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Implied Probability Calculator

Free implied probability calculator. Convert decimal, fractional, American, Hong Kong odds. Overroun

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Why This Statistical Analysis Matters

Why: Statistical calculator for analysis.

How: Enter inputs and compute results.

🎲
ODDS & PROBABILITYExtract true probability from betting odds

Implied Probability — Remove Vig/Overround

Decimal, fractional, American, Hong Kong. Multi-outcome overround. True probability with vig removed.

Expected Value →Roulette Payout →

Real-World Scenarios — Click to Load

Odds Format

Outcomes (2–10) — e.g. 2.00

implied_prob.sh
CALCULATED
$ implied_prob --format="decimal" --outcomes=2
Sum Implied
1.0000
Overround
0.00%
Profit Margin
0.00%
Vig Removed
True prob ✓
Outcome 1
Implied: 50.00%True: 50.00%
Outcome 2
Implied: 50.00%True: 50.00%
Share:
Implied Probability Result
True Probability (Vig Removed)
Overround: 0.00%
Outcome 1: 50.0%Outcome 2: 50.0%
numbervibe.com/calculators/statistics/implied-probability-calculator

Calculation Breakdown

COMPUTATION
Convert each odds to implied
P_i = 1/decimal (or format-specific)
COMPUTATION
Sum implied probabilities
1.0000
Σ P_i
VIG REMOVAL
Overround (vig)
0.00%
Σ P_i − 1
VIG REMOVAL
True probability (no vig)
P_true = P_i / Σ P_i
ext{Vig} ext{removed} — ext{fair} ext{probabilities}

True Probability Distribution (Vig Removed)

Implied vs True Probability

Overround vs Fair Book

For educational and informational purposes only. Verify with a qualified professional.

Key Takeaways

  • • Implied probability is what the odds suggest — P = 1/decimal for decimal odds
  • • Overround (vig) = sum of implied probabilities − 1 — the bookmaker's margin
  • • True probability (no vig) = implied / sum of all implied — removes the bookmaker edge
  • • American +100 = 50% implied; -200 = 66.7% implied
  • • Fractional 5/1 means 1/(5+1) ≈ 16.7% implied

Did You Know?

📊Pinnacle often has the lowest overround (2–3%) — sharp bookmakerSource: Pinnacle Academy
🎰Even money (2.00 decimal) = 50% implied — fair odds for a coin flipSource: Standard definition
🏇UK horse racing traditionally uses fractional odds (e.g., 5/1, 3/2)Source: UK betting conventions
🇺🇸American odds: negative = favorite, positive = underdogSource: US sportsbooks
🇭🇰Hong Kong odds = decimal − 1 (e.g., 2.00 decimal = 1.00 HK)Source: Asian markets
📈Overround above 10% means the book has a large margin — shop aroundSource: Value betting

Expert Tips

Compare overrounds

Lower overround = better value. Pinnacle, Betfair often best.

Use true probability for value

If your model says 55% and true is 48%, that's potential value.

Watch for arbitrage

If sum of implied < 1 across books, arbitrage exists.

Know your format

US = American, UK = fractional, Europe = decimal.

Odds Format Comparison

FormatExampleImplied %Formula
Decimal2.0050%P = 1/decimal
Fractional5/116.7%P = b/(a+b)
American ++15040%P = 100/(X+100)
American --20066.7%P = X/(X+100)
Hong Kong1.0050%P = 1/(HK+1)

Frequently Asked Questions

What is implied probability?

The probability suggested by the odds. For decimal 2.00, implied = 1/2 = 50%. It reflects the bookmaker's view plus their margin.

What is overround?

Overround = sum of implied probabilities − 1. For a fair book it would be 0. A 5% overround means the book keeps 5% of stakes.

How do I remove the vig?

True probability = implied / sum of all implied. This normalizes so the probabilities sum to 1.

What are American odds?

Negative = favorite (e.g., -150 means bet $150 to win $100). Positive = underdog (+150 means bet $100 to win $150).

How do fractional odds work?

a/b means you profit a for every b staked. 5/1 = profit $5 per $1. Implied = b/(a+b) = 1/6.

When is a bet +EV?

When your estimated probability exceeds the true (vig-removed) probability. Compare your model to true prob.

Why do implied probabilities sum to more than 100%?

The overround is the bookmaker's profit margin. They set odds so the sum exceeds 1.

What is Hong Kong odds?

HK odds = decimal − 1. So 2.00 decimal = 1.00 HK. Implied = 1/(HK+1).

By the Numbers

1/x
Decimal formula
5–10%
Typical overround
2–3%
Pinnacle margin
4
Odds formats

Disclaimer: This calculator is for educational purposes. Gambling involves risk. Please gamble responsibly. Odds and implied probabilities do not guarantee outcomes.

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