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March 15, 2025

Understanding Betting Odds: Formats, Conversion, and Parlays

A complete guide to American, decimal, and fractional odds — how to convert between them, extract implied probabilities, and calculate parlay payouts.

Three Odds Formats

Every sportsbook displays odds in one of three formats. They all encode the same information — the ratio of profit to stake — just differently.

American odds use a +/- system anchored to 100.Afavoriteat−150meansyourisk100. A favorite at -150 means you risk 150 to profit 100.Anunderdogat+150meansyourisk100. An underdog at +150 means you risk 100 to profit $150.

Decimal odds express total return per dollar wagered. Decimal 2.50 means a 100betreturns100 bet returns 250 total (150profit+150 profit + 100 stake). Decimal odds are always greater than 1.

Fractional odds show the profit-to-stake ratio directly. 3/2 means 3profitforevery3 profit for every 2 staked — the same as +150 or decimal 2.50.

Converting Between Formats

From American to decimal:

d={1+∣A∣100if A>01+100∣A∣if A<0d = \begin{cases} 1 + \frac{|A|}{100} & \text{if } A > 0 \\ 1 + \frac{100}{|A|} & \text{if } A < 0 \end{cases}

From decimal to implied probability:

pimplied=1dp_{\text{implied}} = \frac{1}{d}

A line at -150 converts to decimal 1.667, which implies a 1/1.667=60%1/1.667 = 60\% win probability. But that 60% includes the book’s vig — the true probability is lower.

Break-Even Win Rate

The implied probability is also your break-even win rate. At -110 (decimal 1.909), you need to win 1/1.909=52.4%1/1.909 = 52.4\% of the time just to break even. This is why -110/-110 markets are the book’s bread and butter — both sides need 52.4%, totaling 104.8%.

That extra 4.8% is the overround, and it is the book’s margin on every dollar wagered.

Parlay Math

A parlay combines multiple independent bets. The combined decimal odds are the product of each leg’s decimal odds:

dparlay=d1×d2×⋯×dnd_{\text{parlay}} = d_1 \times d_2 \times \cdots \times d_n

A 3-leg parlay at -110, -110, -110:

dparlay=1.909×1.909×1.909=6.96d_{\text{parlay}} = 1.909 \times 1.909 \times 1.909 = 6.96

The implied probability of hitting all three legs (assuming independence):

pparlay=p1×p2×p3=0.5243=14.4%p_{\text{parlay}} = p_1 \times p_2 \times p_3 = 0.524^3 = 14.4\%

The Compounding Vig Problem

Here is the catch with parlays. Each leg carries vig, and vig compounds multiplicatively. A single -110 bet has about 4.8% overround. A 3-leg parlay at -110 per leg:

Fair odds=2.003=8.00vs. actual 1.9093=6.96\text{Fair odds} = 2.00^3 = 8.00 \quad \text{vs. actual } 1.909^3 = 6.96

The effective overround on the parlay is 8.00/6.96−1=14.9%8.00/6.96 - 1 = 14.9\%. The book’s margin nearly triples from a single bet to a 3-legger. This is why sportsbooks promote parlays so aggressively.

Practical Tips

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