If you have ever wondered how much you should bet on a game, you are not alone. Most bettors either pick a random amount or bet the same flat amount every time. But there is a mathematical answer to this question, and it has been around since 1956.
The Kelly Criterion is a formula that tells you exactly what percentage of your bankroll to wager when you have an edge. It was invented by John Kelly, a scientist at Bell Labs who was trying to solve a completely unrelated problem involving telephone signals. He probably never imagined his formula would become the gold standard for bankroll management in sports betting, poker, and investing.
Here is all you need to know about the backstory: a physicist at Bell Labs in 1956 realized that the math behind sending clear signals through noisy telephone wires was the same math behind growing a bankroll with imperfect information. John Kelly was not thinking about sports betting. He was solving an engineering problem. But the formula he published turned out to answer one of gambling's hardest questions: given that you have an edge, how much should you risk? If you want the full history, including how the formula traveled from an obscure academic journal to the desks of Wall Street traders and Las Vegas syndicates, our Kelly Criterion calculator and history page tells the complete story. For this guide, what matters is the idea: Kelly treats your bankroll the way an engineer treats a signal, and it finds the exact bandwidth for maximum growth.
Here is the fundamental question Kelly answers: If you have a genuine advantage on a bet, how much should you risk?
Bet too little, and you leave money on the table. Your edge exists, but you are not capitalizing on it. Bet too much, and a few losses in a row could devastate your bankroll, even if you have a long-term edge.
Kelly finds the sweet spot. It calculates the exact bet size that maximizes your long-term growth rate while never risking so much that you could go broke.
The Kelly formula looks intimidating at first, but it boils down to a simple idea:
Bet a percentage of your bankroll equal to your edge divided by the odds.
Your "edge" is the difference between your estimated win probability and the break-even probability implied by the odds. If the sportsbook thinks a bet has a 50% chance of winning, but you believe it has a 55% chance, your edge is 5%.
The formula then adjusts this edge based on the payout. Higher odds mean you can bet a smaller percentage. Lower odds mean you can bet more, if your edge is the same.
You have probably seen the formula written as f* = (bp - q) / b. If you want a variable-by-variable walkthrough and an interactive calculator, that is what our Kelly Criterion calculator is built for. Here, let's focus on what the formula is actually doing under the hood, because understanding the logic matters more than memorizing the notation.
The formula asks two questions. First: how much better are my chances than break-even? That is your edge. If the sportsbook's odds imply a 50% win rate, but you estimate 55%, your edge is 5%. Second: how much do I get paid when I win? That is the payout. A bet at even money pays 1-to-1. A bet at +200 pays 2-to-1.
Kelly then divides your edge by the payout. A bigger edge means a bigger bet. A bigger payout means a smaller bet (because you do not need as much money on high-payout wagers to capture the same growth). And if your edge is zero or negative, the formula returns zero, telling you to sit this one out. That zero result is one of the most underrated features of the Kelly Criterion: it forces you to skip bets where you do not have an advantage, which is something most bettors never discipline themselves to do.
The Kelly formula technically uses decimal odds, but you do not need to memorize conversion tables. Our Kelly Criterion calculator accepts American odds directly and handles the conversion automatically. The short version: for favorites like -110, the payout factor is 100 divided by the odds number (so 0.909). For underdogs like +150, it is the odds number divided by 100 (so 1.50). But honestly, just use the calculator and focus your energy on estimating your win probability accurately, which is the part that actually requires skill.
Imagine you have a $1,000 bankroll. You find a bet at -110 odds (standard juice), and after doing your research, you believe you have a 55% chance of winning. The break-even at -110 is about 52.4%.
Your edge is 55% minus 52.4% = about 2.6%. The Kelly formula says to bet roughly 5.5% of your bankroll, or $55.
That number might seem small if you are used to betting $100 or $200 per game. But Kelly is playing the long game. Over hundreds of bets, this sizing optimizes your growth. You can find more worked scenarios like this in our Kelly Criterion examples page.
The genius of Kelly is that it automatically scales your bets based on two things: your edge and your bankroll.
When you win, your bankroll grows, and Kelly tells you to bet more in absolute dollars. When you lose, your bankroll shrinks, and Kelly tells you to bet less. This prevents you from ever going completely broke, because you are always betting a percentage, not a fixed amount.
At the same time, Kelly bets more when your edge is larger and less when your edge is smaller. This means you are putting more money on your best opportunities and less on marginal ones.
Here is something that surprises a lot of people: Kelly does not maximize your expected profit on any single bet. It maximizes the expected logarithm of your wealth, which mathematically translates to the fastest possible long-term growth rate. This distinction matters more than you might think.
Imagine two bettors, both with a 55% edge on -110 bets. Bettor A uses Kelly sizing (about 5.5% of bankroll per bet). Bettor B bets 25% of their bankroll every time because they want to "go big." After 100 bets, Bettor A's bankroll has grown steadily. Bettor B, despite having the same edge, has almost certainly gone broke or suffered a devastating drawdown. A string of five or six losses, which is completely normal even with a 55% win rate, wipes out most of Bettor B's bankroll.
The mathematical insight is that maximizing log-wealth is equivalent to maximizing the geometric growth rate of your bankroll. Over many bets, geometric compounding dominates everything. A strategy that grows at 3% per bet will absolutely crush a strategy that grows at 5% per bet but occasionally drops 40%, because the recovery from those drops eats up all the extra growth and then some. Kelly finds the exact point where growth is maximized without risking catastrophic drawdowns.
You can see this principle in action for yourself using our Kelly simulation tool, which lets you run thousands of simulated bets at different Kelly fractions and watch how the bankroll trajectories diverge over time.
Kelly is ideal for:
Kelly is not for everyone:
The Kelly Criterion is powerful, but it rests on several assumptions that do not perfectly hold in the real world of sports betting. Understanding these limitations is just as important as understanding the formula itself.
Assumption 1: You know your true edge. Kelly requires an accurate estimate of your win probability. If you think you win 58% of the time but you actually win 52%, Kelly will tell you to bet far too much. Overestimating your edge is the single most dangerous mistake a Kelly bettor can make, and it is incredibly common. Most bettors overrate their own skill. If you don't have a large sample of tracked bets to draw from, your probability estimates are unreliable. For a deeper dive into this and other pitfalls, check out our guide on common Kelly Criterion mistakes.
Assumption 2: Each bet is independent. The formula assumes that the outcome of one bet does not affect the outcome of the next. In practice, sports bettors often have correlated bets, like betting on multiple games in the same league on the same night. When bets are correlated, optimal sizing changes, and standard Kelly may overexpose you.
Assumption 3: You can bet any fractional amount. Kelly might tell you to bet 3.7% of your bankroll. If your bankroll is $500, that is $18.50. Some sportsbooks have minimum bets or only accept round numbers. These practical constraints mean you can rarely bet the exact Kelly amount, though rounding to the nearest dollar is close enough for most purposes.
Assumption 4: Odds are fixed and known. The formula uses a specific payout ratio. But in sports betting, odds shift constantly. The line you see when you run the Kelly calculation might not be the line you get when you place the bet. This is another reason to build in a margin of safety.
Full Kelly betting assumes your edge estimate is perfectly accurate. In reality, nobody estimates edges perfectly. This is why most professionals use fractional Kelly, betting only 25% to 50% of what the formula recommends.
Fractional Kelly gives you most of the growth benefit with much less volatility. It is a safety buffer against the inevitable errors in your probability estimates. The mathematics are surprisingly generous: cutting your bet size in half costs you far less than half of your long-term growth rate, while dramatically smoothing out the ride. For most sports bettors, especially those still building their track record, something in the range of 25% to 50% Kelly is the sweet spot. Our fractional vs full Kelly comparison covers the exact tradeoffs between different fractions.
The choice between different Kelly fractions depends on your confidence in your edge estimates, your tolerance for bankroll swings, and how large your sample size is. If you have 2,000 tracked bets and a well-documented 54% win rate at -110, you can confidently use a higher Kelly fraction. If you have 100 bets and a 57% win rate that might just be a hot streak, dial it way down. We cover the tradeoffs in detail in our fractional vs full Kelly comparison.
Ready to put this into practice? Use our Kelly Criterion bet sizing calculator to see exactly how much to bet based on your bankroll, odds, and estimated win probability. You can also run a simulation to see how different Kelly fractions perform over hundreds of bets. And if you are new to all of this, our beginner's guide to Kelly walks through the basics step by step.
The Kelly Criterion is one of the few betting strategies with real mathematical backing. It tells you exactly how much to bet when you have an edge, preventing both overbetting and underbetting. Born from information theory at Bell Labs in 1956, it has survived nearly seven decades of scrutiny from mathematicians, gamblers, and Wall Street traders alike. That kind of staying power says something.
It is not magic. It will not help you if you do not actually have an edge. And it demands discipline, because the formula often recommends bet sizes that feel too small when you are confident and too large when you are nervous. But if you do have an edge, and you are playing the long game, Kelly is the optimal way to grow your bankroll over time. Pair it with solid bankroll management principles and a well-defined unit system, and you have the foundation that separates serious bettors from recreational ones.
Start with the formula. Track your results. Use fractional Kelly until you trust your numbers. And let the math do the heavy lifting.