The Kelly Criterion: Mathematical Approach to Bet Sizing

The Kelly Criterion is a mathematical formula used to determine the optimal size of a bet in order to maximize long-term bankroll growth while minimizing the risk of ruin. Unlike flat staking or emotional betting, the Kelly Criterion relies purely on probability, expected value, and disciplined bankroll management.

Originally developed by John L.

Kelly Jr.

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in 1956, the Kelly Criterion has since been adopted not only by sports bettors, but also by investors, traders, and professional gamblers who focus on long-term profitability rather than short-term wins.

What is the Kelly Criterion?

At its core, the Kelly Criterion answers a simple but critical question: how much of your bankroll should you stake on a single bet when you believe you have an edge?

Instead of betting a fixed amount or percentage every time, the Kelly Criterion adjusts stake size based on:

• The probability of winning • The odds being offered • The size of your betting bankroll

The goal is not to win every bet, but to grow capital at the fastest possible rate over many bets.

The Kelly Criterion Formula Explained

The standard Kelly formula is:

f = (bp − q) / b

Where:

f = fraction of bankroll to bet b = decimal odds − 1 p = probability of winning q = probability of losing (1 − p)

This formula calculates the exact percentage of your bankroll that should be staked on a given bet to achieve optimal growth.

Example of the Kelly Criterion in Betting

Assume you have identified a bet where:

• Decimal odds: 2.50 • Your estimated probability of winning: 50% (0.50)

First, calculate b:

2.50 − 1 = 1.50

Now apply the formula:

f = (1.50 × 0.50 − 0.50) / 1.50 f = (0.75 − 0.50) / 1.50 f = 0.25 / 1.50 f ≈ 0.1667

This means you should bet approximately 16.7% of your bankroll.

If your bankroll is $1,000, the optimal stake would be about $167.

Why the Kelly Criterion Is Powerful

The strength of the Kelly Criterion lies in its mathematical foundation.

It ensures that you:

• Bet more when you have a stronger edge • Bet less when your edge is small • Avoid overbetting when odds are poor • Avoid underbetting when value is high

Over a large number of bets, this approach mathematically maximizes the logarithmic growth of your bankroll.

Kelly Criterion vs Flat Betting

Flat betting uses the same stake size regardless of value or confidence.

While simple, it ignores key information such as probability and odds.

The Kelly Criterion, on the other hand, dynamically adjusts stake size based on expected value.

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This makes it far superior for bettors who can accurately estimate probabilities.

However, this also introduces a critical requirement: your probability estimates must be accurate.

Poor estimates can lead to excessive risk.

Risks and Drawbacks of the Kelly Criterion

Despite its mathematical elegance, the Kelly Criterion is not without risks.

One major drawback is volatility.

Full Kelly staking can result in large swings in bankroll, especially during losing streaks.

This can be psychologically difficult for many bettors.

Additionally, if your probability assessment is wrong, Kelly staking can amplify losses rather than protect against them.

Fractional Kelly: A Safer Alternative

To reduce volatility, many bettors use fractional Kelly, which involves betting only a portion of the recommended stake.

Common approaches include:

• Half Kelly (50% of Kelly stake) • Quarter Kelly (25% of Kelly stake)

Fractional Kelly sacrifices some growth potential in exchange for lower risk and smoother bankroll curves.

For most bettors, this is a more practical and sustainable approach.

When to Use the Kelly Criterion

The Kelly Criterion is best suited for bettors who:

• Can consistently identify value bets • Have reliable probability models • Bet over a long series of events • Prioritize bankroll growth over short-term wins

It is not ideal for casual bettors, accumulator betting, or situations where probabilities are guessed rather than calculated.

Kelly Criterion in Modern Sports Betting

Today, the Kelly Criterion is widely used in advanced betting models, including those powered by data analytics and AI.

Many professional bettors integrate Kelly staking into automated systems that calculate stake sizes instantly based on live odds and probability outputs.

However, even in modern betting, the principle remains the same: bet proportionally to your edge, not your emotions.

Conclusion

The Kelly Criterion represents one of the most important mathematical tools in sports betting and investment theory.

When used correctly, it provides a disciplined, logical, and optimal framework for bet sizing.

While it requires accurate probability assessment and emotional control, the Kelly Criterion rewards patience and consistency.

For bettors serious about long-term profitability, it offers a clear path away from reckless staking and toward mathematically sound decision-making.

In betting, knowing what to bet on is important — but knowing how much to bet is what separates professionals from amateurs.