Market Mathematical Analysis

What is Arbitrage (Surebet) and How Math Works

Feb 10, 2026 12 min read

Introduction to Arbitrage (Surebet)

Sports arbitrage (commonly known as surebet) is a mathematical strategy that allows you to secure calculated returns by covering all possible outcomes of an event. Unlike traditional speculation, arbitrage seeks to neutralize market risk when executed correctly.

The concept is based on simple mathematical principles accessible to anyone with basic financial arithmetic knowledge.

How Opportunities Arise

Arbitrage opportunities emerge when different marketplaces offer discrepant prices (odds) for the same event. This can happen for several reasons:

  • Different analyses: Each platform has its own team of analysts who may evaluate the market differently
  • Update speed: Some platforms are faster to update prices when new information emerges
  • Market strategies: Marketplaces may offer more competitive prices in certain areas to attract volume
  • Market volume: Market behavior can make prices move differently in each location

The Mathematics Behind It

To understand if an arbitrage opportunity exists, we need to use the concept of implied probability.

Calculating Implied Probability

Decimal odds represent the inverse of the estimated probability. For example, odds of 2.50 mean a potential return of 2.50 units for every 1.00 unit invested.

Implied probability is calculated as:

Implied Probability = 1 / Decimal Odds

For example, odds of 2.50 have an implied probability of 1 / 2.50 = 0.40 or 40%.

Identifying the Opportunity

To verify if arbitrage exists, we sum the implied probabilities of all possible outcomes:

Sum of Probabilities = (1 / Odds1) + (1 / Odds2) + ... + (1 / OddsN)

If the sum is less than 1 (or 100%), a mathematical opportunity exists. The difference between 1 and this sum represents the potential return margin.

Practical Step-by-Step Example

Let's work through a real example of an event with two possible outcomes:

Scenario

  • Marketplace A offers odds of 2.50 for Outcome 1
  • Marketplace B offers odds of 2.20 for Outcome 2
  • You have a capital of $100 to allocate

Step 1: Verify Viability

We calculate the implied probabilities:

  • Outcome 1: 1 / 2.50 = 0.4000 (40%)
  • Outcome 2: 1 / 2.20 = 0.4545 (45.45%)
  • Total Sum: 0.4000 + 0.4545 = 0.8545 (85.45%)

Since 0.8545 < 1, the operation is viable! The margin will be 1 - 0.8545=0.1455 or 14.55%.

Step 2: Calculate Allocation

To distribute the $100 proportionally:

Allocation on Outcome 1 = Total × (Implied Prob. 1 / Total Sum)

Allocation 1 = 100 × (0.4000 / 0.8545) = $46.81

Allocation on Outcome 2 = Total × (Implied Prob. 2 / Total Sum)

Allocation 2 = 100 × (0.4545 / 0.8545) = $53.19

Step 3: Calculate Returns

Now let's see the result in each scenario:

  • If Outcome 1 occurs: 46.81 × 2.50 = $117.03
  • If Outcome 2 occurs: 53.19 × 2.20 = $117.02

In both cases, total return is approximately $117.00, resulting in a positive result of about $17.00 on the $100 capital.

Important Factors to Consider

1. Timing is Crucial

Market prices change constantly. An opportunity can disappear in seconds. Execution needs to be fast.

2. Operational Limits

Platforms impose maximum operation limits. You may not be able to allocate the full calculated amount, which affects the strategy.

3. Operational Costs

Consider transfer and conversion fees. They can impact your results, especially on opportunities with thin margins.

4. Diversification

You'll need access to multiple marketplaces to find the best discrepancies.

Calculation Variations

Events with More Than 2 Outcomes

For events with three possible outcomes (Win A, Draw, Win B), the principle is the same:

Sum = (1 / OddsA) + (1 / OddsDraw) + (1 / OddsB)

If sum < 1, opportunity exists. Distribute capital proportionally to the implied probabilities.

Using Alternative Formulas

Some analysts prefer to calculate directly:

Allocation1 = Total / (1 + Odds1 / Odds2)

Allocation2 = Total - Allocation1

This simplified formula works perfectly for two-outcome events.

Tools and Resources

Identifying opportunities manually is time-consuming. Consider using:

  • Arbitrage Calculators: Like our Arbitrage Calculator, which automates all calculations
  • Market Scanners: Services that monitor multiple marketplaces simultaneously
  • Management Spreadsheets: To track portfolio performance

Conclusion

Arbitrage represents a strategy based on pure mathematics. While margins are conservative (1-5%), risk management makes it attractive for analytical profiles.

Success requires:

  • Solid understanding of mathematical principles
  • Access to multiple marketplaces
  • Speed in execution
  • Rigorous capital management
  • Discipline

Use our Arbitrage Calculator to start simulating opportunities today. Remember: mathematical knowledge is your best tool.