Kelly criterion


Contents

Kelly criterion is a financial betting strategy developed by John Kelly in 1956, which determines bets in percentage, depending on the total amount of the bank.

For proper operation of this strategy, a punter needs to assess the likelihood of the outcomes he is planning to bet on himself. If such probability is lower than the one offered by a bookmaker, it’s necessary to abstain from the bet in this case.

How does Kelly criterion work?

The idea of Kelly criterion is that a player appropriates a small part of his bank for each bet.

At the beginning of the process it is necessary to calculate the betting amount on one or another event. A punter should consider how big his bank is, the odds proposed by a bookmaker and give his own assessment of the probability of the event.

Example

Let’s take a football match as an example in order to see this formula in action.

For example, a punter places a bet on Manchester United’s win with 2.20 odds. This means that a bookmaker estimates the probability of this outcome by 45.5 percent. But the player believes that Manchester United has 55 percent chances to win the game.

Here comes the formula:

(The punter’s estimates times the odds minus 1) / (the odds minus one)

Meaning:

(0.55 * 2.20 — 1) / (2.20 — 1) = (1.21 — 1) / 1.20 = 0.21 / 1.20 = 0.175

According to Kelly criterion, the punter should bet on the outcome 17.5 percent of the bank.

Fractional Kelly criterion

Thorough assessment of the probability of the outcome of an event is very important when using Kelly criterion. It is necessary to try to determine the probability of the outcome more accurately than a bookmaker does.

Trying to best protect themselves from total bankruptcy, many players are using the principle of fractional Kelly criterion.

It means that punters don’t that use the percentage of the bank, obtained by calculations, but only a part of it.

In this case the bank growth slows down, but the risk of losing the entire bank is lower.

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