The Kelly Criterion: How to Size Your Bets for Maximum Growth
Finding a +EV bet is only half the problem. The other half — often underestimated by beginners — is deciding how much to stake. Bet too little and your edge barely moves the needle on your bankroll. Bet too much and a single bad run can wipe you out before your edge has a chance to compound. The Kelly Criterion is the mathematical answer to this problem. It's the optimal stake sizing formula used by professional bettors and investors alike.
What Is Stake Sizing — and Why Does It Matter?
Stake sizing is the process of determining how much of your bankroll to risk on any given bet. It's not about how confident you feel. It's about the mathematical relationship between your edge size and the optimal amount to wager to maximize long-term growth.
Consider two bettors with identical +3% EV edges. One bets 10% of their bankroll on every wager. The other bets 2%. After 200 bets, the second bettor will almost certainly be ahead — not because they found a bigger edge, but because they managed their risk better. Over-betting bleeds your bankroll through variance. Under-betting leaves growth on the table. Kelly finds the sweet spot.
The Kelly Formula Explained
John Larry Kelly Jr. developed this formula in 1956 at Bell Labs, originally to solve problems in information theory. It was quickly adopted by card counters and eventually by sports bettors and financial investors. Here's the formula:
Where:
- f = the fraction of your bankroll to bet ( Kelly fraction)
- b = the decimal odds − 1 (net odds received on a winning bet)
- p = your estimated probability of winning
- q = your estimated probability of losing ( q = 1 − p)
Let's walk through this with real numbers so it clicks.
Example: You find a bet at decimal odds of 2.80. You estimate Team A has a 45% chance of winning ( p = 0.45, q = 0.55). The fair odds — based on your probability — would be 1 / 0.45 = 2.22. The bookmaker is offering 2.80, which implies only 35.7% probability. You've found a value bet.
Now apply Kelly: b = 2.80 − 1 = 1.80. p = 0.45. q = 0.55.
f = (1.80 × 0.45 − 0.55) / 1.80 = (0.81 − 0.55) / 1.80 = 0.26 / 1.80 = 0.144
Kelly says: bet 14.4% of your bankroll on this wager. With a €1,000 bankroll, that's €144.
Breaking Down the Variables
The key insight of Kelly is that your stake should scale with two things: how large your edge is and how generous the odds are. If either the odds are worse or your probability estimate is lower, the optimal stake drops. If both are in your favour, Kelly rewards you with a larger position.
Think of it this way: Kelly is asking "how much can I rationally risk given what I know?" A 10% edge at odds of 1.50 produces a very different Kelly fraction than a 10% edge at odds of 5.00. The latter gives you more profit per winning bet, so Kelly allocates more capital to it.
Full Kelly vs. Fractional Kelly
Full Kelly — betting the exact fraction the formula prescribes — maximises long-term bankroll growth mathematically. But it has a significant practical problem: it's volatile. Full Kelly bettors experience massive swings in their bankroll, with drawdowns that can exceed 50–60%. Most people find this psychologically unbearable, and some abandon the strategy at exactly the wrong moment.
This is why sharp bettors almost universally use Fractional Kelly: betting a fixed fraction of the Kelly recommendation (25%, 50%, etc.). The math is compelling:
- Half Kelly (50%): Achieves roughly 75% of the long-term growth of full Kelly while cutting volatility in half. Manageable swings and still strong compounding.
- Quarter Kelly (25%): Achieves roughly 50–60% of full Kelly's growth but reduces bankroll volatility dramatically. Popular with bettors with lower risk tolerance.
Why sharps use fractions: The goal isn't mathematical purity — it's sustainable growth. A 50% drawdown sounds survivable in theory, but when it actually happens after a bad week, many bettors panic, abandon their staking plan, and either stop betting entirely or chase losses with increased stakes. Fractional Kelly is the discipline that keeps you in the game.
For a practical example: if your Kelly fraction is 14.4% of bankroll, Half Kelly would be 7.2% (€72 on a €1,000 bankroll) and Quarter Kelly would be 3.6% (€36). Quarter Kelly is conservative but it significantly smooths the ride while still compounding your edge.
Kelly in Practice: A Real Example
Scenario: Premier League — Tottenham vs. Arsenal
You assess Tottenham at a 40% probability to win. The bookmaker offers odds of 2.90 (implied probability 34.5%). You believe the true probability is higher — you've spotted something in the team news and tactical matchups.
- b = 2.90 − 1 = 1.90
- p = 0.40
- q = 0.60
- Kelly f = (1.90 × 0.40 − 0.60) / 1.90 = (0.76 − 0.60) / 1.90 = 0.16 / 1.90 = 0.084
Full Kelly: bet 8.4% of your bankroll. On a €2,000 bankroll, that's €168. Quarter Kelly (recommended): €42.
Result: If Tottenham wins, you collect €168 × 2.90 = €487.20 — a profit of €319.20 on the €168 stake. If they lose, you lose €168.
Common Kelly Mistakes
Mistake 1: Over-betting with Full Kelly. Many beginners try full Kelly, hit a 5-bet losing streak, and watch their bankroll halve. Their emotional response is to either give up or double down — both wrong. If you can't stomach full Kelly swings, use half or quarter immediately. There's no shame in it.
Mistake 2: Confusing estimated probability with overconfidence. The Kelly formula will generate large stakes if your probability estimate is very high relative to the odds. But if your probability estimates are wrong — systematically overestimated — Kelly will destroy your bankroll faster than flat betting would. Calibration matters enormously. Track your bets and compare your pre-bet estimates to actual results.
Mistake 3: Chasing with Kelly after a loss. Kelly is a fixed formula — your stake should be a function of your edge and odds, not your emotional state. If you lose a big Kelly bet, the next bet with a smaller edge doesn't deserve a bigger stake to "get it back." That's chasing, and it's the fastest way to blow through a bankroll.
Other mistakes include applying Kelly to correlated bets (two legs of the same game are not independent events — you can't simply sum their Kelly fractions), and using Kelly in markets where your probability estimates are essentially guesses (props with no statistical basis, for example).
Kelly in Excel and Google Sheets
Setting up a Kelly calculator in a spreadsheet takes five minutes. Here's the formula for Google Sheets / Excel:
Cell A1: Enter your estimated probability (e.g., 0.45)
Cell B1: Enter decimal odds (e.g., 2.80)
Cell C1: Enter this formula: =((B1-1)*A1 - (1-A1)) / (B1-1)
Cell D1: Multiply by your bankroll: =C1 * 1000 (for a €1,000 bankroll)
For fractional Kelly, just multiply the result by 0.25, 0.50, etc.
One-column Kelly tracker: Add columns for Date, Event, Odds, Your Probability, Kelly %, Stake (€), and Result. Use conditional formatting to flag negative Kelly results (odds worse than fair) in red — these are the rows where Kelly says "don't bet."
Kelly and Bankroll Management
Kelly is a stake sizing tool, not a complete bankroll management system. It works best when:
- Your probability estimates are reasonably accurate and consistently calibrated
- You track all bets so you can evaluate whether your edge is real or imagined
- You use a fractional Kelly version (50% or 25%) to keep variance manageable
- Your bankroll is large enough that a 25–50% drawdown wouldn't force you to stop betting
For beginners, flat betting (fixed % of bankroll, typically 1–3%) is easier to manage and produces less dramatic swings. As you build confidence in your probability estimates and grow comfortable with the emotional demands of variance, you can gradually move toward Kelly-style sizing. For a complete walkthrough of bankroll management principles, see our dedicated guide.