When it comes to making long-term profit through gambling, managing your betting bank correctly and finding the right staking plan is as important as identifying a winning strategy based on finding value in the market. Even if you have an edge and can identify value – which is where the bookies offer higher odds than you’d expect – you could still find yourself out of pocket with a depleted betting bank if your staking plan is not up to scratch.

There are a number of different staking plans out there, all of which have their merits and downsides. Some of the most common staking systems include:

• Fixed or Level Staking where you put the same stake down regardless of the odds, such as $20 per bet whether the odds are 1.20 or 2.40
• Variable Staking where you put a stake on to win a fixed amount per bet, rather than staking a set amount, such as always ensuring your return is $20 per bet
• Percentage of Bank Staking where you bet the same percentage of your current bank balance regardless of size, for example, 5% per bet whether the bank is at $10 or $1000
• Progressive Staking where you increase or decrease the size of your stake after each bet depending on whether it won or lost, such as the Martingale System where you double up after a loss

The Kelly Criterion – also known as Kelly Strategy or Kelly Staking Plan – takes elements from Fixed, Percentage and Progressive staking to create somewhat of a hybrid staking plan. It was developed in 1956 by John Larry Kelly Jr. to identify how to maximise the long term growth rate of investments and has since been used successfully by gamblers across a range of sports and games, as well as those looking to invest in the stock market.

Defining and deriving Kelly's criterion in Part 1 was an important exercise in order to understand the underlying mechanisms of the formula so we can apply it correctly. We will now focus on understanding and applying Kelly's Criterion starting from a basic coin toss examples up to a soccer betting example. Kelly Criterion Betting – Measuring Out Your Bets Can Be a Recipe for Success. Thin on the ground are the punters that need not employ a betting system in order to turn a profit in the long run, but there are many systems that raise more question marks than give answers in the mind of the unpracticed gambler.

The Criterion looks at your current betting bank, the odds available and the edge you think you have in order to determine the optimal size of your bets. If you believe you have a significant edge on a particular bet, then your stake would be larger than a bet in which you only had a slight edge. For example, if you were and English Premiership fan betting on Tottenham to win at evens, you could place a 15% stake if you had a significant edge or a 5% stake if you had less of an edge, as calculated using the Kelly formula.

There are a number of variations of the Kelly Criterion – some of which look much scarier than others – however the one that makes most sense to me is written below. This formula is based on bets with two outcomes – i.e. you either lose all of your stake, or your stake and profit are returned if you win – although several variations have emerged for different circumstances. Luckily, there are multiple Kelly calculators online which can take away some of the pain, particularly https://www.albionresearch.com/kelly/default.php and https://bettify.com/tools/kelly.

Stake = ((Decimal Odds x % Chance Win) – 1) / (Decimal Odds – 1) * 100

Where:
Stake = Optimal size of stake
Decimal Odds = Odds offered by bookie
% Chance Win = Estimated probability of bet winning

Using the Tottenham example above, betting on Spurs to win at evens (decimal odds of 2.0) with a 53% probability and £500 bank would result in the following calculation:

Stake = ((2.0 x 0.53) – 1) / (2.0 – 1) x 100
Stake = ((1.06 – 1) / 1) x 100
Stake = 6% of bank or £30 if bank is £500

A couple of points for consideration when using the formula. If you have a zero edge – i.e. your probability is the same as the bookies’ – then the Criterion states that you should not bet. Similarly, if you have a negative edge – i.e. your probability is lower than the bookies’ – then you could either avoid the bet or you could consider laying it. It is also recommended that you don’t bet more than the calculated Kelly stake as this is known to negatively affect your bank in the long term.

The main – and somewhat significant – flaw to the Kelly Criterion is that it assumes that you know the true probability of an event happening. Whereas this is easier to ascertain when flipping a coin, it becomes near on impossible to predict for a football game involving 22 players or a horserace with 10 runners. If you cannot be sure your probabilities are entirely accurate, then this could cause detrimental effects on your bank roll, particularly if you have a habit of overestimating the likelihood of winning rather than underestimating!

Another drawback is that the percentage result from the Criterion is often a significant proportion of your bank balance, meaning that large stakes may be required. The Kelly Criterion aims to increase your betting bank at the optimal – or maximum – rate possible, which is a relatively aggressive approach. Most professional bettors would not risk anywhere near 10% of their bank on a single bet, whereas the Kelly formula rarely suggests low single digits.

A common strategy employed by some gamblers to overcome the two issues above is to use a ½ Kelly or even a ¼ Kelly strategy to ensure they are not overexposed – this is simply halving or quartering the suggested Kelly stake. With problems associated with overestimating and predicting accurate probabilities, it is always sensible to be risk averse and bet less than the Kelly amount.

Whether the Kelly Criterion is the right approach for you comes down to personal preference. It is sensible to approach your betting in a professional manner though, so concepts such as bank management and staking plans should be in your thinking while trying some of the best sports betting websites. If it’s not using Kelly, then simple concepts related to the theory such as ensuring you research your bets, creating a betting bank separate to your other accounts and eliminating emotion from any betting decisions can significantly help.

Ready For More?

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.

Kelly Criterion Football Cards

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.

Kelly Criterion Football Betting

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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