🧮 How to Calculate a Sure Bet — Step by Step with Examples

Understanding the math behind arbitrage is essential. This guide walks you through the calculations step by step.

The Arbitrage Formula

For a two-outcome event:

Combined Implied Probability = (1 / Odds₁) + (1 / Odds₂)

If this sum is less than 1.0 (100%), an arb exists.

Profit % = (1 / Combined Probability - 1) × 100

Worked Example: Two-Way Market

NBA Game: Lakers vs Celtics

• DraftKings: Lakers 1.90
• FanDuel: Celtics 2.20

Step 1: Calculate combined implied probability

• (1 / 1.90) + (1 / 2.20) = 0.5263 + 0.4545 = 0.9808 (98.08%)

Step 2: Calculate profit percentage

• (1 / 0.9808 - 1) × 100 = 1.96% profit

Step 3: Calculate stakes for $1000 total

• Stake on Lakers: $1000 × (1/1.90) / 0.9808 = $536.44
• Stake on Celtics: $1000 × (1/2.20) / 0.9808 = $463.56
• Total staked: $1000

Step 4: Calculate returns

• If Lakers win: $536.44 × 1.90 = $1019.24
• If Celtics win: $463.56 × 2.20 = $1019.83
• Guaranteed return: ~$1019.50 (regardless of outcome)
• Guaranteed profit: ~$19.50 (1.96%)

Worked Example: Three-Way Market

Soccer: Real Madrid vs Barcelona (1X2)

• Bookmaker A: Home Win 2.80
• Bookmaker B: Draw 3.50
• Bookmaker C: Away Win 3.00

Combined probability: (1/2.80) + (1/3.50) + (1/3.00) = 0.3571 + 0.2857 + 0.3333 = 0.9761

Profit % = (1/0.9761 - 1) × 100 = 2.45%

For $500 total stake:

• Home Win: $500 × 0.3571/0.9761 = $183.00
• Draw: $500 × 0.2857/0.9761 = $146.36
• Away Win: $500 × 0.3333/0.9761 = $170.64

Use the Calculator

Skip the manual math and use our arbitrage calculator. Enter the odds and your total stake — it does the rest.