Take the quote, divide 1 by it, then multiply by 100 to get a percentage. Example: a decimal quote of 2.50 implies 1 ÷ 2.50 = 0.40 → 40%. A decimal quote of 1.80 implies 55.56%. This single step turns a market number into a clear target: your estimated win rate must exceed that percentage to justify a stake.

For American notation, convert first: for negative numbers use 1 + 100/|A|; for positive numbers use 1 + A/100. Example: -150 becomes 1 + 100/150 = 1.6667 → implied win rate 60%. Example: +200 becomes 1 + 200/100 = 3.00 → implied win rate 33.33%. For fractional notation, turn it into decimal via (a/b) + 1; 5/2 becomes 3.50 → 28.57%.

To separate the bookmaker’s margin, normalize the win rates across all outcomes. Two-way market example: decimal quotes 1.91 vs 1.91 give raw win rates 52.36% + 52.36% = 104.72%. Divide each by 1.0472 to get fair estimates: 50% vs 50%. Use this adjusted baseline when comparing with your own model; a 2–3% edge is meaningful only after removing the built-in margin.

Convert American, Decimal, and Fractional Odds into a Single Comparable Format

Use decimal quotation as the single yardstick: it shows total return per 1 unit staked, so every market quote becomes directly comparable.

From American format, convert with two cases. For +X: decimal = 1 + (X/100); example +150 → 1 + 150/100 = 2.50. For -X: decimal = 1 + (100/X); example -200 → 1 + 100/200 = 1.50. This removes sign-based confusion and gives one number where higher means larger payout per unit.

From fractional form A/B, use decimal = 1 + (A/B). Example 5/2 → 1 + 2.5 = 3.50; 1/4 → 1 + 0.25 = 1.25. Keep A and B as payout-to-stake, then add the returned stake as the final “+1”.

Once everything is in decimal, convert to a unified win-rate estimate with p = 1/decimal. Examples: 2.50 → 0.40 (40.0%), 1.50 → 0.6667 (66.67%), 3.50 → 0.2857 (28.57%), 1.25 → 0.80 (80.0%). Use this number to compare lines across books without mixing formats.

Reverse conversions stay consistent. From decimal D to American: if D ≥ 2.00, American = +100×(D−1); 2.50 → +150. If D < 2.00, American = −100/(D−1); 1.50 → −200. From decimal to fractional: (D−1) as a ratio; 3.50 → 2.50 = 5/2, 1.25 → 0.25 = 1/4.

For quick checks, sanity-test with stake=1. Decimal 2.50 must return 2.50 total, profit 1.50; American +150 must profit 1.50 per 1; fractional 3/2 must profit 1.50 per 1. If the profit figures mismatch, the conversion is wrong.

When rounding, keep decimal to 2–3 digits (e.g., 1.91, 2.05) and p to at least 4 decimals before percent display; small rounding shifts can move p by 0.2–0.5 percentage points near even-money quotes.

Calculate Implied Probability from Each Odds Type (Including Favorites vs Underdogs)

Convert any price into a win-chance share by dividing the stake by total return for example using Winpesa; for fractional 5/2 use 2/(5+2)=0.2857 (28.57%), while 1/4 uses 4/(1+4)=0.8000 (80.00%).

For decimal format, use 1/price: 1/1.80=0.5556 (55.56%), 1/3.40=0.2941 (29.41%), 1/10.00=0.1000 (10.00%). Lower decimals signal a favorite; higher decimals signal an underdog, and the conversion stays identical.

For American “minus” lines (favorite), use x/(x+100): −150 → 150/(150+100)=0.6000 (60.00%); −110 → 110/210=0.5238 (52.38%); −400 → 400/500=0.8000 (80.00%).

For American “plus” lines (underdog), use 100/(x+100): +200 → 100/300=0.3333 (33.33%); +450 → 100/550=0.1818 (18.18%); +120 → 100/220=0.4545 (45.45%).

Favorites vs underdogs can be spotted without math: decimal below 2.00, fractional below 1/1, or American with a minus sign typically marks the side expected to win more often; the formulas above quantify that expectation into a single percentage.

To compare across formats, translate to the same chance share: decimal 1.67 equals 59.88%; fractional 2/3 equals 60.00%; American −150 equals 60.00%–small gaps usually come from rounding rather than real disagreement.

For two-way markets, add both sides’ shares to detect margin: Team A at 1.80 gives 55.56% and Team B at 2.10 gives 47.62%, sum=103.18%; the extra 3.18% is the book margin embedded in the prices.

For three-way markets, repeat per selection: 2.50 → 40.00%, 3.20 → 31.25%, 3.00 → 33.33%, sum=104.58%; use the shares to compare value, especially when a longshot’s percentage looks inflated relative to your own estimate.

Remove the Bookmaker Margin (Vig/Overround) to Get “True” Implied Probabilities

Normalize the market so the outcome shares sum to 100%: take each outcome’s raw share from the posted price, then divide by the total of all raw shares.

For decimal quotes, convert each selection to a raw share with 1/decimal. Example (3-way): Home 2.10, Draw 3.40, Away 3.60.

• Raw shares: Home 1/2.10 = 0.47619; Draw 1/3.40 = 0.29412; Away 1/3.60 = 0.27778
• Total = 1.04809 → market load = 4.809%
• Normalized shares (“true”): Home 0.47619/1.04809 = 0.4544 (45.44%); Draw 0.29412/1.04809 = 0.2806 (28.06%); Away 0.27778/1.04809 = 0.2650 (26.50%)

The same adjustment works for 2-way lines. Decimal quotes 1.80 vs 2.10 give raw shares 0.55556 + 0.47619 = 1.03175 (load 3.175%); normalized shares: 53.84% vs 46.16%.

For American quotes, first convert to decimal: positive +150 → 2.50; negative -120 → 1 + 100/120 = 1.8333. Then proceed with raw share = 1/decimal and normalize.

Quick formula set for n outcomes:

1. Raw share for outcome i: r_i = 1/d_i
2. Total: R = Σ r_i
3. Market load: (R − 1) × 100%
4. Normalized share: p_i = r_i / R

Use normalized shares for comparisons across shops: two books can post different loads (e.g., 2.5% vs 6%), while pointing to nearly identical “true” shares after normalization.

Avoid removing the load by subtracting a fixed percentage from each outcome; that distorts skewed markets. Only normalization preserves relative differences across all selections, including longshots.