Understanding Betting Odds: Formats, Conversion, and Parlays

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. A favorite at -150 means you risk$150 to profit $100. An underdog at +150 means you risk$100 to profit $150.

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

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

Converting Between Formats

From American to decimal:

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

From decimal to implied probability:

$$p_{\text{implied}} = \frac{1}{d}$$

A line at -150 converts to decimal 1.667, which implies a $1/1.667 = 60\%$ 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 $1/1.909 = 52.4\%$ 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:

$$d_{\text{parlay}} = d_1 \times d_2 \times \cdots \times d_n$$

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

$$d_{\text{parlay}} = 1.909 \times 1.909 \times 1.909 = 6.96$$

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

$$p_{\text{parlay}} = p_1 \times p_2 \times p_3 = 0.524^3 = 14.4\%$$

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:

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

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

Practical Tips

• Always think in implied probability, not odds format — it makes comparisons across books and formats instant
• Parlays are not inherently bad, but understand that the vig scales with the number of legs
• Use the Odds Converter, Sharp Implied, and Parlay Calculator to run these conversions instantly