Kelly Criterion Sports Betting
THE KELLY CRITERION IN BLACKJACK SPORTS BETTING, AND THE STOCK MARKET1 EDWARD O. Thorp and Associates, Newport Beach, CA 92660, USA Contents Abstract 2 Keywords 2 1. Introduction 3 2. Coin tossing 4 3. Optimal growth: Kelly criterion formulas for practitioners 8 3.1. The probability of reaching a fixed goal on or before n.
The Kelly Criterion is to bet a predetermined fraction of assets, and it can seem counterintuitive. It was described by J. Kelly, Jr, a researcher at Bell Labs, in 1956. For an even money bet, the Kelly criterion computes the wager size percentage by multiplying the percent chance to win by two, then subtracting one. So, for a bet with a 70%. Professional Sports Bettor, Professional Poker Player and Trademate Sports Co-founder, Jonas Gjelstad, explains what staking strategy he uses for his sports. The Kelly criterion has several issues when it comes to the world of sports betting, as it is almost impossible to find identical events. Each event will come with its own set of challenges and outcomes. For the Kelly betting system to succeed, the punter will need a value opportunity and a positive edge.
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.
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?
It is in the heart of every bettor to see their bets turn into fruition. But not once or twice they have been forced to contend with multiple bet failures. Unprecedented turns of events has seen many quitting betting or seek alternatives due to excessive loss of money. But must things be so? Must one always suffer from a backlash of poor betting? The answer could be simple as it gets. It is about time we take a look at Kelly’s criterion.
Developed by J.L. Kelly, in 1956, the mathematical formula has over the years served as the best alternative of maximizing profit while minimizing risk. Unlike other betting criteria which never bother on bettors money, Kelly’s criterion have become the bettors choice due to its ability to bridge the gap between losing a bet and losing the entire bankroll.
Kelly’s Formula
Kelly’s formula directs a bettor on the most appropriate amount to bankroll a certain bet by using the available odds and the chances of winning.
F= (BP - Q) / B
B = the Decimal odds -1
P = the probability of success
Q = the probability of failure (i.e. 1-P)
Extensive explanation of the inputs
“B” is the entire amount one can win after a particular bankroll. In the “b to 1 ” system it is simply the stated odd less one, that is, if a speculated winning team carries odd @5, and you place a bet of $10, you win +$40
“P” is likelihood of a particular bet winning. For a team having a 20% winning chance, the probability becomes 0.2.
“Q” is the chance of losing in a particular bet. That is, in the case of a team that has winning probability of 20% the same team stands 80% chance of losing. “Q” therefore becomes 0.8. Which means it can be simplified into 1 - “P”
“F” is Kelly’s advice on the appropriate amount to bankroll a particular bet.
Application of the formula
Take an instance of a match between two teams, say Liverpool and Barcelona with odds of 2.8, 3.2, and 2.4 for win, draw and win respectively. Given that Liverpool’s probability to win is 25%, draw is 40% and that for FC Barcelona winning is 35%, using “b to 1” decimal system it follows that:
Liverpool win: FL [0.25(2.8 - 1) - 0.75] / (2.8 - 1) = - 0.375
Game Draw: FD [0.4(3.2 - 1) - 0.6] / (3.2 - 1) = 0.1273
Barcelona win: FB [0.35(2.4 - 1) - 0.65] / (2.4 - 1) = - 0.1142
Interpretation of the values
As an investor the best option for this bet would be Draw. The negative value for Barcelona and Liverpool win implies neither of the team has a sure winning potential and should not be considered while betting. With the above returns you stand to lose 11.4% of your stake for bets placed on Barcelona and 37.4 % for bets laid for Liverpool.
Pros
Kelly’s formula is fairly comprehensible and all is required from a bettor is to hunt for teams and feed the data in the formula to screen most appropriate amount to wage on a team. The criterion also ensures that a potential investor suffers the least risk at the expense of maximizing profits.
Cons
Kelly Criterion In Blackjack Sports Betting And The Stock Market
Though the point behind the criterion is to ensure there is minimum risk in the hunt for maximum profits, mistakes arising due to improper computation while using the criterion, may cost ones money to the extent of impoverishing their accounts. Secondly, since bets are never guaranteed, you stand to lose a huge amount of bankroll in the event that the formula proposes heavy betting on one outcome.