> For the complete documentation index, see [llms.txt](https://developer.aiodds.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://developer.aiodds.com/help-center/other/margin-calculation.md).

# Margin Calculation

## Calculation Steps

### Step1  Calculate the Total Implied Probability <a href="#h2-0" id="h2-0"></a>

First, convert the odds for all possible outcomes of a single betting market into probabilities and sum them up.

Assuming a market has $n$ possible outcomes (e.g., the 1X2 market has 3 outcomes, Under/Over has 2 outcomes), with corresponding odds of $O\_1, O\_2, ..., O\_n$.

The formula for the Total Implied Probability is:

<figure><img src="/files/UJjoMXLvfnvBbGJB1Ffp" alt=""><figcaption></figcaption></figure>

{% hint style="warning" %}
Note: Because the bookmaker needs to take a margin (profit), this total sum T will always be greater than 1 (i.e., > 100%).
{% endhint %}

### Step2  Calculate the Payout Ratio <a href="#h2-1" id="h2-1"></a>

The payout ratio is simply the reciprocal of the total implied probability.

The formula for the Payout Ratio is:

<figure><img src="/files/I0Q2bQDM4zQuVDE8w1Uj" alt=""><figcaption></figcaption></figure>

## Classic Application Example

### Football 1X2 (Match Winner)

Assume the odds for a specific match are: Home 2.10 | Draw 3.40 | Away 3.50

#### Step1  Calculate and sum the implied probabilities

Home Implied Probability = 1 / 2.10 ≈ 0.4762

Draw Implied Probability = 1 / 3.40 ≈ 0.2941

Away Implied Probability = 1 / 3.50 ≈ 0.2857

Total Implied Probability T = 0.4762 + 0.2941 + 0.2857 = 1.0560

#### Step2  Calculate the Payout Ratio

Payout Ratio $R = (1 / 1.0560) \* 100% ≈ 94.70%

Derivative Metric: Bookmaker Margin (Overround)

The bookmaker margin is simply 1 minus the payout ratio: **Margin = 100% - 94.70% = 5.30%**


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