How Betting Odds Work: American Odds and Implied Probability

Betting odds are prices. Each one tells you how much a bet pays, and it also hides a probability: the chance the sportsbook's price implies, with its margin built in. This guide covers the three odds formats, implied probability, the vig and why lines move.

All the worked examples below are our own arithmetic, rounded to two decimals. We don't link to sportsbooks or quote any book's current lines.

American odds#

American (moneyline) odds are the default in the US, and most bettors here read them. Favorites carry a minus sign and underdogs a plus, as the American Gaming Association's Basics of Sports Betting shows:

• A minus number is what you risk to win $100. At -150, you risk $150 to win $100. A win returns $250: your $150 back plus $100.
• A plus number is what a $100 bet wins. At +200, $100 wins $200, and a win returns $300.
• +100 is even money: risk $100 to win $100.

Profit (winnings) is what you gain; total return is profit plus your stake back. American odds describe profit.

For any stake, the profit is stake × 100 ÷ the odds on a minus price, and stake × the odds ÷ 100 on a plus price. So $20 at -125 wins $16 (a $36 return), and $20 at +175 wins $35 (a $55 return).

Decimal and fractional odds#

Europe and many betting tools use other formats for the same prices, and many US apps let you switch the display to decimal (and sometimes fractional), though the settings vary by app:

• Decimal odds show the total return for each $1 staked, including the stake. At 2.50, $1 returns $2.50: $1.50 of profit plus your $1. So +150 is 2.50, and -110 is about 1.91.
• Fractional odds show winnings relative to the stake. At 3/2, every $2 staked wins $3.

To convert:

• American to decimal: for plus odds, 1 + odds ÷ 100 (+150 is 2.50). For minus odds, 1 + 100 ÷ the odds (-150 is 1.67).
• Decimal to American: at 2.00 or above, (decimal - 1) × 100, as a plus number (3.00 is +200). Below 2.00, -100 ÷ (decimal - 1) (1.50 is -200).
• Fractional to decimal: the fraction plus 1 (3/2 is 1.5 + 1 = 2.50).

Implied probability#

Implied probability is the chance of winning that a price represents. It's also your break-even win rate at that price: win more often than this and the bet comes out ahead over time; win less and it loses.

• Minus odds: odds ÷ (odds + 100). -150 is 150 ÷ 250 = 60%.
• Plus odds: 100 ÷ (odds + 100). +250 is 100 ÷ 350 = 28.57%.
• Decimal odds: 1 ÷ the price. 2.50 is 1 ÷ 2.5 = 40%. Economist Karl Whelan's explainer on bookmaker margins uses the same reciprocal.

The probability a book implies isn't the "true" chance of the outcome. It's the true chance as the book estimates it, plus its margin.

The vig and the hold#

Add up the implied probabilities on both sides of a market and you get more than 100%. The extra is the vig (also called juice): the sportsbook's built-in margin.

Example 1: a standard spread at -110 on both sides.

1. Each side implies 110 ÷ 210 = 52.38%.
2. Together: 104.76%. The 4.76 points over 100% is the overround.
3. The hold, the share of money bet that the book keeps if action is balanced, is 1 - 1 ÷ 1.0476 = 4.55%. It isn't simply the 4.76 points: Whelan notes that subtracting 1 from the overround overstates the margin.

You can check that last step directly: two bettors each risk $110 on opposite sides. The book takes in $220, pays the winner $210 and keeps $10, which is 4.55% of $220.

Example 2: a moneyline at -150 / +130.

1. -150 implies 60.00%. +130 implies 100 ÷ 230 = 43.48%.
2. Together: 103.48%.
3. Hold: 1 - 1 ÷ 1.0348 = 3.36%.

To strip the vig out, the simplest method (the "basic" method in odds software such as the implied R package) divides each side by the total: 60.00 ÷ 103.48 = 57.98% and 43.48 ÷ 103.48 = 42.02%. Those "no-vig" probabilities convert back to a fair price of about -138 / +138. Many odds tools build fair prices along these lines, often from several books; our guide to sports betting tools explains how +EV finders use them.

Moneylines, spreads and totals#

• Moneyline: you pick who wins.
• Point spread: the favorite has to win by more than the spread. At Team A -6.5 / Team B +6.5, a bet on A wins only if A wins by 7 or more; a bet on B wins if B wins or loses by 6 or fewer. Economist Steven Levitt describes the standard spread bet as risking 110 to win 100, which is -110. With a whole-number spread, landing exactly on it is a push, and stakes are refunded.
• Total (over/under): you bet on the combined score being over or under a number, such as 47.5. Totals are commonly priced the same way: a study of NFL totals in The Sport Journal treats each bet as risking $11 to win $10.

Parlays combine bets by multiplying their decimal odds, which also stacks the vig. Two legs at -110 pay 1.909 × 1.909 ≈ 3.64, or about +264, where two true coin flips would pay +300. Our guide to units, ROI and records shows how that adds up over a three-leg parlay.

Why lines move#

Odds change between when they open and when the game starts. Sportsbooks don't publish how they set prices, but common reasons include news (injuries, lineups, weather), the bets they take on each side, and prices at other books. The last price before the game is the closing line.

Movement changes what you need to win. If a line moves from -110 to -130, your break-even rate rises from 52.38% to 130 ÷ 230 = 56.52%. Getting a better number than the close is a sign bettors watch closely, and so do books: a Massachusetts Gaming Commission staff memo found that players who consistently beat the closing line were more likely to have their limits lowered.

The break-even rate at -110#

Because -110 is a common price on spreads and totals, 52.38% is the number to remember. Levitt and the totals study both round it to 52.4%. Over 100 bets of $110 each:

• winning 52.38 of them wins 52.38 × $100 = $5,238, and losing 47.62 costs 47.62 × $110 = $5,238, so you break even;
• winning exactly 50 wins $5,000 and losing 50 costs $5,500, a loss of $500, or 4.55% of the $11,000 staked.

So a bettor who wins half their bets loses steadily, and someone advertising a high win rate needs to show the odds behind it.

Understanding odds doesn't give you an edge#

Knowing the math shows you what each bet costs. It doesn't change the price. Levitt's research also found bookmakers predict outcomes better than bettors, with little evidence of bettors who systematically beat the bookmaker.

Where odds knowledge helps:

• Reading claims. A record means little without the odds behind it. Our guide to picks scams covers what to watch for, and our guide to picks groups explains what to check before paying.
• Seeing the real cost of parlays and bad prices.
• Budgeting. Treat the vig as the cost of entertainment. Our guide to responsible gambling tools explains how to set limits.

Odds and tools on OOSClub#

OOSClub lists betting tools and picks groups in the sports betting niche and on the tools hub. We don't link to sportsbooks or publish anyone's betting results.