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Wagering Tools - Kelly Tool

What is the Kelly Criterion?

The Kelly Criterion is a money management and dutching system that is designed to maximize the growth of your bankroll over the long term. Put another way, it gives bettors a method of calculating the optimal amount to bet on a horse and the best way to take advantage of overlays and underlays. Developed by John Kelly working at AT&T's Bell Labs in 1956, it's been tossed around and mentioned in numerous handicapping books and always seems to pop up when the topic of money management comes up.

This article isn't going to delve into the mathematics behind the Kelly Criterion; rather, it'll try to discuss some of the strenths and weaknesses of this money management system as well as point out a few related web sites on the internet.

How does the Kelly Criterion Work?

The Kelly system works by leveraging the odds...finding spots where there are overlays and betting a portion of your bankroll based on how much of an overlay it is. By taking into the account the expected rate of return and the risk involved Kelly's utility function maximizes the overall growth of your bankroll. Betting more than the suggested Kelly amount is an undue risk; betting less than the Kelly amount will cause your bankroll to grow more slowly.

Of course, bankroll growth isn't a guaranteed thing. Using the Kelly Criterion successfully requires that you be able to find overlays when they arise and taking advantage of them. So to use the system properly, you need to be able to accuratly assess each horse's chance to win a race and you need to be able to do it better than the crowd as a whole. If you can do this, the Kelly system is the ultimate method for taking advantage of overlays.

So using the Kelly Criterion properly means that you'll need to create your own morning line ahead of time to get an idea of how you feel the race is going to shape up. For instance, let's look at an imaginary three horse race; let's assume you've done the handicapping ahead of time and come to the conclusion that horse #1 has a 30% chance to win the race, horse #2 has a 50% chance to win the race and horse #3 has a 20% chance to win the race. However, on the tote board, the crowd has given horse #1 a 25% chance to win the race. Using the Kelly Criterion, you'll be able to figure out what percentage of your bankroll you should wager on the #1 horse. While that may be a simplification of the system, it's essentially how it works, bet when you spot overlays, hold back when you don't.

With the Kelly Criterion, you are always betting percentages of your bankroll so as your bankroll grows, so do your bets. Likewise, when your bankroll shrinks, your bets will shrink. The suggested percentages to wager can vary drastically depending on the expected rate of return on a specific bet, but you'll never find that you'll need to wager your entire bankroll on a single horse, nor a large portion of it unless you spot a huge overlay.

The math behind the system is pretty complicated. Kelly's original paper is all but unreadable to non math majors. Some useful links for figuring out the mathematics of the system and a calculator which will do all the math for you are provided at the bottom of this article.

What are the problems with the Kelly Criterion?

There are a number of problems with the system, but none that are critical or make it impossible to use. The Kelly Criterion works best when you know the final odds of all the horses involved. Since this isn't practical in pari-mutuel betting, you'll have to make do with odds taken a few minutes prior to post. It also assumes that you can judge each horse's chance of winning better than the crowd at large can (in other words, that you can accuratly spot overlays and underlays). To make money with the Kelly Criterion this is essential because the amount you are supposed to bet depends for the most part on the difference between a horse's actual odds and the fair odds as you perceive them.

The Kelly Criterion is also meant to be a long-term money management system. Rather than going to the track each weekend with $100 in your pocket and betting it all, it's assumed that you are keeping track of your overall bankroll for a long period of time, not replenishing it with new money each time you head out to the track. For most handicappers this is a complete change in the way you deal with your money and it'll require you to set aside a bankroll which you'll need to stick with for a while. Using the Kelly Criterion any other way is pointless because it defeats the purpose of Kelly's system which is long term bankroll growth.

The Kelly Criterion also becomes less practical to use when your backroll gets smaller. In his original paper, John Kelly assumed that you could always bet a percentage of your bankroll, even when that percentage amounted to less than a dollar. Mathematically this works great, bet 50 cents of the one dollar remaining in your bankroll, if you lose, bet 25 cents, etc. However, at a track that only allows $2 minimum bets you'll quickly realize how silly this is. So if your bankroll goes down to a few dollars, it's probably a good time to make a mental note that your ability to spot overlays isn't as good as you thought it was and start over from scratch.

It's also very possible that the Kelly Criterion will advise you to make a wager (albeit a small one) on a horse with negative expected rate of return. In other words, a horse may be at odds of 40-1 on the board and you might perceive its fair odds to be 35-1, but you'll be told to bet a small amount on the horse anyway. That's just the way the math works and it's the exception, not the rule.

The Kelly Criterion also requires some preparation before heading to the track and a lot of math. Many handicappers aren't used to creating their own morning line before heading out to the track, but if you want to use Kelly's method, it's a must. Some simplifications of the system allow you to simply figure out how much to bet based on the odds of a horse and the odds you feel it should be at, but I wouldn't reccommend using those variations unless you're too lazy to build your own morning line.

For most people, it's simply too much math to do in one's head or to use a calculator at the track as a result, many handicapping books have boiled Kelly's method down to simple statements such as:

Bet more money as your bankroll grows and less when it shrinks.


Bet a certain percentage of your bankroll.


Bet more on a horse when you perceive it to be an overlay and less when it's an underlay.

While all true, these statements may do more harm than good because if put into use without underlying math, they do no more than make you feel like you're using good judgement. The actual Kelly Criterion allows you to quantify exactly how much you should bet on a given horse based upon its odds and what you consider to be fair odds. The above statements do no more than summarize some of the aspects of the Kelly Criterion.

While there are some mathematical simplifications of the Kelly Criterion that make it easier to use, they are also approximations and don't always suggest the proper amount to wager on each horse. To be used at the track, you'll need a computer program or programmable calculator to do all the number crunching for you.

Fortunatly, I've written a Kelly Criterion calculator and have made it available as a Free free download for Windows users along with instructions on what the various fields mean and how to use it

Scaling Back on the Optimal Kelly Wager

For some people, maximizing the growth of your bankroll may not be the most important objective. While you have to admit that it sounds appealing, isn't it just as important to ensure that you don't lose everything? If safety is your prime concern, but you still like the idea of growing your bankroll, some studies have suggested fractional Kelly methods. For instance, instead of betting the optimal Kelly amount, wager 1/2 or 1/4 of the suggested amounts. Such strategies have the benefit of reducing the liklihood you'll lose all your money. At the same time they'll tend to slow down the expected growth of your bankroll. It really depends what's a more important long term goal for you, growth or safety.

There are also times when the suggested Kelly bet may be larger than you can stomach. In these cases, it's sometimes suggested that you scale back just to be safe. If that horse you felt had a 2-1 shot to win the race is showing up on the tote board at 40-1, it might be suggested that you wager a large portion of your bankroll. Unless you are truly sure you're 2-1 assesment is correct, it might be wise to wager a little less.

Related Links

  • Josh Kuperman's Kelly Criterion Page

    For a fairly simple explanation of the mathematics behind the Kelly Criterion (note that this page also contains a small error, the example calculation .240 - 0.584 / 0.510 should read .240 - 0.584 / 8.14).

    Also, since it's not quite clear on Josh's page, the 'bet' column reflects the percentage of your bankroll that you should bet on that horse. .205 means 20%. That may seem scary to some people, but if you see a horse with a fair value of 3-1 going off at odds of 10-1, it's a good bet (assuming your fair value is right).

  • John Kelly's Original Paper

    In Adobe Acrobat format and only for the mathematically inclined. Otherwise it'll all seem like jibberish.

  • Free Kelly Criterion Calculator for Windows Users and instructions on what the various fields mean and how to use it

    Non-racing related pages

    There are plenty of articles, reasearch papers, and discussions about the Kelly Criterion online as they related to other types of gamling. Just type in Kelly Criterion in any search engine and you'll get a nice list of pages. Some that I'd recommend

  • Kelly Betting Index -- A collection of articles and research papers on the Kelly Criterion.

  • Odds N' Edge Tool -- Information and a free download for a system similar to the Kelly Criterion, but with a couple important differences.
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