What is the Kelly Criterion Betting System?
Rumen Morfov
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The Kelly Criterion betting system is a mathematical formula bettors can use to determine their optimal bet size. Like most betting strategies and staking systems, the Kelly Criterion is not without risk. In this article, we will explain how the Kelly betting model works, provide an example of the formula in action, and offer tips for using it correctly.
Dr Catalin Barboianu, Mathematician and Philosopher of Science PhD
The Kelly Criterion optimizes the expected growth rate of your bankroll. Its formula returns the optimal size of your stake relative to your bankroll, given the net payout rate and probabilities of winning and losing the bet; there is no profit/loss or profit rate that is subject to optimization, but your bankroll itself. The growth rate of your bankroll is maximized by this strategy, only under conditions of a positive expected value, that is, in a theoretically profitable play. This limitation makes the Kelly Criterion inapplicable in casino games, where all bets have negative expectation. In sports betting, with subjective true odds in the role of the probability of winning, we can apply the Kelly formula, as long as the true odds are higher than the payout odds (condition satisfied for bets selected as a result of effective handicapping).
The Kelly Criterion is an expectation-based strategy and it works like a statistical average over the long run; the gain is expected to materialize much harder than in a regular optimal play, since the conditions are much more limited.
The Kelly strategy is not for those chasing surprises or short-term big wins. It is a relatively safe defensive strategy, suited to those bettors focused on consolidating bankrolls by a safe conservative play.
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The Kelly Formula & Gambling
The Kelly Criterion is primarily used to determine bet size when a bettor has an estimated probability of winning and a positive expected value. It is particularly relevant to sports betting and investing, where identifying an edge over the available odds or market is possible. It is generally not applicable to standard casino bets, because these bets have a negative expected value due to the house edge.
The Kelly Criterion formula is:
f = (bp – q) / b
Each letter in the formula stands for:
- f – the fraction of your bankroll to wager.
- b – the net decimal odds, calculated as decimal odds minus 1.
- p – the probability of the bet winning.
- q – the probability of the bet losing.
The Kelly Criterion is a mathematical formula used by investors and bettors to determine an appropriate bet size. Developed in the 1950s by John L. Kelly Jr., the Kelly betting approach considers the available odds and your estimated probability of winning to determine the optimal proportion of your bankroll to stake.
The goal of the Kelly Criterion is to maximize the long-term growth rate of your bankroll when you have a positive expected-value opportunity. It does not predict individual results or guarantee a profit.
Although the Kelly Criterion has applications in areas such as investing and sports betting, it should not be presented as a way to overcome the house edge in casino games. If the underlying bet has a negative expected value, changing the stake size does not turn it into a profitable wager.
Key Statistics & Facts:
- The Kelly Criterion determines the optimal proportion of your bankroll to wager based on odds and estimated probabilities.
- The formula is designed for situations where the bettor has a positive expected value.
- The Kelly Criterion does not guarantee that an individual bet will win.
- The accuracy of your estimated probability is crucial when using the Kelly Criterion.
Teodor Todorov, Betting Expert & Writer for SilentBet
I have used the Kelly Criterion betting system for a while. There are downsides to using it, but when applied correctly to a bet where you have an edge, it can be a useful way to manage your bankroll.
How Does the Kelly Criterion Work?
Many bettors do not put much thought into determining their bet size. They may base their wagers on a fixed amount, a percentage of their bankroll, or simply bet based on intuition. The Kelly Criterion takes a more mathematical approach by linking the size of the wager to the bettor’s estimated probability of winning and the available odds.
The Kelly staking plan is designed to allocate a larger portion of your bankroll when you believe the available odds offer a significant edge and a smaller portion when your edge is weaker. However, the calculation is only as reliable as your probability estimate. This is where the Kelly Criterion becomes more complicated for the average bettor.
To use the formula correctly, you need to estimate the true probability of an outcome. For example, if you believe the Boston Celtics have a 35% chance of winning, you need to be reasonably confident that 35% is a realistic estimate. In reality, determining whether the true probability is 35%, 32%, or even 28% can be extremely difficult.
If your probability estimate is wrong, the Kelly Criterion may recommend a stake that is too large for the actual edge you have. In other words, the Kelly Criterion does not create an advantage for you. You need to identify the advantage first, and the formula then determines how much you should theoretically wager based on that advantage.
Speaking of the latter, here is a simplified Kelly Criterion example at work:
- The Boston Celtics have +250 odds (3.50 decimal).
- +250 odds correspond to an implied probability of approximately 28.6%.
- You estimate the Celtics’ probability of winning at 35%.
- p = 0.35
- q = 0.65
- b = 2.50
- Formula: (2.50 × 0.35 – 0.65) / 2.50 = 0.09
- Kelly bet size = 9% of your bankroll.
Based on this example, a $1,000 bankroll would result in a full Kelly stake of $90 on a single event. While this is mathematically correct based on the assumptions above, it is also a relatively aggressive stake. Sports betting involves variance, and even bettors with a genuine long-term edge can experience several consecutive losses.
This is one reason many bettors prefer a fractional Kelly approach. Instead of using the entire 9% recommended by Full Kelly, you could use half Kelly (4.5%) or quarter Kelly (2.25%). This reduces the size of individual wagers, limits volatility, and also gives you some protection against errors in your probability estimates.
The trade-off is that using fractional Kelly also reduces the expected growth rate of your bankroll. However, for many bettors, accepting slower growth in exchange for smaller drawdowns is a more practical approach.
Tips for Using the Kelly Criterion the Right Way
The results you achieve using the Kelly Criterion depend largely on the accuracy of your probability estimates. If you are unsure whether the Kelly Criterion is right for you, you can check out our full list of betting strategies. In the meantime, here are some tips for using the Kelly Criterion correctly.
- Tip 1: Improve your handicapping skills – If you want to use the Kelly Criterion for sports betting, you need to make a realistic estimate of the probability of winning. Effective handicapping can help you identify situations where your estimated probability is higher than the probability implied by the available odds.
- Tip 2: Consider fractional Kelly – Full Kelly can produce relatively large wagers when you believe you have a strong edge. Using half Kelly or quarter Kelly can reduce the size of your wagers and limit volatility, although it also reduces the expected growth rate.
- Tip 3: Use a Kelly Criterion calculator – While the mathematical formula behind the Kelly Criterion is not particularly complicated, a calculator can make the process easier and reduce the risk of calculation errors. It allows you to enter your odds, estimated probability and bankroll to determine the suggested stake.
Teodor Todorov, Betting Expert & Writer for SilentBet
I am aware that the Kelly Criterion can be an intimidating betting strategy. However, once you understand the formula and how to estimate probabilities, it becomes a much more structured way to approach bet sizing.
Pros & Cons
Like most betting strategies, the Kelly Criterion has advantages and limitations. It provides a mathematical framework for determining bet size, but it requires accurate probability estimates and is not suitable for every betting situation.
- Advantages of Using the Kelly Criterion for Betting
- Provides a mathematical approach to determining bet size
- Adjusts the stake according to your estimated edge
- Can help optimize long-term bankroll growth when a positive expected value exists
- Offers lower-risk alternatives through fractional Kelly
- Limitations and Risks of the Kelly Criterion
- Relies heavily on the accuracy of your probability estimates
- Can produce relatively large wagers when the estimated edge is high
- Full Kelly can result in significant short-term volatility
- Is not suitable for standard casino bets with negative expected value
The Bottom Line: Is the Kelly Criterion Worth Using?
Should you use the Kelly Criterion betting system? It can be useful for bettors who understand probability, have a reliable way to estimate true odds, and can identify bets with positive expected value. However, it is important to understand that the Kelly Criterion does not guarantee profits and is not designed to eliminate betting risk.
The strategy is most relevant to sports betting and investing, where a bettor may be able to identify an edge over the available odds or market. It should not be treated as a system for beating casino games, where the house edge generally gives bets a negative expected value.
If you are using the Kelly Criterion for sports betting, a calculator can help you apply the formula correctly. Fractional Kelly can also be considered if you want to reduce the size and volatility of your wagers.
Teodor Todorov, Betting Expert & Writer for SilentBet
I know the Kelly Criterion is not suitable for every bettor. However, for bettors who understand probability and have identified a genuine edge, it can be a useful tool for managing bankroll growth.
FAQs
Can the Kelly Criterion be applied to any type of betting?
No. The Kelly Criterion is most useful when you can estimate the probability of an outcome and identify a positive expected-value opportunity. It is commonly associated with sports betting and investing. Standard casino bets generally have a negative expected value because of the house edge, making the Kelly Criterion unsuitable for them.
How do I determine my bankroll when using the Kelly Criterion?
The Kelly Criterion does not determine how much money you should have available for betting. Your bankroll should consist only of money you can afford to lose. The formula then determines the suggested stake as a percentage of that bankroll.
How does the Kelly Criterion calculate optimal bet size?
The Kelly Criterion uses the available odds and your estimated probability of winning and losing to calculate the proportion of your bankroll that should theoretically be wagered. The formula is f = (bp – q) / b.
Are there any common mistakes to avoid when using the Kelly Criterion?
Yes. Common mistakes include overestimating your probability of winning, using inaccurate odds, staking too much of your bankroll, and treating the Kelly calculation as a guarantee of profit. Using full Kelly when your probability estimate is uncertain can also create unnecessary volatility.
How does the Kelly Criterion compare to other betting systems?
The Kelly Criterion differs from many traditional progression systems because it does not determine the next bet based on whether the previous bet won or lost. Instead, it uses the bettor’s estimated edge and available odds to determine an appropriate stake size.
Who should use the Kelly Criterion for betting?
The Kelly Criterion is best suited to experienced bettors who understand probability, can estimate true odds reasonably well, and are able to identify positive expected-value opportunities. It is not a suitable strategy for anyone looking for guaranteed profits or a way to overcome the house edge in casino games.
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