What are betting odds?
Betting odds are prices. They translate beliefs about chance into payoffs. When you see a price, you’re seeing a compact statement about probability and reward.
Formats & conversions
There are three common formats: fractional (5/2), decimal (3.50), and moneyline (+250 or −200). They are interchangeable.
A fractional a/b means you win a units for every b staked; the decimal price is ; the implied probability is .
A decimal price d pays stake × d if you win; its implied probability is .
Moneyline uses a sign: +X means you win X for every 100 staked (implied probability
);
−Y means you must stake Y to win 100 (implied probability
).
Break-even follows directly. At −110 the break-even probability is
.
At +150 it is .
At −200 it is .
If your true chance beats the break-even, the bet has positive expected value.
Margin (“vig”) and fair prices
Implied probability is not the bookmaker’s belief in isolation. It embeds margin (also called vig or overround). Add up implied probabilities across all mutually exclusive outcomes and you will usually get more than 100%. That excess is the margin. On a typical spread −110/−110 market, each side implies 52.38%; the total is 104.76%, so the overround is 4.76%. That is the house edge in price form.
To estimate “fair” probabilities from posted odds, remove the vig. A quick method is to normalize: divide each implied probability by the sum of all implied probabilities. For a three-way soccer line of 2.10 / 3.30 / 3.60, the implied probabilities are 47.62%, 30.30%, and 27.78%. They sum to 105.70%. Normalize them by that sum to get fair estimates of ~45.05%, 28.67%, and 26.28%, which correspond to fair decimal odds of ~2.22, 3.49, and 3.81. The difference between the quoted and fair prices is the margin.
American lines often display the vig asymmetrically. Suppose a moneyline reads −120 / +105. The implied probabilities are 54.55% and 48.78%, totaling 103.33%. Normalizing yields fair chances of ~52.79% and 47.21%. Those convert to fair decimal odds of ~1.894 and ~2.118 (about −112 / +112). The gap between the quoted and fair tells you how much you are paying.
How sportsbooks set and move lines
How do sportsbooks set odds? They start from a model of true chances. They add a margin. They post opening lines. Then the market moves them. Sharp action, injury news, weather, and limits shift prices. Books also shade prices toward public bias (for example, popular teams) and toward their own liability. Some books originate prices; many copy or move with the market. Early lines are more opinionated; closing lines (just before the event) tend to be more efficient.
Operational constraints matter. Limits determine how much sharp action can move a line. Some shops move the number (spread/total). Others move the price (the juice) while holding the number. Market microstructure creates timing edges (beating slow movers) but also risks account limits for consistent arbitrage.
Expected value & bankroll
Expected value (EV) converts belief into dollars. For stake S and decimal price d, net profit on a win is ; loss on a miss is . If your win probability is p, then
Positive EV requires . Bankroll strategy matters: the Kelly fraction for price d and edge p is
Use fractions of Kelly to reduce volatility.
Market types & settlement nuances
Not all markets price margin equally. Live (“in-play”) betting often carries higher vig due to time pressure and uncertainty. Niche props and player markets also tend to be pricier. Major pregame markets (NFL sides, Champions League totals) are tighter. Exchanges replace margin with commission on net winnings; the effective edge shows up in the spread between the best back and lay prices plus the commission.
Handicaps and totals encode probability via both spread and juice. Team A −3 (−110)
means you lay three points and pay −110. Push rules matter: land exactly on −3 and your stake is refunded. Asian handicaps split stakes across quarter lines (e.g., −0.25 means half at 0 and half at −0.5), allowing half-wins and half-pushes. In soccer and golf, dead-heat and Rule 4 deductions (for late withdrawals) change settlement and therefore the effective price you paid.
Parlays multiply prices and also multiply margin. If each leg is fairly priced, the fair parlay price is the product of fair decimal odds; when legs are correlated (same-game parlays), the naive product overstates payout. Books account for correlation in their builder pricing; many disallow strongly correlated combinations outright. Teasers trade spread for a different juice; their value hinges on “key numbers” (e.g., 3 and 7 in NFL scoring).
Nuances around language frequently cause confusion. In probability, “odds” can mean the ratio of failure to success (q:p). In betting, “odds” usually mean a payout multiplier or a moneyline. Keep the definitions straight to avoid mixing ratios with prices. Also note settlement specifics: voids for postponed events, partial payouts for place terms in each-way bets, and time-based rules in props. Small print changes value.
Worked examples
Two quick worked examples tie this together. First, a two-way market at −110/−110. The margin is 4.76%. De-vigging gives fair 50%/50% chances and fair decimal 2.00/2.00. Your model must exceed 52.38% on a side to beat the price.
Second, a three-way line at 2.10 / 3.30 / 3.60. Implied probabilities are 47.62% / 30.30% / 27.78%; margin is 5.70%. Fair (de-vigged) chances are ~45.05% / 28.67% / 26.28%. If you think the draw is 31%, you have an edge because 31% > 28.67%.
In practice, treat odds as a living summary of beliefs, costs, and rules. Convert to probability. Remove the vig. Compare to your estimate. Understand settlement. Then decide if the price clears your break-even and bankroll thresholds. That is the logic behind every good bet.