Implied Probability: what it is, how to calculate it, and how to remove the bookmaker’s margin

TL;DR

• Implied probability = the probability hidden inside the odds.
• Decimal odds → implied %: p(%) = 100 / odds.
• Bookmakers add a margin (overround/hold), so raw implied % sum to >100%.
• Normalize back to 100% to get fair (no-vig) probabilities and fair odds.
• If book odds ≥ fair odds, you’ve likely found value.

Use right now: Implied Probability Calculator • Hold/Overround Calculator • EV Calculator • Kelly Calculator • Edge Finder

1) Implied probability in one line

If an outcome is priced at 1.80, then p = 100 / 1.80 = 55.56% (before removing the margin). Do this for every outcome in the market.

2) Why totals are >100% (the margin)

In a truly fair (no-vig) market, outcome probabilities would sum to 100%. Bookmakers add a margin so they profit on average → your raw implied % will sum to >100%.

Overround (margin) % = (sum of raw implied %) − 100

3) Convert implied % → fair probabilities (no-vig)

Normalize the raw implied % so the total is exactly 100%:

For each outcome i: fair_pi = raw_pi / (Σ raw_p) × 100%

Then get fair odds (no-vig): fair_oddsi = 100 / fair_pi

These are your breakeven numbers. If the book offers odds equal to fair odds, long-term EV is ≈0 (ignoring fees).

4) Two quick examples

A) Two-way market (no draw)

Odds: 1.80 vs 2.05

1. Raw implied %
   100/1.80 = 55.56%  •  100/2.05 = 48.78%
   Sum = 104.34% → Overround = 4.34%
2. Normalize to fair (divide by 104.34%)
   53.25% and 46.75%
3. Fair odds (no-vig)
   100/53.25 = 1.878  •  100/46.75 = 2.139

Is there value? Compare book odds to fair odds: 1.80 vs 1.878 and 2.05 vs 2.139 → both below fair → no value on either side.

B) 1X2 market (draw included)

Odds: Home 2.20, Draw 3.40, Away 3.10

1. Raw implied %
   Home: 100/2.20 = 45.45%  •  Draw: 100/3.40 = 29.41%  •  Away: 100/3.10 = 32.26%
   Sum = 107.12% → Overround = 7.12%
2. Normalize to fair
   Home: 45.45 / 107.12 = 42.43%
   Draw: 29.41 / 107.12 = 27.46%
   Away: 32.26 / 107.12 = 30.11%
3. Fair odds
   Home: 100/42.43 = 2.357
   Draw: 100/27.46 = 3.642
   Away: 100/30.11 = 3.321

Spotting value: If your book offers Home 2.40, then
EV% ≈ p × odds − 1 = 0.4243 × 2.40 − 1 = +1.84%, or
EV% ≈ (book_odds / fair_odds) − 1 = 2.40 / 2.357 − 1 = +1.84%.
That’s a potential value bet.

5) From fair probabilities to expected value (EV)

Use fair probability (your best “true p”) to compute EV:

• With decimal odds O and p_true (e.g., 53.25% → 0.5325):
  EV% = p_true × O − 1
• If you already have fair odds:
  EV% ≈ (book_odds / fair_odds) − 1 (same result because fair_odds = 1 / p_true)

Rule of thumb: On liquid markets, look for ≥1–2% EV before thinking about stake size.

6) Simple workflow (copy this)

1. Take the market odds.
2. Convert each to raw implied % (100/odds).
3. Add them up → this total minus 100% is the margin.
4. Normalize to get fair % and fair odds (no-vig).
5. If book odds ≥ fair odds, you may have value.
6. Confirm EV% and size your stake with a conservative fractional Kelly (e.g., 0.25–0.5×).
7. Track your results and CLV (did you beat closing?) over a decent sample.

7) Common mistakes (avoid these)

• Skipping de-vig: Raw implied % are inflated—normalize every time (especially on 1X2).
• Comparing the wrong lines: Use closing or a consistent snapshot; compare softbooks to a sharper reference.
• Mixing formats: Keep units straight (decimal vs American vs fractional).
• Over-rounding: Calculate with full precision; round only for display.
• Chasing tiny edges: <1% edges can vanish with slippage, limits, or model error.