LineAmerican odds in two rules
Negative number = what you risk to win $100. At -150, you risk $150 to profit $100. Negative numbers mark favorites; the bigger the number, the heavier the favorite.
Positive number = what you win by risking $100. At +130, a $100 bet profits $130. Positive numbers mark underdogs; the bigger, the longer the shot. The scale is symmetric around +100 (even money), and everything scales linearly — $10 at +130 profits $13.
Every price is a probability wearing a costume
The conversions worth memorizing, because they turn every line on the board into a percentage you can argue with:
| Odds type | Implied probability formula | Example |
|---|---|---|
| Negative (-X) | X / (X + 100) | -150 → 150/250 = 60% |
| Positive (+X) | 100 / (X + 100) | +130 → 100/230 = 43.5% |
The famous one: -110 implies 52.4%. That's why 52.4% is the break-even hit rate quoted everywhere — it's not a mystical betting constant, it's just the price -110 charges, converted.
Finding the vig
Convert both sides of any market and add them. A fair market would sum to exactly 100%; a real one always sums higher. Two sides at -110 each: 52.4% + 52.4% = 104.8%. That extra 4.8% is the vig — the book's fee, spread invisibly across both prices. It's why a bettor who picks pure coin flips doesn't break even; they lose at precisely the rate of the overround. Every strategy on this site — +EV hunting, unit discipline, CLV tracking — is ultimately a way of dealing with that 4.8% headwind. Removing the vig proportionally (divide each side's implied probability by the total) gives you the no-vig line: the market's actual opinion, which is the correct benchmark for judging any price anywhere else.
Decimal and fractional, briefly
Decimal odds (Europe, and most betting exchanges) state total return per $1 staked: 2.50 returns $2.50, meaning $1.50 profit — equal to +150. Convert: positive American = (decimal − 1) × 100; negative American = −100 / (decimal − 1). Implied probability is simply 1/decimal, which is why quants prefer them. Fractional odds (UK, horse racing) state profit over stake: 5/2 means $5 profit per $2 staked, equal to +250. If you build any tooling — bet logs, calculators, a Kelly sizer — convert everything to decimal internally and translate at the edges; American odds are a display format, not a math format.
The mental shift that matters
Once odds become probabilities, betting stops being "who do I think wins?" and becomes "is 60% the right number?" — a fundamentally different and more answerable question. You'll never look at the Rays at -150 again; you'll see the market says 60%, and your only job is deciding whether the true number is higher. Every article in this library builds on that one reframe.