The Kelly Criterion Is Misunderstood—Here’s What We Should Really Focus On

Introduction

If you’ve ever delved into discussions about optimal betting strategies—whether for investing, poker, or other forms of gambling—you’ve likely come across the Kelly Criterion. Most treatments of the topic focus almost exclusively on the “fraction” of your bankroll to bet. In poker circles, you’ll often hear about “fixed bets” or “all-in” approaches that don’t seem to match the Kelly “fraction.” Meanwhile, the investing crowd endlessly debates how much of your portfolio to invest according to the Kelly formula. This often leads to confusion, misapplication, and a misunderstanding of what the Kelly Criterion is actually achieving.

The Core Idea: Maximizing Geometric Growth

The Kelly Criterion is fundamentally about maximizing the expected growth rate of your bankroll (or investment). It’s derived from a simple but powerful idea: rather than aiming to maximize expected value in a single bet, aim to maximize the expected logarithm of your wealth. The logarithm function naturally captures the idea that doubling your money from $1,000 to $2,000 is a bigger “relative jump” than going from $100,000 to $101,000—yet both scenarios add $1,000. In other words, Kelly is about relative growth over time, not absolute gains in a single instance.

The Fraction Versus Fixed Bets Confusion

1. Fraction-Focused Literature: When you read about Kelly, you’ll typically see an equation that spits out a fraction of your bankroll to wager. For example, if the formula says “0.25,” it means bet 25% of your bankroll each time. The key assumption here is that you are placing repeated bets in a scenario with positive expected value and want to grow your bankroll at the highest possible rate.
2. Poker’s Fixed Bets: In poker, you’re not always free to choose a fraction of your bankroll for each hand. The table stakes, blinds, and the progression of betting rounds force you into a more or less fixed structure. Yet professional poker players still talk about “bankroll management,” which is effectively choosing which stakes to play. By picking the right stakes, you are indirectly controlling the fraction of your total bankroll at risk in any given session. While you can’t precisely apply the Kelly fraction to each hand, you can still follow the principle of maximizing expected logarithmic growth by managing how much of your roll you commit overall.
3. What If It’s Just One Bet? Many people think Kelly only makes sense if you are making a large number of repeated bets. While it’s true that the Kelly approach shines in repeated scenarios (because of compounding and the law of large numbers), even if you are making just one bet for the sake of maximizing the expected log of your end wealth, the Kelly fraction is still optimal. It shows you the bet size that maximizes your growth from $X to your new expected wealth.

The Mota Approach: A Real-World Twist on Growth Maximization

In poker tournaments and other long-form events, you’re often investing more than just money—you’re also investing time. One real-life extension of Kelly-based logic is the Mota approach, which also focuses on expected growth but incorporates dynamic selling of action at markup.

• Selling Action at Markup: Players can reduce risk and realize partial gains by selling “pieces” of themselves to backers at a markup. This effectively changes the fraction of their bankroll at risk, making it more flexible than a one-size-fits-all approach.
• Growth Rate Per Unit Time: Because tournaments can last for many hours (or even days), the Mota approach can also be extended to measure growth per time invested. It allows you to compare different tournaments or games by their expected growth rate relative to how much of your finite resource—time—you invest.

This perspective rates the quality of each available game or tournament in relation to your bankroll by effectively boiling everything down to a growth metric per unit of money and time. It’s a more holistic way to decide which opportunities to pursue, ensuring you’re always aiming at the highest overall growth of your capital and your time.

Why We Care About Logarithmic (Geometric) Growth

• Geometric Growth Reflects Real-Life Wealth Changes: Humans experience wealth changes multiplicatively. Gaining or losing 10% of your bankroll has a more profound effect on future opportunities than a fixed dollar amount.
• Protecting Against Ruin: By not over-betting, you avoid catastrophic drawdowns that can cripple your ability to recover. Over-betting beyond Kelly might yield a higher expected value in theory, but it also massively increases variance and the risk of ruin.
• Long-Term Outperformance: Over many repeated opportunities, consistently betting the Kelly fraction (or at least staying under it) tends to outperform any other consistent strategy in terms of final bankroll size.

Common Misunderstandings

1. “Kelly Only Works for Infinite Repetitions.” While repeated bets highlight Kelly’s advantage, the math behind the fraction still identifies the bet size that maximizes expected log for any single wager.
2. “Kelly Maximizes Expected Value.” It doesn’t; it maximizes expected logarithmic value, which often leads to more conservative bets than a strategy purely aiming for highest expected monetary value.
3. “You Always Need the Fraction.” The fraction is an outcome of the underlying objective—maximizing growth. Once you shift your focus to growth (logarithmic), the fraction emerges naturally. It’s the means, not the end.

Bringing It All Together

The big takeaway is that focusing on the fraction alone can distract from the core principle: we’re trying to maximize the growth rate of our bankroll. Whether you’re making one bet or many, the Kelly logic tells us what size of a bet would theoretically maximize your long-term (geometric) growth. Yes, in day-to-day life—especially in poker or constrained trading environments—you might not apply it verbatim. But the spirit of Kelly remains a guide to help you stay within safe yet growth-oriented boundaries.

The Mota approach takes this a step further by recognizing the time element in tournaments (or any investment) and allowing players to dynamically sell action at markup. This not only smooths out variance but also helps compare different opportunities by their expected growth per unit time. If you’re looking for the most efficient way to grow your bankroll—and do it repeatedly—the combined lessons of Kelly and Mota can help you prioritize the best long-term plays.

In the end, the conversation shouldn’t be “What’s the Kelly fraction?” but rather “How do I maximize my growth rate?” Because once you define your goal as maximizing growth, the right fraction—or set of betting guidelines—naturally follows. And if you factor in the Mota approach for dynamic selling of action, you can optimize not just for risk-adjusted growth, but also for the most efficient use of your time. That’s the heart of the Kelly Criterion (and its modern extensions), and it’s too often missed when people fixate on the fraction itself.

Final Thoughts

If you’re tired of the confusion around Kelly and want clarity, always circle back to the original objective: maximize the expected log of your bankroll. If you incorporate dynamic selling of action and growth-per-unit-time concepts from approaches like Mota’s, you’ll have an even more refined system for selecting and sizing your bets—one that’s closer to real-world conditions, especially in tournaments. Focus on the growth rate, and let the fraction follow from that.