What Is the Kelly Criterion for Blackjack?

Blackjack is a popular casino game that has been played for centuries. It is a game of skill and chance, where players try to beat the dealer by getting as close to 21 points as possible without going over.

In recent years, many players have turned to mathematical strategies and systems to improve their odds of winning. One such system is the Kelly Criterion.

The Kelly Criterion is a mathematical formula used in gambling and investing that helps determine the optimal size of a bet based on the expected value of a given investment or bet. It was developed by John L. Kelly Jr., a researcher at Bell Labs, in the 1950s.

In the context of blackjack, the Kelly Criterion can be used to determine how much money to bet on each hand based on the player’s edge over the house. The player’s edge in blackjack is determined by counting cards and keeping track of which cards have already been played.

To use the Kelly Criterion in blackjack, you first need to calculate your expected win rate per hand. This can be done by counting cards and keeping track of which cards have already been played. Once you know your expected win rate per hand, you can plug that number into the Kelly Criterion formula.

The formula for the Kelly Criterion is:

f* = (bp – q) / b

Where:
– f* = fraction of bankroll to bet
– b = odds received on winning bet (decimal)
– p = probability of winning
– q = probability of losing (q = 1 – p)

Let’s say you have an edge over the house of 1%. This means that for every $100 you bet, you can expect to win $1 on average. If you have a bankroll of $10,000 and are playing at a table with minimum bets of $10, your initial bet size would be 1% * $10 = $100.

Using the Kelly Criterion formula, we can calculate the optimal bet size for each hand. Let’s assume the odds of winning a hand are 50%, or 0.5 in decimal form. The odds received on a winning bet would be even money, or 1.0 in decimal form.

Plugging these numbers into the Kelly Criterion formula, we get:

f* = (0.5*1 – 0.5) / 1
f* = 0

This means that according to the Kelly Criterion, you should not bet anything on this hand since your expected win rate is not high enough to justify risking any of your bankroll.

However, if your expected win rate per hand was higher, say 2%, you could use the Kelly Criterion to determine your optimal bet size for each hand.

Using the same bankroll of $10,000 and minimum bet size of $10, your initial bet size would be 2% * $10 = $200.

Plugging these numbers into the Kelly Criterion formula again, we get:

f* = (0.5*2 – 0.5) / 1
f* = 0.5

This means that according to the Kelly Criterion, you should bet half of your bankroll on this hand since your expected win rate is high enough to justify risking a portion of your bankroll.

It is important to note that while the Kelly Criterion can help determine optimal bet sizing based on expected value and probability, it does not guarantee a win and can still result in losses if luck is not on your side.

In conclusion, the Kelly Criterion is a mathematical formula that can be used in blackjack and other forms of gambling and investing to determine optimal bet sizing based on expected value and probability. It is important to remember that while this system can improve your odds of winning, it does not guarantee success and should be used with caution.