The two basic shapes: + and −
Every American odds line is either a positive number (e.g. +150) or a negative number (e.g. −180). The sign tells you the favorite/underdog direction; the magnitude tells you the price.
| Odds | Bet $100, win... | Risk to win $100 | Implied probability | Favorite or underdog? |
|---|---|---|---|---|
+150 | $150 profit | $67 | 40.0% | Underdog |
+200 | $200 profit | $50 | 33.3% | Underdog |
+450 | $450 profit | $22 | 18.2% | Underdog (longshot) |
−110 | $91 profit | $110 | 52.4% | Slight favorite (typical "vig") |
−180 | $56 profit | $180 | 64.3% | Favorite |
−500 | $20 profit | $500 | 83.3% | Heavy favorite |
Converting American odds to implied probability
Implied probability is what the price suggests the chance of winning to be. There are two formulas:
For POSITIVE odds: probability = 100 / (odds + 100) For NEGATIVE odds: probability = odds / (odds + 100)
Worked examples:
+150: 100 / (150 + 100) = 100 / 250 = 40.0%+450: 100 / (450 + 100) = 100 / 550 = 18.2%−180: 180 / (180 + 100) = 180 / 280 = 64.3%−110: 110 / (110 + 100) = 110 / 210 = 52.4%
Important: implied probability includes the sportsbook's margin (the vig). When you sum implied probabilities across both sides of a typical market, the total exceeds 100%. The excess is the vig — the operator's built-in edge. See our no-vig calculator to strip the vig out and compute fair-odds probability.
Why −110 is the "standard" sportsbook line
For coin-flip-close markets (most NFL spreads, NBA totals), the typical price is −110 on both sides. Each side has 52.4% implied probability. Sum: 104.8%. The 4.8% over 100% is the operator's margin — about $4.55 of every $100 bet on either side, on average, accrues to the book.
This is why a flat-bet bettor needs to win 52.4% of −110 bets just to break even, not 50%.
Converting to decimal odds
Decimal odds are the European standard and represent total return per $1 bet (including your stake).
For POSITIVE odds: decimal = (odds / 100) + 1 For NEGATIVE odds: decimal = (100 / odds) + 1
+150→ 1.50 + 1 = 2.50 (a $100 bet returns $250 total)−180→ 0.556 + 1 = 1.556 (a $100 bet returns $156 total)−110→ 0.909 + 1 = 1.909 (a $100 bet returns $191 total)
Converting to fractional odds
Fractional odds are the UK standard and represent profit-to-stake ratio.
For POSITIVE odds: fractional = odds/100 (then simplify) For NEGATIVE odds: fractional = 100/odds (then simplify)
+150→ 150/100 → 3/2 (win $3 for every $2 staked)+200→ 200/100 → 2/1 ("two-to-one")−180→ 100/180 → 5/9 (win $5 for every $9 staked)
The mental shortcut: "magnitude tells you price"
You don't need to memorize formulas to read American odds quickly. The mental model:
- Higher positive number = bigger underdog = bigger payout for $100 risked. +500 pays more than +200.
- Higher negative number = bigger favorite = more $$ you must risk to win $100. −500 requires more risk than −200.
- The cutoff is +100 / −100 (even money). Anything between (e.g. +110, −110) is essentially a coin flip with vig.
Common confusing edge cases
Pick'em / "EV" / "+100"
When a sportsbook lists a market as EVEN or PK (pick'em), the price is +100 on both sides — no favorite. This is rare in main markets (sportsbooks usually structure to keep the vig built in via −110/−110), but appears on some props.
Why both sides of a totals bet are usually −110
For an NBA total of 220.5, both Over and Under typically price at −110. The sportsbook isn't predicting which side will hit; it's collecting vig from both sides. Move the line, and prices shift to compensate (e.g. 220 might price Over −115 / Under −105, indicating the book takes 220.5 as fair).
How big a number can American odds get?
In practice: futures longshots can hit +50000 or higher (a 0.2% implied probability before vig, e.g. a 64-1 longshot to win the World Cup). Heavy favorites in lopsided matchups can hit −2000 or worse (95.2%+ implied). Any sportsbook displaying odds beyond these ranges is usually showing a "no bet allowed" placeholder.
How to use this in practice
The single most useful skill: looking at a price and immediately computing whether you think the true probability of the outcome is higher or lower than the implied probability. If you think the true probability is higher, the bet is +EV (positive expected value). If lower, the bet is -EV.
Use our no-vig calculator to convert two-sided market prices to fair-probability estimates. Use our parlay calculator to combine multiple American-odds legs.