Betting Odds Explained: Decimal, Fractional, American and Implied Probability

Where these figures come from

The overround and cost figures come from this site's own devigTwoWay (src/tools/ev-calculator/math.ts), applied to this guide's own worked example plus two more balanced two-way markets, 1.83 / 1.83 and 1.95 / 1.95. The cost conversion is marginCost(margin) = margin / (1 + margin), added to that same file this pass and derived from the identity that betting a market's own price at its devigged fair probability has expected value 1/over - 1 = -margin/(1+margin), where over is the sum of the market's implied probabilities; math.test.ts checks that identity directly rather than assuming it holds. Scoped to balanced two-way markets only, per devigTwoWay's own docblock: on a market with a heavy favorite the proportional method it uses is the weaker model, so this figure does not extend past a symmetric price without the power or Shin methods the no-vig calculator carries. The implied-probability worked examples and the odds-conversion figure's three cross-format rows come from this site's own odds converter (src/tools/odds-converter/lib.ts): decimalToFraction, toAmerican, toProbability and formatDecimal, the same functions the odds converter tool runs. The implied-probability figures are rounded to one decimal place, so 66.7% and 33.3% are roundings of 66.66...% and 33.33...%, not exact equalities.

Verification

Checked against ev-calculator's math.test.ts (devigTwoWay, marginCost, and the -evPerUnit identity marginCost is derived from) and odds-converter's lib.ts (decimalToFraction, toAmerican, toProbability): agrees on the guide's own worked example (4.71% overround, 4.50% cost at 1.91 / 1.91), the two additional balanced points (9.29% overround / 8.50% cost at 1.83 / 1.83, 2.56% overround / 2.50% cost at 1.95 / 1.95), and the guide's twelve implied-probability and cross-format conversion figures, now rendered once in the odds-conversion figure rather than in prose and a list both (verified by src/guides/figures/overround-cost-data.test.ts and src/tools/ev-calculator/math.test.ts, 2026-09-23; src/guides/figures/odds-conversion-data.test.ts, 2026-09-29).

Know the risk

• Treating the 'fair' price, with the bookmaker's margin stripped out, as a verified probability rather than the market's own estimate. Removing the overround tells you what the market is collectively pricing an outcome at, not that the pricing is correct; the fair price is a benchmark to compare your own opinion against, not a guarantee.
• Assuming a market with a low overround is automatically good value. Overround measures the bookmaker's built-in edge across the whole market, not whether your specific opinion on the outcome is right. A tightly priced market and a wrong opinion still loses money.
• Reading a decimal conversion of a fractional price as more precise than the fraction itself. Sportsbooks round fractional odds to the nearest conventional fraction, so converting 3/2 to 2.50 does not recover precision the original price never had.
• Reading the overround itself as what comes out of your bankroll. It is the market's total built-in margin; the actual expected cost of betting either side at its own price is always somewhat lower than that, and confusing the two overstates how expensive a market actually is, though never enough to turn a wrong opinion into a profitable one.

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