The Kelly Criterion is a mathematical formula used to determine the optimal size of a series of bets to maximize long-term growth of your bankroll. It considers both the odds offered and your estimated probability of winning to calculate the ideal stake size as a percentage of your current bankroll.
This formula helps bettors avoid betting too much (which risks significant losses) or too little (which limits potential gains). The Kelly Criterion is particularly useful for professional bettors and those serious about long-term profitability in sports betting.
The Kelly Criterion was developed by John L. Kelly Jr., a physicist at AT&T's Bell Laboratories, in 1956. Kelly originally titled his paper "Information Theory and Gambling," but AT&T executives - concerned about associations with illegal gambling operations - pressured him to rename it "A New Interpretation of Information Rate."
Kelly's work built directly on Claude Shannon's foundational 1948 theory of information. Shannon, Kelly's colleague at Bell Labs, encouraged him to publish after recognizing that gamblers with an edge could use information theory equations to maximize returns. The formula reinterpreted the "information rate" as the exponential growth achievable in a betting scenario.
The Kelly Criterion remained largely academic until the early 1960s, when MIT student Ed Thorp discovered card counting for blackjack. Shannon directed Thorp to Kelly's paper, and Thorp used it to compute optimal bets - first in casinos, then on Wall Street as a hedge fund manager. Thorp's success brought mainstream attention to the formula.
Today, the Kelly Criterion is used by legendary investors including Warren Buffett, Bill Gross, and Jim Simons (founder of Renaissance Technologies). Kelly himself died tragically young at age 41 in 1965, but his formula has become a cornerstone of modern investment theory and professional sports betting strategy.
The Kelly Criterion formula calculates the optimal bet size as a percentage of your bankroll: f* = (bp - q) / b
Where:
This formula maximizes the expected logarithm of your bankroll, which translates to optimal long-term growth while managing risk.
Scenario: You've found an NBA bet with +200 odds (3.0 decimal), and after thorough analysis, you believe there's a 40% chance of winning.
Calculator Inputs:
Calculation:
This bet size maximizes long-term growth while reducing the volatility that comes with full Kelly staking.
| Kelly Type | Multiplier | Volatility | Best For |
|---|---|---|---|
| Full Kelly | 1.0 | Very High | Aggressive bettors with high confidence in probability estimates |
| Half Kelly | 0.5 | Moderate | Balanced approach, 75% of full Kelly growth |
| Quarter Kelly (Recommended) | 0.25 | Low | Conservative, reduces risk of overestimating edge |
| Tenth Kelly | 0.1 | Very Low | Ultra-conservative, beginners |
Most professional sports bettors use Quarter Kelly or Half Kelly to account for uncertainty in their probability estimates and reduce bankroll swings.
How does the Kelly Criterion compare to other popular bankroll management strategies? Here's a breakdown:
| Method | How It Works | Pros | Cons |
|---|---|---|---|
| Kelly Criterion | Bet size varies based on edge and odds | Mathematically optimal growth; scales with confidence | Requires accurate probability estimates; can be volatile |
| Flat Betting | Same dollar amount every bet (e.g., $50) | Simple; predictable; easy to track | Doesn't adjust for edge; doesn't compound growth |
| Fixed Percentage | Same % of bankroll each bet (e.g., 2%) | Adjusts with bankroll size; prevents ruin | Ignores edge size; doesn't maximize growth |
| Fibonacci | Increase bets following Fibonacci sequence after losses | Recovers losses gradually | No mathematical basis; can lead to large bets after losing streaks |
| Martingale | Double bet after each loss | Recovers all losses with one win | Extremely risky; bankroll can explode; betting limits prevent recovery |
Recommendation: Kelly Criterion (specifically Quarter Kelly) is the only method that mathematically accounts for your edge. Flat betting and fixed percentage are acceptable alternatives for beginners, but they leave money on the table. Avoid Fibonacci and Martingale - they have no mathematical basis and can lead to catastrophic losses.
The Kelly Criterion is powerful, but misusing it can devastate your bankroll. Here are the most common mistakes bettors make:
This is the #1 mistake. If you think your model gives you a 70% chance to win a bet priced at 50%, you better be absolutely sure. Kelly only works if your win probability estimate is accurate. If you think you have a 58% edge when your actual edge is 52%, you're overbetting by a massive margin. Even professional handicapping models can overestimate edge by a factor of two.
Full Kelly maximizes long-term growth mathematically, but it assumes your edge estimate is perfect - it's not. Sports betting edges are estimates based on incomplete information, not mathematical certainties like card counting. Full Kelly creates massive volatility. Professional bettors use Half Kelly or Quarter Kelly because you get 75% of the growth with dramatically lower variance.
Kelly is a percentage-based system. A $100 bet from a $1,000 bankroll (10%) becomes 11% if your bankroll drops to $900. Most bettors set their bankroll once at the start of the season and never adjust. Three months later they're betting $100 per game when their bankroll is down to $2,000 - that's 5% per bet, which is reckless.
Kelly tells you when NOT to bet just as much as when to bet. If the formula returns a negative number, you don't have an edge - don't bet. But most bettors ignore this. There are 12 NFL games on Sunday, so they force themselves to find 8 bets even though Kelly only says to bet 3. Discipline is everything.
Kelly is designed for single, independent bets. Correlated bets (like QB touchdown + team win) inflate risk because the outcomes aren't independent. If you must parlay, use 1/4 Kelly at most, and understand the formula's assumptions are being violated.
Track your actual results over at least 100 bets before trusting your win probability estimates. If you think you're hitting 56% on NFL spreads but your actual results show 52%, adjust your estimates down by 4%. Be brutally honest with yourself - overconfidence sabotages the entire formula.
The Kelly Criterion isn't for everyone. Here's who benefits most from Kelly staking:
Who should NOT use Kelly: If you can't honestly assess your win probability, or if you don't have at least 100 tracked bets to validate your estimates, Kelly may lead to overbetting. Start with flat betting until you have data to back up your probability estimates.
Quarter Kelly (0.25 multiplier) is the most popular Kelly variant among professional sports bettors. Here's why it dominates:
Quarter Kelly means betting 25% of what the full Kelly formula recommends. If Kelly says bet 8% of your bankroll, Quarter Kelly says bet 2%.
Use Quarter Kelly (0.25) if you're newer to quantitative betting, your probability estimates come from public models, or you want maximum protection against estimation errors.
Use Half Kelly (0.50) if you have years of tracked results validating your edge, you built your own models with proprietary data, and you can stomach larger drawdowns for faster growth.
Never use Full Kelly (1.0) in sports betting - it assumes perfect probability estimates, which don't exist in sports.
Kelly Criterion is most effective when:
Pro Tip: Combine Kelly Criterion with our Edge Calculator to find value bets, then use our EV Calculator to validate positive expected value before determining your bet size with Kelly.
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There's no minimum bankroll requirement, but Kelly works best when you have enough capital to withstand variance. Most professional bettors recommend starting with a bankroll of $1,000-$5,000 minimum. The key is that your bankroll should be money you can afford to lose - Kelly prevents ruin mathematically, but variance can still lead to significant drawdowns before growth occurs.
True win probability is the hardest part of Kelly betting. Methods include: (1) Building statistical models using historical data, (2) Removing the vig from sharp bookmaker lines (Pinnacle, Circa) to get "fair" odds, (3) Tracking your actual results over 500+ bets to measure your historical accuracy. Use our Implied Probability Calculator to convert odds to probabilities as a starting point.
Flat betting wagers the same dollar amount on every bet regardless of edge. Kelly Criterion adjusts bet size based on your edge - bigger bets when you have a larger advantage, smaller bets when your edge is marginal. Over time, Kelly produces faster bankroll growth than flat betting, but requires accurate probability estimates to work properly.
Kelly can be applied to live betting, but it's more challenging. Live odds move quickly, and you need to estimate win probability in real-time as the game unfolds. Most bettors use smaller Kelly fractions (1/8 or 1/10 Kelly) for live betting due to increased uncertainty. You also need to recalculate your bankroll between bets if you're making multiple live wagers.
Kelly percentage changes because it depends on three inputs: the odds, your estimated probability, and your current bankroll. As odds move, your edge changes. As you win or lose, your bankroll changes. This is by design - Kelly automatically scales your bets up when you're winning and down when you're losing, protecting you from ruin during bad streaks.
Ideally, recalculate before every bet using your current bankroll. At minimum, update your bankroll weekly. Many bettors use a "session bankroll" approach - they set aside a fixed amount for a day or week of betting and recalculate Kelly within that session. The more frequently you update, the more accurately Kelly can optimize your bet sizes.
A negative Kelly value means you have no edge on this bet - the expected value is negative. Do not place the bet. This happens when the bookmaker's implied probability exceeds your estimated probability. Kelly is telling you that betting on this outcome will lose money in the long run. Many bettors make the mistake of betting anyway because they "like the pick" - this is how bankrolls die.
Kelly Criterion works best when combined with other analytical tools. Use these free calculators to sharpen your betting edge:
Note: The Kelly Criterion is a powerful tool for bankroll management, but it requires honest, accurate probability assessment. When in doubt, use a smaller Kelly fraction (Quarter Kelly is recommended for most bettors) to reduce variance and account for estimation errors.