The idea sounds simple enough: if you know that a bet offers value, the Kelly Criterion tells you exactly how much of your bankroll to risk. The challenge, of course, is determining whether you actually have an edge in the first place. In this guide, I’ll explain how the Kelly Criterion formula works, where it can be used, and whether it’s practical for casino players.
What's the Kelly Criterion Formula?
The Kelly Criterion, popularly known as the Kelly strategy or just the Kelly bet, was developed by American researcher John L. Kelly Jr. and first published in 1956 while he was working at Bell Labs.
The original purpose wasn’t gambling at all. Kelly was studying information theory and communication systems, but mathematicians quickly realised that his formula could also be used to determine the optimal size of a bet when a player has an advantage.
Over time, the Kelly Criterion became popular among professional gamblers, sports bettors, poker players, and even famous investors like Warren Buffett.
The system focuses entirely on two factors: your bankroll and your edge, and this is the Kelly Criterion formula itself:
f = (bp − q) ÷ b
Where:
- f = the percentage of your bankroll to wager
- b = the odds received on the bet
- p = your estimated probability of winning
- q = your estimated probability of losing (1 − p)
Explaining the Kelly Criterion Formula
Don’t worry, I’m not trying to send you back to your high school maths class. The strategy itself is much simpler than what the formula makes it seem.
The most important part of the formula is your edge. In gambling terms, an edge exists when the true probability of an outcome is higher than what the odds imply. For example, if a casino offers odds that underestimate your chances of winning, the Kelly Criterion will tell you how much of your bankroll you should risk.
For example, let’s say you find a sports bet that pays even money (2.00 odds), but you believe the true chance of winning is 55% rather than the implied 50%.
Using the Kelly formula:
f = (1 x 0.55 − 0.45) ÷ 1 = 0.10
The result is 0.10, which means you should wager 10% of your bankroll on this bet. Or, if you had a bankroll of A$1,000, you should wager A$100 on this bet.
This is where things get tricky for casino players. In sports betting or poker, it may be possible to identify value and gain an edge over the market based on the information you have. I’ve explained in detail how you can identify value in poker in my 101 poker guide, but in casino games, the house edge means that the casino has the advantage.
Unless you’re playing under very unusual circumstances, even using the perfect blackjack strategy (which offers the highest RTP in all casino games), the Kelly Criterion will suggest that you shouldn’t place a bet at all.
That’s why I suggest using the Kelly Criterion more as a bankroll management tool than a traditional betting strategy. It’s not a typical strategy that suggests when to increase or decrease your bets, but it helps you determine whether a bet is worth taking and how much money should be risked.
How to Use the Kelly Criterion Strategy?
The Kelly Criterion is most commonly used in sports betting and poker because these are two areas where players can realistically gain an edge. In casino games like roulette, online pokies, and baccarat, the house has a built-in advantage, which makes the formula useless.
So, let’s use a poker example:
1
Estimate your winning chances:
Suppose you’re playing Texas Hold’em at one of the best Australian poker sites, and, based on the cards on the table and your opponent’s likely range, you estimate that you have a 60% chance of winning the hand.
2
Calculate the odds:
Let’s say the pot currently contains A$100, and your opponent bets A$50. If you call, you’ll be risking A$50 to win A$150, which gives you odds of 3:1.
3
Apply the Kelly formula:
Using the formula f = (bp − q) ÷ b, where b = 3, p = 0.60, and q = 0.40, the calculation looks like this: f = (3 x 0.60 − 0.40) ÷ 3 = 0.47
4
Determine your stake size:
The result of 0.47 means the Kelly Criterion suggests risking 47% of your bankroll on this opportunity. If your bankroll is A$1,000, the recommended stake would be A$470.
5
Consider using a reduced Kelly approach:
As you probably noticed, the full Kelly bet can be too risky, so most players prefer to use Half Kelly or Quarter Kelly to reduce volatility. In this example, Half Kelly would suggest wagering A$235 instead of A$470.
6
Repeat the process for each opportunity:
With this approach, every bet is calculated independently based on your bankroll and your estimated edge.
As you can see, the Kelly Criterion isn’t difficult to use. The hard part is accurately estimating your edge, which is why it’s much more useful to experienced poker players and sports bettors than casino players.
I also find the full Kelly approach too aggressive. In our example, it suggested risking A$470 from a A$1,000 bankroll on a single hand. If you want to try it yourself, I’d recommend using Half Kelly or Quarter Kelly instead, because the full Kelly bet can be too risky.
Disadvantages of the Kelly Criterion Strategy
The biggest drawback of the Kelly Criterion is that it requires a genuine edge, which is something most casino players simply don’t have. Even at the best Australian casinos, the house always has a mathematical advantage in all the traditional casino games.
PVP poker may be the only exception, but even then, calculating the edge is extremely difficult, and if you were able to calculate the edge of every hand accurately, you’d probably be sitting at the WSOP final table.
Another issue is that the formula is only as good as your estimates. If you overestimate your chances of winning, the recommended bet size can become far too aggressive.
In fact, the most common mistake I see poker players make is overestimating the chances of winning, which, again, makes the Kelly bet too aggressive.
Should You Use the Kelly Criterion Formula?
The Kelly Criterion is an interesting formula and a good bankroll management tool, but it doesn’t make much sense in traditional casino games. Roulette, pokies, baccarat, and most other games have a built-in house edge, which means the formula will often tell you that the bet isn’t worth taking in the first place. So, my answer would be no, you shouldn’t use the Kelly strategy for most casino games.
Where Kelly can be useful is in poker and sports betting, where players may occasionally have an edge. The problem is that you need to be very confident in your estimates, and that’s much easier said than done. In poker, accurately calculating your edge takes a lot of skill and experience. And in sports betting, it’s almost impossible to get an edge.
So while I appreciate the Kelly Criterion and the theory behind it, I wouldn’t lose sleep over it. If you’re a serious poker player or sports bettor, you probably have your own betting strategy already, and for everyone else, there are simpler ways to manage your bankroll, so I’d check out strategies like D’Alembert or Oscar’s Grind instead.
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