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The Kelly's formula is aimed at finding the optimal value for a bet, basing on its related odd. Such optimal value is represented by a percentage of the total budget and it is obtained as a half-way between a too high risk and a too lower income.

What is necessary for the calculation?

In order to calculate the Kelly's formula, it is necessary to know:

• the total available budget [B]
• the odd related to your prediction [Q]
• the percentage of success (estimated probability) related to your prediction [P]

The formula

The recommended value to bet [I] is calculated as follows:

I = [(Q x P/100 - 1) / (Q-1)] x B

Example

Considering the match Barcellona vs. Empoli, I want to bet on 1 (Barcellona wins).
• Total budget: B = 200€
• Odd related to 1: Q = 1.98
• estimated probability of success 1: P = 60%

Recommended value to be bet on 1: I = [(1.98 x 65/100 - 1) / (1.98-1)] x 200 = 58.87€

Variants

In order to mitigate the possibility of budget loss (caused by wrong estimatation of the probability of success), there is a more "conservative" variant, called Kelly/2. This method considers to bet only helf of the obtained value form the formula, i.e. I/2.

Notes

• In order to calculate the Kelly's formula, the estimation of the probability of success for our bet, i.e. P, is fundamental. Due to the fact that this term affects the final result, it should be necessary to be really careful in calculating it.
• About Kelly/2, even if the less you bet the less you will earn, it has been proved that it has an higher income for long periods.