Kelly Criterion: Casino Strategy & Formula Explained

In the world of casino games and sports betting, knowing how much to wager is just as crucial as choosing the right bet. The Kelly Criterion, a mathematical formula developed in the 1950s, offers a rigorous strategy to maximize long-term profits while limiting the risk of ruin. Used by professional bettors as well as some investors, this system is based on a probabilistic estimation of a bet's success.

What is the Kelly Criterion?

The Kelly Criterion is a mathematical method designed to optimize the management of your bankroll in the context of gambling and sports betting. The strategy is based on a simple principle: invest an optimal fraction of your capital on each bet to maximize long-term growth while avoiding ruin. The system was developed by John L. Kelly in 1956 and is still a benchmark for professional players today.

The Kelly Formula Explained Simply

Here is the classic Kelly Criterion formula:

f* = (bp - q) / b

Where:

• f*: fraction of the bankroll to bet
• b: decimal odds (minus 1)
• p: estimated probability of success
• q: 1 - p (probability of failure)

Practical Example: You estimate that a bet at odds of 2.50 has a 50% chance of winning.

b = 2.50 - 1 = 1.5
p = 0.50
q = 0.50
f* = (1.5 * 0.5 - 0.5) / 1.5 = 0.25

You should therefore wager 25% of your bankroll on this bet using the Kelly Criterion.

Using a Kelly Calculator

To simplify the application of this formula, many players use an online Kelly calculator. These tools allow you to input the odds and estimated probability, and they instantly return the fraction to bet.

Here is a sample table for illustration:

⚠️ Warning: if the probability is misestimated, the system can lead to losses.

Applying the Kelly Criterion in Casino Games

The Kelly Criterion does not apply to all casino games. It is only relevant when the player can estimate a mathematical advantage over the house.

Games suitable for Kelly:

• Blackjack (with advanced strategy and card counting)
• Video Poker (with perfect play)
• Certain video roulette games with known technical biases

Games unsuitable for Kelly:

• Slot machines (no possible edge, fixed RTP)
• European Roulette (negative expected value)

In short, no predictable edge = no Kelly.

Sports Betting and the Kelly Strategy

Sports betting is one of the best fields for the Kelly method. Where bookmakers publish odds based on estimations, the player can assess whether there is a hidden value (value bet).

Example:

• Bookmaker odds: 2.10
• Estimated probability by the player: 55%
• b = 2.10 - 1 = 1.10

f* = (1.10 * 0.55 - 0.45) / 1.10 = 0.10

=> Recommended bet: 10% of your bankroll.

This approach lets you adjust your bet based on the perceived bias between odds and true probability.

Practical Examples of Kelly-Based Bets

Let’s imagine an initial bankroll of €1000 and three bets:

This kind of bankroll management helps limit losses during bad streaks while maximizing long-term growth.

Half-Kelly and Other Variants

Many players prefer to use a reduced Kelly (half-Kelly, 1/4 Kelly) to avoid high volatility.

Why?

• Probabilities are often imperfectly estimated.
• Full Kelly can lead to significant losing streaks.

Growth Comparison (simulation over 100 bets):

The choice of the best Kelly depends on the player’s risk profile.

Frequently Asked Questions About the Kelly Criterion

• What is a Kelly? It is a unit of optimal bet sizing based on your estimated edge.
• Kelly formula or betting formula? The same thing in this context.
• Difference between Kelly and Kelley? None: "Kelley" is a misspelling.
• Does the Kelly strategy really work? Yes, if your estimates are accurate and your discipline is solid.

Conclusion

The Kelly Criterion is a powerful yet demanding strategy. It relies on a key assumption: you must be able to estimate probabilities better than chance or the bookmaker. If so, the system allows you to maximize your long-term profits while limiting risks. It’s a rigorous mathematical approach, ideal for serious players and bettors.