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%.

That means:

- 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.

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