The Kelly Criterion is a mathematical formula that helps gamblers determine optimal bet sizes and maximize profits. Kelly Criterion gambling is especially popular in sports betting and can potentially help you become a successful bettor.
This guide explains how the Kelly Criterion works and why it’s so good for sports betting. It also covers examples of using this formula and its pros and cons. Additionally, you’ll find out if the Kelly Criterion applies to casino games and other types of gambling.
What is Kelly Criterion Gambling?
The Kelly Criterion formula is applicable to sports betting and investing. It weighs the odds of winning and losing to help you maximize profits on winning bets. You can see the formula below:
f = (bp – q) / b
Here’s what each letter stands for:
- f is the bet size based on a percentage of your bankroll.
- b is the bet’s decimal odds – 1 (eg 3.0 odds – 1 = 2)
- p is the probability of winning the wager (eg 45% chance = 0.45).
- q is the probability of losing the bet, which is expressed as 1 – p (eg 1- 0.45 = 0.55).
The decimal odds can be confusing when you’re betting at US online sportsbooks like BetMGM and Caesars and are used to American odds. But some betting sites give you the option to toggle between American and decimal odds.
Alternatively, you can find odds conversion charts at various websites. If the American odds are +150, for example, they would convert to 2.5 for the formula.
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How Does Kelly Criterion Gambling Work?
Most sports bettors don’t put much analysis into their wager sizes. They may loosely consider their bankroll (eg $50 bets with a $500 bankroll) when deciding wagers. As a result, they fail to capitalize on the most profitable opportunities while risking too much on less favorable outcomes.
Kelly Criterion gambling helps solve this problem by providing more accurate bets based on the situation. It features a known entity (the bet’s odds) with two estimated variables (probabilities of winning and losing). Speaking of the latter, you must use handicapping skills to assess the chances of winning. Here’s an example:
- The Indiana Pacers have +250 odds (3.5 decimal).
- +250 odds = 28.6% implied probability of winning.
- You handicap the game and feel that Indiana’s actual win probability is 35%.
- p = 0.35
- q = 0.65
- Formula: 0.09 = (2.5 x 0.35 – 0.65) / 2.5
- Bet 9% of your bankroll.
Your success with the Kelly Criterion betting system will largely hinge on your handicapping abilities. That said, we suggest learning sports handicapping tips before employing the Kelly Criterion system in real-money situations.
Kelly Criterion Examples
At this point, you likely understand how the Kelly Criterion works. But how does it look in real sports betting situations? The following examples illustrate common scenarios when betting with this formula. American odds are in parenthesis alongside decimal odds.
- Buffalo Bills 1.44 (-225); implied probability is 69.2%.
- You handicap the Bills at 1.36 (-275); your estimated win probability is 73.3%.
- b = 0.44 (1.44 – 1)
- p = 0.73
- q = 0.27 (1 – 0.73)
- Formula: 0.116 = (0.44 x 0.73 – 0.27) / 0.44
- Bet 11.6% of your bankroll.
- Chicago Bulls 3.20 (+220); implied probability is 31.3%.
- You handicap the Bulls at 2.80 (+180); your estimated win probability is 35.7%.
- b = 2.2 (3.2 – 1)
- p = 0.36
- q = 0.64
- Formula: 0.069 = (2.2 x 0.36 – 0.64) / 2.2
- Bet 6.9% of your bankroll.
Perhaps you’ll feel comfortable doing your own Kelly calculations like those above. If not, you can find a Kelly Criterion calculator to do the mathematical work for you. Just enter your variables and hit enter/calculate to find your bet size.
Modified Quarter and Half Systems
You may feel that Kelly Criterion gambling is too risky in its purest form. After all, this formula calls on you to wager a higher bankroll percentage with a significant edge. You can lower the risk factor by using modified half or quarter versions:
- Half Kelly Criterion – Divide bet size (f) by 2.
- Quarter Kelly Criterion – Divide wager size (f) by 4.
You can use the half or quarter options on every bet to truly minimize risk. Alternatively, you could use these versions anytime that you get a percentage worth 20% or higher.
Whatever the case, you can add flexibility to Kelly Criterion betting based on your risk preferences.
Pros and Cons of the Kelly Criterion Betting System
Like any gambling system, the Kelly Criterion has upsides and downsides. You can consider the following pros and cons when deciding if Kelly Criterion gambling is worthwhile.
Pros & Cons
- Unique betting strategy that guides bet sizes
- Helps you maximize profits (when done right)
- Half and quarter alternatives if you want to lower risk
- Can rapidly increase your bankroll
- Popular among some professional bettors
- Kelly strategy fails if you’re bad at handicapping
- Higher learning curve than simple systems like the Martingale or Paroli
- Requires a significant portion of your bankroll in certain instances
- Might require modifications so that you don’t risk too much
- Not a great strategy for beginners who are learning the ropes
Kelly Criterion in Sports Betting
Most betting systems don’t perfectly lend themselves towards sports betting. Strategies like the Martingale and D’Alembert are built for even-money casino wagers. They can apply to -105 and -110 sports bets, but they’re not perfect matches.
Kelly Criterion differs from the average betting system. It’s not about doubling bets after wins or losses, or any other pattern-based form of wagering. Instead, it measures the chances of your bet winning to determine an optimal wager size.
Handicapping plays a large role in this gambling strategy. You must handicap games and assess the true odds rather than relying on implied odds (based entirely on the sportsbook’s stated odds). Your skills in properly assessing teams’ real chances of winning will make or break your Kelly betting success.
Therefore, you might consider a more-conservative strategy as a newer or recreational bettor. You could stick to only risking 1-2% of your bankroll per bet while slowly improving your handicapping. When you’re more confident, you could switch to the aggressive Kelly gambling strategy.
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Kelly Criterion with Casino Games
You’ve seen how Kelly Criterion gambling can work with sports betting. But does this formula apply to casino games as well?
No, the Kelly Criterion does not work with casino games. The problem is that online casinos offer negative-expectation games. Casino game numbers produce a negative bankroll percentage when plugged in the Kelly formula.
Here’s an example:
- You play a blackjack game with 99% RTP (1.01 decimal odds).
- b = 0.01 (1.01 – 1)
- p = 0.99
- q = 0.01
- Formula: -0.01 = (0.01 x 0.99 – 0.01) / 0.01
- -1% of your bankroll.
This negative number means do not place the bet. You can still win with casino games through a mixture of strategy and luck, but you’re facing a long-term disadvantage. That said, the Kelly Criterion betting system won’t help with blackjack and other casino games.
Contrast this situation to sports betting, which can offer positive expected value to skilled bettors. Of course, most sports gamblers lose money over time and don’t benefit from the Kelly. But the key is that Kelly Criterion betting has a chance of working in sports wagering.
Kelly Criterion with Poker
Like sports gambling, poker is a game that is beatable in the long run. Therefore, it’s worth considering if the Kelly Criterion works at poker sites.
Poker already has enough useful mathematical concepts for deciding what to do with hands. Pot odds, implied odds, and reverse implied odds apply specifically to poker—so no need for the Kelly here.
Alternative Betting Systems to the Kelly Criterion
If you’re interested in the Kelly, you might want to know more betting strategies. The following gambling systems are good for casino games and sports bets with around -110 odds:
Negative Progression Systems – Raising Bets to Recoup Losses
- D’Alembert – Increase your stake by 1 unit (eg $10 unit size) after every loss. Meanwhile, you decrease your wager by 1 unit following each win.
- Labouchere – Write down a profit goal (eg 15 units) and a sequence that adds up to this goal (eg 3, 2, 5, 3, 2). Add the first and last number to determine your bet (3+2 = 5). Cross both numbers off if you win (new sequence = 2, 5, 3). Add the bet to the sequence if you lose (new sequence = 3, 2, 5, 3, 2, 5). The goal is to cross off every number and earn your desired profit.
- Martingale – Start at 1 unit and double bets after every loss. You return to 1 unit following any win. Ideally, you’ll always win back losses and net a small profit.
Positive Progression System – Raising Bets to Win More During Hot Streaks
- 1-3-2-6 – Follow this progression after every win. In other words, you’ll bet 1, 3, 2, and 6 units during a four-round winning streak. Meanwhile, you start the sequence over following any loss. Likewise, you start over (or quit) if you win four bets and reach the end.
- Paroli – Increase your bet by 1 unit following every win. You return to 1 unit after winning three straight bets.
- Oscar’s Grind – Raise your wager by 1 unit following each win and keep your bet the same after losses. You start the sequence over after winning 1 unit or more in profit.
Kelly Criterion Gambling Tips
You can get more out of Kelly Criterion betting by following the tips below:
- Work on your handicapping abilities
You need good handicapping skills to more accurately determine teams’ probabilities of winning and losing. Otherwise, your Kelly bets will be way off and you won’t gain anything from this strategy.
- Switch to the half or quarter strategy if necessary
The Kelly Criterion is one of the more aggressive betting strategies. You may want to modify this strategy with the half or quarter Kelly, especially as you adjust to it.
- Consider using a Kelly calculator
The mathematical formula behind this betting system isn’t overly complicated. Nevertheless, you might want to use a Kelly calculator make the process even easier.
- Don’t use the Kelly strategy on casino games
This betting strategy works with positive-expectation bets, not negative-expectation wagers like casino games.
Where did this Betting Strategy Originate?
John L. Kelly developed the Kelly Criterion formula while working for AT&T’s Bell Labs in 1956. His goal was to help Bell Labs reduce signal noise issues with AT&T’s long-distance calls.
Interestingly enough, sports bettors realized that Kelly’s formula applied to gambling. Investors like Warren Buffet later picked up on the Kelly Criterion as well to help in sizing trades.
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