🔢 Betting Math — Odds Formats, Probability & Expected Value

Understanding betting mathematics is crucial for anyone who wants to treat betting as more than entertainment.

Odds Formats

Decimal Odds

The default in Europe, Australia, and Canada.

• Decimal odds of 2.00 mean you receive $2 for every $1 staked (including your stake).
• Your profit = Stake × (Odds - 1)
• Example: $100 at 2.50 → Profit = $100 × 1.50 = $150, Return = $250

American Odds

The default in the US.

• Positive (+150): Bet $100 to win $150 profit
• Negative (-200): Bet $200 to win $100 profit
• Converting: American > 0 → Decimal = (American/100) + 1; American < 0 → Decimal = (100/|American|) + 1

Fractional Odds

Common in the UK and horse racing.

• 3/1 means you win $3 for every $1 staked
• 5/2 means you win $5 for every $2 staked
• Converting to decimal: (numerator/denominator) + 1

Implied Probability

Every set of odds implies a probability:

Implied Probability = 1 / Decimal Odds

When a bookmaker offers 2.00 on a coin flip (which should be 50%), the 0% margin seems fair. But they typically offer 1.90, implying 52.6% — that 2.6% is their margin (vig).

Expected Value (EV)

EV = (Probability of Winning × Amount Won) - (Probability of Losing × Amount Lost)

Example: Betting $100 at odds of 2.50 on an event you believe has a 45% chance:

• EV = (0.45 × $150) - (0.55 × $100) = $67.50 - $55.00 = +$12.50
• This is a +EV bet — you expect to profit $12.50 per $100 bet over time.

The Vig (Bookmaker's Margin)

The bookmaker builds in a margin by offering odds that imply more than 100% total probability.

Two-way market:

• Team A: 1.85 (implied 54.05%)
• Team B: 1.85 (implied 54.05%)
• Total: 108.1% → 8.1% vig

To find the true probability, remove the vig:

• True probability of Team A = 54.05% / 108.1% = 50%

Use our odds converter calculator to quickly switch between formats and see implied probabilities.