Bookmaker Margin Calculator

Defaults are Odds 1 = 1.90, Odds 2 = 1.90, Odds 3 (optional) = 0. A two-way market at even 1.90s. Submit. Bookmaker Margin is 5.26% and Overround is 105.26%. Inverse sum inv = 1/1.90 + 1/1.90 = 2/1.90 ≈ 1.052632. Margin is (inv − 1) × 100 ≈ 5.263. Overround is inv × 100 ≈ 105.263. The two rows are the same information: juice as a percent of a fair 100%, and the raw implied-probability total.

Leave the third field at 0 to stay two-way. Enter a third price only for 1X2 or any trichotomy. Example: 2.40, 3.40, 3.20. inv = 1/2.40 + 1/3.40 + 1/3.20 ≈ 0.41667 + 0.29412 + 0.31250 = 1.02329, margin ≈ 2.33%, overround ≈ 102.33%. That is a sharp three-way. A soft football book might look like 2.10, 3.40, 3.40: inv ≈ 0.47619 + 0.29412 + 0.29412 = 1.06443, margin ≈ 6.44%.

If both two-way prices are 2.00, inv = 1, margin 0%, overround 100%. That is a fair book, not a commercial one. If both are 1.80, inv ≈ 1.111, margin 11.11%—a typical early or recreational two-way. The optional third default of 0 is a sentinel: values ≤ 0 are ignored so a leftover 0 does not contribute 1/0.

You can paste any complete market whose outcomes are exhaustive and mutually exclusive. Two tennis moneyline prices. Three match-result prices. Do not mix a two-way with a leftover third from a previous search; reset Odds 3 to 0. Do not enter American odds; convert to decimal first.

Reload 1.90, 1.90, 0 to recover 5.26% and 105.26%. That pair is the educational “two equal prices a shade shorter than evens” illustration used in every overround lecture. Convert American −111/−111 to decimal 1.901 first if your sheet is US-style; typing −111 into this form is undefined. A 1X2 leftover in Odds 3 after you switched to tennis will inflate the margin—zero it. Two 1.90s plus a forgotten 3.50 is a three-way the market never offered.

Bookmaker margin, overround, or vigorish in this two- and three-way form is the excess of implied probabilities over 100%. If a two-way is 1.90 and 1.90, each implied probability is 52.63%, they sum to 105.26%, and the margin is 5.26%. The calculator exists to turn a set of decimal prices into that percentage without arguing about which side is “the juice.”

Prices are not probabilities; they are offers. Shin’s models and later literature on favourite-longshot bias treat the overround as a mixture of risk-sharing, information, and monopoly power, not as a single honest edge applied evenly. A 5% two-way can still be 7% on the longshot and 3% on the favourite after Shin inversion. This tool does not invert Shin. It reports the raw sum.

History: paper lists in Britain quoted odds that already contained the overround; the “book” was the sum the clerk computed by hand. Exchange betting (Betfair, 2000s) made 101–103% two-ways visible to the public and forced traditional books tighter on commoditised markets. Soft books remain at 6–12% on minors. The identity (Σ 1/o_i − 1) did not change.

Limits: at most three prices. No Shin, no power method, no margin attribution per side. Optional third odd 0 means omit. Mutually exclusive exhaustive outcomes are assumed; if you enter two correlated props, the number is meaningless. Commission-inclusive exchange back odds are not adjusted. Each-way books are not this formula.

Purpose is comparison. A 1.91 / 1.91 two-way (margin ≈ 4.71%) is cheaper than 1.90 / 1.90 on the same event, which is cheaper than 1.83 / 1.83. The calculator will not tell you the true probability of either side. It will tell you how much the quotes add above 100%. That is the cost of using that market as a round-trip, and a lower bound on how much at least one side is shortened. Shin inversion would reallocate that 5.26% unevenly toward the longshot; without a favourite-longshot pair of different prices, the 1.90/1.90 case is symmetric and Shin collapses toward the naive split anyway.

Bookmaker margin, overround, or vigorish in this two- and three-way form is the excess of implied probabilities over 100 percent. Prices are not probabilities; they are offers. If a two-way is 1.90 and 1.90, each implied probability is 1/1.90 ≈ 52.632 percent, they sum to 105.263 percent, and the margin is 5.263 percent. The worksheet turns a set of decimal prices into that percentage without arguing about which side is “the juice.” A coherent fair book would satisfy the sum of 1/o_i equal to one. The excess of that sum over one is the margin as a fraction of stake if you could bet every side in proportion to implieds, a round-trip Dutch at a loss. Overround is the same sum expressed with 100 as the fair baseline.

The defaults are 1.90, 1.90, and a third field of 0 meaning two-way. Inverse sum equals 2 / 1.90 ≈ 1.0526315789. Margin percent equals (1.0526315789 − 1) × 100 ≈ 5.263. Overround percent equals 1.0526315789 × 100 ≈ 105.263. Leave the third field at zero to stay two-way. Enter a third price only for a home-draw-away trichotomy or any other three-way. Example: 2.40, 3.40, 3.20. Inverse sum equals 1/2.40 + 1/3.40 + 1/3.20 ≈ 0.41667 + 0.29412 + 0.31250 = 1.02329, margin about 2.33 percent, overround about 102.33 percent. That is a sharp three-way. A softer football book might look like 2.10, 3.40, 3.40: inverse sum ≈ 0.47619 + 0.29412 + 0.29412 = 1.06443, margin about 6.44 percent.

If both two-way prices are 2.00, inverse sum equals 1, margin 0 percent, overround 100 percent. That is a fair book, not a commercial one. If both are 1.80, inverse sum ≈ 1.111, margin 11.11 percent, a typical early or recreational two-way. Shin’s 1991 and 1993 papers estimate insider-trading probabilities from quoted odds by solving for a z parameter; the additive margin here is the naive precursor. Multiplicative methods scale each implied by 1/inv to recover a “fair” split. This worksheet outputs only the naive additive pair. It does not print the de-vigged 47.37 / 47.37 split of a 1.90 / 1.90 book, which would be each 1/o_i divided by inv.

History is clerical. Paper lists in Britain quoted odds that already contained the overround; the “book” was the sum the clerk computed by hand. Exchange betting in the 2000s made 101 to 103 percent two-ways visible to the public and forced traditional shops to advertise shorter prices. Favourite-longshot bias means a 5 percent two-way can still be 7 percent on the longshot and 3 percent on the favourite after inversion. The additive 5.26 percent does not allocate that bias.

Assumptions: decimal odds, optional third price included only if positive, no place terms, no rule-four, no dead-heat. A listed 0 is unused, not a fourth outcome at infinite odds. The worksheet reports margin and overround. It is the sum of reciprocals minus one, not a Shin inversion and not a forecast of which side is the overlay.