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# Back Kelly

The Kelly criterion was developed by John Larry Kelly Jr. in 1956. It implies betting a predetermined fraction of the current bank, taking into account the gambler’s perceived probability of an outcome occurring and the available odds for that outcome.

The formula used to calculate the fraction for a back bet is:

f = (p × (d – 1) – q) / (d – 1)

where:

**f**= fraction of the current bank to wager.**d**= decimal betting odds.**p**= perceived probability of selection winning.**q**= perceived probability of selection losing, which is 1 – p.

If the commission fee of the bookmaker is taken into account, then the fraction formula becomes:

f = (p × (d – 1) × (1 – c) – q) / ((d – 1) × (1 – c))

where:

**f**= fraction of the current bank to wager.**d**= decimal betting odds.**c**= commission fee decimal value.**p**= perceived probability of selection winning.**q**= perceived probability of selection losing, which is 1 – p.

The fraction value must satisfy the following restriction in order to place the bet:

0 ≤ f ≤ 1

## Settings

The following parameters can be configured in this staking plan:

**Perceived probability of winning for qualified selections:**the perceived probability of winning for each qualified selection, expressed in percent.**Percent of factor to bet**: the percent of fraction value to bet.

The total stake value is calculated as follows:

where:

**stake**= total stake to place for a race.**f**= fraction value.**fp**= percent of factor to bet.**currentBank**= current account balance.

## Example

Let’s assume the following settings:

- Initial bank: £200
- Perceived probability of winning for qualified selections: 40%
- Percent of factor to bet: 50%
- Commission fee not included

**Step 1**

- 1 selection qualifies at decimal odds of 5
- fraction is 0.25
- total stake is £25
- bet wins and the profit is £100
- current bank is £300

**Step 2**

- 1 selection qualifies at decimal odds of 3
- fraction is 0.1
- total stake is £15
- bet losses and the loss is £15
- current bank is £285

**Step 3**

- 1 selection qualifies at decimal odds of 4
- fraction is 0.2
- total stake is £28.5
- bet wins and the profit is £85.5
- current bank is £370.5

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