Arbitrage Calculator
Find and calculate mathematical arbitrage opportunities
Formula Explanation
Arbitrage (sure betting) occurs when you can bet on all possible outcomes of an event and guarantee return regardless of the result. This is possible when different marketplaces have discrepant odds.
Formula
Check if it's Arbitrage:
Implied Probability = (1 / Odds1) + (1 / Odds2)
If < 1 (or 100%), it's arbitrage ✓
Calculate Allocations:
Allocation1 = Total / (1 + Odds1 / Odds2)
Allocation2 = Total - Allocation1
Guaranteed Return:
Return = (Allocation1 × Odds1) - Total
ROI = (Return / Total) × 100
Step-by-Step Guide
Practical Example
Scenario: An event with 2 possible outcomes
- Marketplace A offers 2.50 for Outcome 1
- Marketplace B offers 2.20 for Outcome 2
- You want to invest $100 total
Step 1: Check if it's Arbitrage
Implied Probability = (1 / 2.50) + (1 / 2.20) = 0.4 + 0.4545 = 0.8545
Since 0.8545 < 1, it's arbitrage! ✓
Step 2: Calculate Allocations
Allocation on Outcome 1 = 100 / (1 + 2.50 / 2.20) = $46.81
Allocation on Outcome 2 = 100 - 46.81 = $53.19
Step 3: Calculate Return
If Outcome 1 occurs: 46.81 × 2.50 = $117.03
If Outcome 2 occurs: 53.19 × 2.20 = $117.02
Guaranteed return in both cases: $17.02
ROI: 17.02%