pay for the cut, on every bet.

Taking the cut out

If the prices overstate both sides, the natural fix is to scale them back down so they add to 100%. Divide each side by the total:

fair probability = side's implied probability / sum of both sides

For the −135 / +115 game:

• Home: 57.4 / 103.9 = 55.3%
• Away: 46.5 / 103.9 = 44.7%

Those add to 100%, and they're the market's forecast with the book's margin removed, usually called the fair or no-vig probability. Turn them back into prices with the formula above: 55.3% becomes −100 × 0.553 / 0.447 ≈ −124, and 44.7% becomes +100 × 0.553 / 0.447 ≈ +124. So a book with no cut at all would have hung roughly −124 / +124 on this game instead of −135 / +115. The distance between those two pairs is what you pay for the privilege of betting.

The classic −110 / −110 line works the same way: 52.4 / 104.8 = 50% each. The fair line is a coin flip, which is exactly what −110 on both sides is meant to say.

Once more with the prices from the top of the article, −150 and +130: 60.0 + 43.5 = 103.5%, so the cut is 3.5%. Fair chances: 60.0 / 103.5 = 58.0% and 43.5 / 103.5 = 42.0%.

One honest caveat. Splitting the cut in proportion, as above, is the simplest method and the one the site's price check uses, but it's a choice, not a law. There are other ways to divide the margin between the two sides, and on lopsided games they can give slightly different answers. On most NFL games the difference is small next to everything else that goes into a forecast.

Shopping for a price

Different sportsbooks, and exchanges like Kalshi and Polymarket, don't all post the same number for the same game. The gap is usually small, but it's real, and it's free to take advantage of: if you've already decided you like a side, the only question left is where it's cheapest.

Say Detroit is the underdog. One place offers +133 and another +150.

• +133 charges 100 / 233 = 42.9%
• +150 charges 100 / 250 = 40.0%

Same team, same game, and one price is 2.9 points cheaper than the other. On a $100 bet that wins, it's the difference between $133 and $150 of profit. Over many bets, small differences like that add up, in the same way the cut does.

Exchanges quote a price in cents instead of odds: a contract that pays $1 if the team wins, trading at 40¢, is charging 40%. They also have their own fees; on Kalshi, for instance, buying at 60¢ comes with a fee of 0.07 × 0.6 × 0.4 = 1.68¢, so the real cost is about 61.7%. The prediction markets article covers how that works.

From a price to a verdict

Everything so far builds to one comparison: the percent a price charges versus the percent you think is true.

Take Detroit at +150 again. It charges 40.0%. Suppose your number, or The System's, says Detroit wins 45% of the time. Then the price is 45 − 40 = 5 points under the number. You'd be paying 40% for something worth 45%. That's what "value" means: not that the bet will win (Detroit loses more often than it wins here), but that the price is lower than the chance.

Flip it around. If your number said Detroit wins 36%, the same +150 price would be 4 points over, and you'd be paying 40% for something worth 36%.

This is also why a good forecast matters more than a good feeling. The price check below can only be as good as the number it's compared against. If your 45% is really 40%, the "value" was never there. The calibration article is about how to know whether your numbers can be trusted, and why the market is so hard to beat is about how rarely anyone's number is better than the market's own.

The site's price check

The price check does every step in this article for you. Pick a game and a side, type the price you're looking at, and it shows:

• What the price charges, cut included. +150 shows as 40.0%.
• The fair number. For members that's The System's forecast; for everyone else it's the market consensus with the cut removed. Where Elo and the market are 10 or more points apart, everyone sees the market, because that's where the market has usually been right.
• Each forecaster's edge: how far the price sits from each forecaster's number.
• A verdict. Value if the price is 2 or more points under the number, bad if it's 2 or more over, and fair in between, with the plain advice "fair price, skip it."
• The best price for that side across every book and both exchanges.
• The worst price still worth taking. With a number of 45%, anything 2 or more points under it is value, so the line is 45 − 2 = 43%. Turn that into odds: +100 × 0.57 / 0.43 ≈ +133. So +133 or longer is still value. +125 charges 100 / 225 = 44.4%, less than a point under the number, which makes it fair, not value.

For exchanges it also suggests a limit for a resting order: the highest price in whole cents that would still be 2 or more points under the number after the fee.

The two-point margin is deliberate. Forecasts aren't exact, and a price one point under a number is well inside the error of any forecast, including The System's. Calling that "value" would be flattering noise.

The percent toggle

Book prices on the site can be shown two ways. A toggle switches every price between odds (+150) and the percent it charges (40.0%). Odds are what you'll see at a sportsbook; percents are what you can compare. If you set a 45% pick on a game and the book's price reads 40.0%, you can see the gap at a glance without doing any division.

Book prices refresh every six hours. Kalshi and Polymarket prices refresh every 20 minutes. A book may have moved since the last reading, so the price you type into the price check is the one that counts.

A calm word, since prices lead to betting: this site is a forecasting game, and nothing here is advice to bet. If you do, bet only where it's legal, only if you're of age, and only with money you can afford to lose.

Where to see it on the site

• Price check: type any price, see what it charges, the fair number and a verdict.
• Markets: every game's home win percent from the books, Kalshi and Polymarket side by side, the biggest gaps between them, and how lines have moved.
• Predictions: the market next to Elo and The System for every game.
• How it works: prices: the short reference version of this article.
• Bets: a tracker that settles your bets and compares each price you got to where the market closed.
• Next: Parlays, and why the cut compounds and Closing-line value.

A few terms

• American odds: a price with a sign. −150 means risk $150 to win $100; +130 means risk $100 to win $130.
• Decimal odds: the total returned per dollar staked. 2.50 returns $2.50 on $1.
• Implied probability: the chance a price is charging you for. +150 implies 40.0%.
• The cut: the amount by which a book's two sides add up to more than 100%. Also called the vig, the juice or the hold.
• Fair (no-vig) probability: a side's implied probability with the cut taken out, so both sides add to 100%.
• Value: a price that charges less than your forecast of the chance. On the price check, 2 or more points under the number.
• Best price: the cheapest place to take a side, across every book and exchange.