Kelly Criterion 2021
The Kelly criterion is a strategy that guarantees that you will make money from various betting types. It takes into account the likelihood of bets coming to fruition and tells you how much money to stake.
The man who invented the Kelly formula, J. L. Kelly Jr, was a renowned researcher and math enthusiast. However, most people these days remember him for increasing the wealth of many bettors and successful individuals such as Warren Buffett.
What is a Kelly bet?
A Kelly bet is when players calculate the optimal stake sizes before they place their wagers. They do this by utilizing the Kelly formula.
Bettors find the size of a Kelly bet after entering things such as the likelihood of a win, likelihood of a loss, and the odds of a bet.
The size of the bet that players get is the fraction of their betting budget that they should stake. This means that for the Kelly criterion to work, bettors must have a bankroll they use for wagering.
Having a betting bankroll is essential in any wagering endeavor and is something that betting beginners must have right from the start.
Kelly formula for calculating stake size
The formula looks a little difficult when you first see it, but it isn’t once you start using it frequently. This is how it works:
- f = (b * p – q) / b
- f – Fraction of the wagering bankroll you need to stake;
- b – Total (net) decimal odds of the wager – 1;
- p – Likelihood of a win;
- q = (1 – p) – Likelihood of a loss.
For example, let’s say that you are betting on a wager which comes with probability of 58% and decimal odds of 1.85 (-117 American). This is how the formula would look with these values in it:
- b – 1.85 – 1 = 0.85;
- p – 0.58;
- q = 1 – 0.58 = 0.42;
- f = (0.85 * 0.58 – 0.42 / 0.85 = 08
Stake in this case will be 8% of your wagering bankroll (0.08 * 100).
This means that if you ever find yourself in a situation in which the probability is 58%, but you are given odds of 1.85 (-117 American), you would need to stake 8% of your wagering budget.
If your monthly betting bankroll is $1000, you would need to back this proposition with an $80 stake. That might seem like a large portion of your budget. However, the criterion estimates that you have a very favorable likelihood and odds ratio here. This means that you will have an excellent return on investment.
Whenever f is positive, this means that you should back the bet with the bankroll percentage that the formula gives you.
Explaining the Kelly criterion with a coin toss
The best way to learn the Kelly criterion is to use as many simple examples as possible. The best one here is a biased coin toss. This is because a coin toss comes with only two possible outcomes and is fairly easy to explain.
Let’s say that this is a biased coin toss in which the outcome Heads happens 60% of the time, while the outcome Tails happens 40% of the time. The bookmaker is aware of this and gives you decimal odds of 1.67 for Heads (-150 American) and 2.5 for Tails (+150 American). These odds reflect the likelihood of each outcome and this is how wagering on them would look like:
- Wagering on Heads
- b – 1.67 – 1 = 0.67;
- p – 0.6;
- q = 0.4.
- f = (0.67 * 0.6 – 0.4) / 0.67 =003
You should back the Heads outcome with 0.3% of your wagering budget.
- Wagering on Tails
- b – 2.5 – 1 = 1.5
- p – 0.4
- q – 0.6
- f = (1.5 * 0.4 – 0.6) / 1.5 = 0
You shouldn’t back the Tails outcome.
It is obvious that when the probability for a successful outcome is higher, the percentage you need to bet is positive. This is evident from the Heads example.
In contrast, in the second example, the formula tells you that you shouldn’t back the Tails outcome. And this makes sense when you think about it. If the Heads outcome is the winning one and comes with a positive Kelly result, why would you back Tails? There cannot be two successful outcomes in a 2-way bet.
It is very important to remember that you should only back positive values. When you get a 0, you shouldn’t place a bet on that outcome.
The Kelly criterion and a basketball game
All of the odds in the coin toss example come without bookmakers’ edges. This means that they perfectly reflect the likelihood of them coming to fruition.
Unfortunately, in the real world, all bookmakers work with edges and this complicates determining the likelihood of an outcome from its odds. When you are not completely sure about the likelihood of an outcome, it’s more difficult to use the Kelly criterion.
Let’s explain how the Kelly principle would work in the real world with an example from the NBA. Let’s say the Chicago Bulls are playing the Cleveland Cavaliers. Let’s also say that you are wagering on the betting line market with a point spread of 4.5. These are the odds you would get at a real bookmaker:
4.5 point spread: Chicago Bulls -4.5 (-110) – Cleveland Cavaliers +4.5 (-110).
It is evident from this example that the two basketball teams come with the same probability to win in the betting lines market. They both have the same odds of -110 (1.91 decimal) so this means that the likelihood for each team to win should be 50%, right?
Well, not quite. The problem here is that the bookmaker has offered this NBA game with a slight edge. You can see this if you turn those -110 odds into probability. When you do this, you see that each team comes with a 52.4% bookmaker’s likelihood of winning. This comes to a total of 104.8% and that means that the bookmaker works with a 4.8% margin. In case you are unfamiliar with betting odds and edges, you can consult our betting odds guide.
This is how the formula for the NBA game will look like (we are only going to use one of the teams in this example as they both come with the same odds):
- Betting on Chicago Bulls with the Kelly formula
- b – 1.91 – 1 = 0.91
- p – 0.5
- q – 0.5
- f = (0.91 * 0.5 – 0.5) / 0.91 = -0.04
As you can see, the value is negative here and that means only one thing – don’t bet on this outcome. Placing a bet on any of these teams doesn’t make sense as their odds and probabilities don’t make for a good bet.
In addition to this rule, it is also important to only use the correct probabilities in the formula. Otherwise, it would give you incorrect values.
For example, when wagering on a 2-way moneyline market in which both teams come with the same odds for winning, the probability is 50% for each of the teams. That’s the reason why we changed the bookmaker’s probability of 52.4% with the real likelihood of 50% for both teams above. If we didn’t do that, the percentage we would have got would have been incorrect.
When to use the Kelly criterion
The Kelly criterion is best used when you can ascertain the likelihood of an outcome accurately. If you can do that, the formula would give you an optimal stake amount for each bet.
If you can always do this and always know the exact probability of an outcome, your cash flow will increase in the long run. Sure, there will be ups and downs in this. However, if you use the Kelly criterion properly, you will make a profit when wagering.
Unfortunately, determining the likelihood of an outcome is very difficult and there are several reasons for this. Firstly, you can never be sure whether the assumption you make about an outcome is the real likelihood.
Also, some wagering markets come with more than two possible outcomes. In general, the more outcomes there are, the more difficult it is to calculate probability.
Lastly, many factors influence the likelihood of an outcome. For instance, the probability of an NFL team winning after their best player is injured changes dramatically. Similarly, when two soccer players from the same team are sent off, the likelihood for that team to win also changes.
Advantages of the Kelly strategy
As you can see from the examples above, the approach comes with lots of benefits. After all, if this wasn’t the case, billionaires such as Warren Buffett wouldn’t use it in the first place.
Correct stake amounts
The Kelly criterion is great if you want to always know how much money to wager on a bet. Oftentimes people aren’t sure whether they should go with a $15 or $25 stake when placing a bet.
This is remedied instantly when they use the Kelly formula. If you know the exact likelihood of an outcome, using the equation will always tell you how much you need to stake. This would help you a lot with your sports betting money management.
No bad bets
If the formula gives you a positive value, this is a good bet. This means that the chance for making a bad bet is completely reduced.
Whenever you get 0 or negative value from the formula, that’s a bad bet and you should avoid it. Once again, determining a good bet is only possible if you know the correct likelihood of an outcome.
Low accrued losses
It goes without saying that if you only bet on good bets, you would reduce losses in the long run. Most wagering strategies achieve this goal, but the Kelly criterion is the best in this regard.
Disadvantages of the Kelly strategy
The strategy also has its shortcomings. And this is to be expected too. If it was perfect, everybody would win tons of money and bookmakers will have to shut down shop.
Aggressive amount of money
In some situations in which there are favorable wagering opportunities, the Kelly criterion would say that you need to bet lots of money. Something similar is true for other approaches such as the Martingale strategy and the Fibonacci approach. This definitely might be a problem for the budget bettor.
The key strength of this strategy is the fact that you maintain a positive cash balance but in the long run. This is not ideal for bettors who find it difficult to place large bets in short intervals.
You have to know each probability
This is the biggest drawback of the Kelly criterion. For it to be successful, you simply must know the likelihood of a wagering outcome. This is particularly difficult for betting beginners who are not always well-versed to make that guess.
Fortunately for bettors, there are experts who know their bets and probabilities out there. They make sure that each pick is a winning proposition and do their due diligence before suggesting it. That’s pretty much the case with Billy and his betting picks, so make sure to give them a try.
Kelly criterion: Try it now at one of the top 5 betting sites
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