Texan-born computer scientist John L. Kelly devised his eponymous formula as part of a paper he wrote in 1956 entitled “A New Interpretation of Information Rate”. It went on to become a revered staking plan among sports bettors and stock market investors striving to gain an edge. Even billionaire investor Warren Buffett is an advocate. Yet Kelly, who died of a brain hemorrhage on a Manhattan sidewalk at just 41 years old, reportedly never used the criterion to make money.
A common quandary bettors find themselves in is fathoming how much of their bankroll to stake on each bet.
How do you decide what a bet is worth?
As, ultimately, staking too much or too little will have a massive impact on your long-term profitability.
While most players trust in their instincts, there are a number of methods that allow you to trust in the more dispassionate world of mathematics and probability. Instead of trusting in themselves, they trust in Kelly. Or more precisely the Kelly Criterion.
The Kelly Criterion is a money-management formula that calculates the optimal amount you should bet when there’s a difference between the true odds and the given odds. Although it may appear confusing, it’s actually pretty simple. The formula is as follows:
- f = the fraction of the bankroll to bet
- b = the decimal odds – 1
- p = the probability of winning
- q = the probability of losing, which is 1 – p
Let’s break it down in practical terms: the chance of a thrown dice landing on a 1, 2, or 3 is 50%. Likewise, a 4, 5, or 6 outcome is 50%. But imagine if that same dice was loaded so that the chance of it coming to rest displaying a 1, 2, or 3 was now 60%.
- b = 2 – 1, which is 1
- p = 0.60
- q = 1 – 0.60 = 0.40
So the calculation is as follows: (1 × 0.60 – 0.40) ÷ 1 = 0.2
Therefore, the formula suggests that you stake 20% of your bankroll. If the dice bias were less, at 53%, the Kelly Criterion recommends staking 6%.
If you repeatedly bet too much (over 20%) on a low number appearing, there’s a good chance you’ll eventually go broke. Conversely, under-betting (less than 20%) should produce a modest profit.
Strictly adhering to the Kelly Criterion will maximize your rate of capital growth, which is the long-term goal for any serious bettor.
A Sporting Chance
Now let’s say the Seattle Seahawks are due to lock horns with the Denver Broncos in the Super Bowl. It’s a fairly evenly matched encounter with the Seahawks the slight favourites at 1.9 on the betting exchanges. The odds suggest they have a 52.6% chance of winning.
However, your analysis indicates that the Seahawks’ true odds are significantly shorter; you believe they have a 55% implied probability of lifting the Vince Lombardi trophy. That’s around 1.8 in odds.
Using the Kelly Criterion, the calculation is:
- b = 1.9 – 1
- p = 0.55
- q = 0.45
- (0.9 × 0.55 – 0.45) ÷ 0.9 = 0.05
Therefore, you should bet 5% of your capital on the Seahawks.
A positive percentage implies favourable odds.
However, it’s important to note that you should only bet when f > 0 (the fraction of the bankroll is greater than zero). If the calculation spits out zero or a negative number, it means the criterion suggests betting nothing and walking away because the odds aren’t in your favour. For example, if your homework assesses the Seahawks’ chances as 50/50, or 2.0, rather than the 1.9 on offer then the Kelly Criterion formula is:
- (0.9 × 0.5 – 0.5) ÷ 0.9 = –5.55
A negative outcome could perhaps mean it pays to lay the Seahawks on a betting exchange. Or you could back the Broncos if you believe they are overpriced. That’s for you to decide.
Overall, the Kelly Criterion is widely considered a smart and disciplined staking strategy, as opposed to simply betting to level stakes. One potential downside is that you’ll need to accurately assess the percentage chance of a selection winning, so it may be wise to experiment with ‘paper’ bets to see how you get on.
Another option is to use ‘Fractional Kelly’, which means only betting a certain fraction of a recommended bet. For instance, only half the recommended Seahawks bet, or 2.5% of your stack. Although it’s a more cautious method, it reduces the impact of possibly over-estimating your edge and depleting your bankroll.
If all this number-crunching is too arduous, you’ll find plenty of handy online Kelly Criterion calculators and mobile apps to do all the hard work for you.