Kelly Betting
Kelly betting The so called Kelly criterion was worked out more than half a century ago and it does not lose its popularity now. For all who starts to investigate deeply the sport betting strategies and betting it is necessary to get acquainted with the general tendencies of this method. Because the Kelly Criterion seeks to calculate the optimum stake for any value bet so as to maximise that value as well as maximise the growth of your betting bankroll. Kelly Calculator is a guideline for sports betting. Find out how much you should stake based on the odds & projected winning percentage. 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.
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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Introduction
J.L.Kelly, in his seminal paper A New Interpretation of Information Rate (Bell System Technical Journal, 35, 917-926 see below) asked the interesting question: how much of my bankroll should I stake on a bet if the odds are in my favor? This is the same question that a business owner, investor, or speculator has to ask themself: what proportion of my capital should I stake on a risky venture?
Kelly did not, of course, use those precise words — the paper being written in terms of an imaginary scenario involving bookies, noisy telephone lines, and wiretaps so that it could be published by the prestigious Bell System Technical journal.
Kelly Betting Strategy
Assuming that your criterion is the same as Kelly's criterion — maximizing the long term growth rate of your fortune — the answer Kelly gives is to stake the fraction of your gambling or investment bankroll which exactly equals your advantage. The form below allows you to determine what that amount is.
Kelly Betting Calculator
Disclaimer
Kelly Bettinger Facebook
- The Kelly Strategy Bet Calculator is intended for interest only.
- We don't recommend that you gamble.
- We don't recommend that you place any bets based upon the results displayed here.
- We don't guarantee the results.
- Use entirely at your own risk.
Kelly Strategy Bet Calculator
Results
- The odds are in your favor, but read the following carefully:
- According to the Kelly criterion your optimal bet is about 5.71% of your capital, or $57.00.
- On 40.0% of similar occasions, you would expect to gain $99.75 in addition to your stake of $57.00 being returned.
- But on those occasions when you lose, you will lose your stake of $57.00.
- Your fortune will grow, on average, by about 0.28% on each bet.
- Bets have been rounded down to the nearest multiple of $1.00.
- If you do not bet exactly $57.00, you should bet less than $57.00.
- The outcome of this bet is assumed to have no relationship to any other bet you make.
- The Kelly criterion is maximally aggressive — it seeks to increase capital at the maximum rate possible. Professional gamblers typically take a less aggressive approach, and generally will not bet more than about 2.5% of their bankroll on any wager. In this case that would be $25.00.
- A common strategy (see discussion below) is to wager half the Kelly amount, which in this case would be $28.00.
- If your estimated probability of 40.0% is too high, you will bet too much and lose over time. Make sure you are using a conservative (low) estimate.
- Please read the disclaimer below.
More Information
The BJ Math site used to contain a great collection of papers on Kelly betting, including the original Kelly Bell Technical System Journal paper. Unfortunately it is now defunct, and only contains adverts for an online casino. However, you can find much of the content through the Wayback Machine archive. The Internet Archive also contains a copy of Kelly's original paper which appeared as A New Interpretation of Information Rate, Bell System Technical Journal, Vol. 35, pp917-926, July 1956. (If this link breaks — as it has done several time since this page was written — try searching for the article title).
Kelly Betting Strategy
We based the above calculations on the description given in the book Taking Chances: Winning With Probability by John Haigh, which is an excellent introduction to the mathematics of probability. (Note that there is a misprint in the formula for approximating average growth rate on p359 (2nd edition) and the approximation also assumes that your advantage is small. There is a short list of corrections which can be found through John Haigh's web page).
Kelly Betting Blackjack
Note that although the Kelly Criterion provides an upper bound on the amount that should be risked, there are sound arguments for risking less. In particular, the Kelly fraction assumes an infinitely long sequence of wagers — but in the long run we are all dead. It can be shown that a Kelly bettor has a 1/3 chance of halving a bankroll before doubling it, and that you have a 1/n chance or reducing your bankroll to 1/n at some point in the future. For comparison, a “half kelly” bettor only has a 1/9 chance of halving their bankroll before doubling it. There's an interesting discussion of this (not aimed at a mathematical reader) in Part 4 of the book Fortune's Forumla which gives some of the history of the Kelly criterion, along with some of its notable successes and failures.
Jeffrey Ma was one of the members of the MIT Blackjack Team, a team which developed a system based on the Kelly criterion, card counting, and team play to beat casinos at Blackjack. He has written an interesting book The House Advantage, which examines what he learned about managing risk from playing blackjack. (He also covers some of the measures put in place by casinos to prevent the team winning!)
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