Strategy - Kelly Criterion

Kelly's formula The main problem of the players is finding and making a bet with a positive outcome. It is also important for players to be able to manage their money and know how much to bet. A player can be called an investor who wants a good return on his investment. The application of the Kelly criterion maximizes the expected value of the logarithm of the return of its total capital.

In 1956, Bell Labs scientist Larry John Kelly Jr. published a paper: "A New Interpretation of Information Transfer Rate." In this work, Kelly showed that in order to achieve maximum income growth, a player must maximize the expected value of the logarithm of his capital when placing bets. Since the logarithm has an additive property and the law of large numbers is applicable to it. It is also assumed that the player's capital is infinitely divided and the profit again enters the market (reinvested). This system is complex in that it requires an estimate of the probabilities of outcomes to work properly.

To put it simply, the Kelly formula gives an answer to the question that interests all players - how to place a bet with a positive expectation of winning.

Kelly's Formula for Blackjack

  • b is a chance to win
  • p - probability of winning
  • q - the probability of losing

The sum of the probabilities of winning and losing is one, so q can be calculated as 1 - p.

The formula shows that for a correct calculation, you need to correctly assess the odds, and for this you need to be able to calculate cards in blackjack as accurately as possible. Let's consider an example:

Example Kelly's formula

Let's assume the probability of winning is 65%. Therefore, p = 0.65, and q = 1 - 0.65 = 0.35. If the chance of winning is 1 to 1, then b = 1. Substitute the obtained data into the formula:

We got f = 0.3, which means that the player will get the maximum profit if he bet 30% of the pot. The pot size must contain at least 20 bets.

And finally, economists are skeptical about the Kelly system. A notable attack on the system was a 1979 paper by Samuelson that appeared in the Journal of Banking and Finance. In it, he pointed out the fact that with a large number of losses, a player can lose a lot.