Making the most of your betting money is important if you want to win more often and build your winnings steadily. The Kelly Criterion is a method that can help you do this. But what exactly is the Kelly Criterion, and how does it work?
This APWin Academy guide explains the betting concept using simple examples. We also reveal how the Kelly calculator works, how to use Kelly Criterion in betting, and common mistakes to avoid when using this formula.
What Is the Kelly Criterion?
John L. Kelly Jr. introduced the Kelly Criterion in 1956 as a mathematical formula for determining how much to invest in a specific asset to grow wealth over time. However, the concept soon found applications in sports betting and casino games.
When applied to betting, the Kelly Criterion tells you how much of your bankroll you should stake if you have an edge. The main aim is to grow your money steadily over time while keeping the risk of losing it as low as possible.
In simple terms:
Kelly tells you the exact amount for each bet to maximise long-term growth.
It prevents you from betting too much and going broke
It also stops you from betting too little and missing out on potential growth.
Like many betting strategies, the Kelly Criterion is not foolproof. The calculation is extremely sensitive to your input probability. As a result, overestimating your edge can lead to losses.
The Kelly Criterion Formula
The Kelly Criterion formula finds the sweet spot between risk and reward. When you overbet, you are at risk of losing your entire bankroll. At the same time, a stake that is too low will limit your bankroll growth.
With this formula, you can achieve an exponential increase in your bankroll over time, provided you get your estimates right. The formula for Kelly Criterion is: f* = p − (q / b)
Where:
f* = fraction of your bankroll to bet (Kelly percentage)
p = probability of winning (your estimate)
q = probability of losing = 1 − p
b = “to-1” odds (how much profit per unit stake)
How to Calculate the Kelly Criterion Step-by-Step?
Understanding the formula is one thing, but applying it correctly is an entirely different matter. We have broken down the process using easy-to-understand examples to show how to calculate Kelly Criterion betting step by step.
Example: Palmeiras (3.10) vs. Flamengo (1.85). For this bet option, we are backing Flamengo (1.85) to win due to their recent form in the league. Here is how we use the formula;
Step 1: Convert Odds to profit per unit stake (b)
Calculate the unit per stake, with decimal odds of 1.85:
b = “to-1” odds
b = 1.85 - 1 = 0.85
b = 0.85
Your profit will be 0.85 units for every 1 unit staked.
Step 2: Estimate Probability of Winning (p)
Carry out your assessment and determine the winning chances of your chosen team. You must do this on your own, as no values are available. After analysing the teams, we believe Palmeiras has a 65% chance of winning.
The formula for finding the winning Probability: chance of winning (%) ÷ 100
So, for our example: 65% ÷ 100 = 0.65.
p = 0.65
Step 3: Calculate Probability of Losing (q)
Next, calculate the probability of losing (q). The formula to use is: q = 1 - p.
For our example: p = 0.65
1 - 0.65 = 0.35
q = 0.35
Step 4: Apply the formula
Now the only thing you have to do is apply the formula:
f* = 0.65 − (0.35 / 0.85)
f* = 0.65 − 0.412
f* ≈ 0.239 → 23.9%
With a bankroll of $1,000, these are the bets you can place on Flamengo to win based on these calculations:
Full Kelly = $239 stake
Half Kelly = $119.5 stake
Quarter Kelly = $59.75 stake
Note that most bettors use half or quarter Kelly to manage volatility. Sticking to this practice could help you avoid overexposure to risks.
Kelly Criterion Calculator
There are two significant ways to calculate the Kelly Criterion. The most traditional way is to use the step-by-step example above and do it manually. On the flip side, you can also use online calculators to calculate the Kelly criterion.
You can use a Kelly Criterion calculator to save time and reduce mistakes. Most calculators ask for:
Your estimated win probability (p)
The decimal odds (converted to b)
Whether you want full, half, or quarter Kelly
Popular free calculators include:
OddsJam Kelly Calculator
Albion Research Kelly Calculator
Betting exchange toolkits
Tip: The calculator is only as good as your ‘p’ estimate, which means you may still lose money if you overestimate your edge.
Applying the Kelly Criterion in Betting
Applying the Kelly Criterion in betting means you calculate exactly how much of your bankroll to wager based on your edge over the odds.
Now, let’s look at examples of using the Kelly Criterion in various divisions.
Example 1
Boca Juniors (2.80) vs River Plate (2.00). You estimate Boca Juniors has a 50% chance of beating River Plate at odds of 2.80
b = 2.80 - 1 = 1.80
q = 1 − 0.50 = 0.50
f* = 0.50 − (0.50 / 1.80) = 0.50 − 0.277 ≈ 0.223 → 22.3%
For a $2,000 bankroll, the full Kelly = $446, the half Kelly bet = $223, and the quarter Kelly = $111.5
Example 2
Club Brugge (2.50) vs Anderlecht (1.65). If your estimated win probability for a Brugge victory is 55% (p = 0.55)
b = 2.50 -1 = 1.50
q = 0.45
f* = 0.55 − (0.45 / 1.50) = 0.55 − 0.30 = 0.25 → 25% stake
For a $1,000 bankroll, the full Kelly = $250, the half Kelly bet = $125, and the quarter Kelly bet = $62.5
Why to Use Fractional Kelly?
Full Kelly provides the potential for huge payouts but comes with high volatility. That’s why fractional Kelly (e.g., half-Kelly or quarter-Kelly) is best for you. Full Kelly maximises growth on paper but also maximises volatility. You could lose 30-40% of your bankroll with one bad streak.
Below you can find the benefits of using fractional Kelly instead of full Kelly
Reduces drawdowns: It helps you control your betting money better, so you can make small profits and avoid big losses when your bets don’t win. Smaller losses are also easier to handle mentally.
Compensates for inaccurate p estimates: In cases of overly optimistic projections, fractional Kelly adds a margin of safety. It helps to preserve your funds for future betting opportunities.
Keeps emotions in check during losing streaks: Smaller bet sizes mean losing streaks feel less damaging. That way, it is easier to avoid emotional choices in future betting sessions.
Tips For Using the Kelly Criterion for Sports Betting
The Kelly Criterion is easy to understand in theory. But in real life, there are often limits that make it hard to follow the system exactly.
Here are some tips to help you use the Kelly Criterion in real situations:
Build a reliable probability model using stats, form, injuries, and local conditions (e.g., team performance against certain opponents)
Compare model p to the market implied probability. Do not ignore the market's implied probability or overestimate the chances of your chosen team accomplishing your desired result.
Calculate your Kelly stake using the formula or a sports betting Kelly criterion calculator.
Apply fractional Kelly (half or quarter) by default.
Limit any single bet to a maximum percentage of your bankroll (suggested not more than 5%).
Keep detailed records of all bets, outcomes, and your p estimates for future references.
Common Mistakes to Avoid
Mistakes often occur in two main ways: misunderstanding how the Kelly Criterion works or failing to apply it with precision. However, knowing these potential mistakes can allow you to use this system safely.
Overestimating Probability: If you think Palmeiras wins 60% of the time when the actual number is 45%, you’ll over-bet and lose faster. So, ensure you carefully understand your team’s winning potential and bet accordingly.
Wrong Odds Conversion: Using the correct values and formula when making the odds conversion is crucial to getting the correct bet amount. If you mess up even a small conversion, the whole formula gets thrown off, and you’ll end up with the wrong numbers. So double-check the odds before you use the sports betting Kelly criterion calculator.
Ignoring Bankroll Segmentation: Keep separate bankrolls for different strategies, especially if you are in other sports. Don’t mix sports betting with poker or day trading.
Never Blindly Use Full Kelly: Even with an edge, the variance that comes with sports betting can hurt you badly with full Kelly. So, opt for quarter or half Kelly as your default option.
Pros and Cons of Using the Kelly Criterion
Now that you understand how the Kelly criterion works, let’s examine its benefits and disadvantages.
Pros
Keep these advantages in mind
Maximises long-term bankroll growth: Excellent strategy for getting the highest possible growth rate over time when applied correctly.
Enforces disciplined staking: it removes emotional decision-making by providing an objective, mathematical approach to bet sizing.
Adjusts stakes based on your edge: For a bigger perceived advantage, Kelly suggests larger bets; when your edge is smaller, the formula recommends smaller stakes. This automatic adjustment ensures you're always betting proportionally to your expected value.
Aligns with compounding wealth models: With this system in place, you will always experience a compounding effect on your funds. As your bankroll grows, this model ups the size of your bets. In contrast, as your betting funds shrink, it reduces the size of your bets.
Cons
Do not forget that the Kelly criterion is not foolproof. Therefore, it would be good for you to remember the following disadvantages.
Sensitive to inaccurate probability estimates: Small errors in probability estimates can lead to losses. If you overestimate the winning probability, you could suffer bigger losses.
High volatility with full Kelly: Full Kelly can encourage you to place aggressive bets. As a result, you could lose most of your bankroll on just a few bets.
Complex for multi-outcome events: This strategy is not suitable for betting markets with multiple betting outcomes. The calculations for such events are usually complex and time-consuming.
Conclusion
Now you know how to use the Kelly criterion in betting. With this system, you are not just applying a formula, but building a disciplined and data-driven approach to betting. When you have an edge, the Kelly criterion shows you exactly how much you need to stake to balance growth with risk.
With fractional Kelly, you set probabilities based on the league’s conditions and track every single outcome with precision. When applied correctly, Kelly Criterion betting guarantees steady growth of your bankroll long-term.
