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Wagering Tools - Kelly Tool

Windows users may download a fully functional free demo copy of this tool. You should download and run the tool to follow along with the rest of the page.

The Kelly Criterion is a betting, money management and dutching system which is designed over time to maximize the growth of your bankroll. For a good description of what the Kelly Criterion is, its advantages and disadvantages, see my Kelly Criterion Page. Or if you're interested in the specifics and mathematics behind the system can be found on the Josh Kuperman's Kelly Criterion Page or if you're really into mathematics you can download a pdf version of John Kelly's Original Paper..

The Kelly tool itself is quite a bit like a cross between the Win Tool and the Dutching Tool in the complete wagering tools package. An example is pictured to the right in which we have a race with 8 horses.

Along the top the fields should be self explanitory. In the upper left is an area to enter the takeout rate at the track you're playing. It's been preset to reflect wagering in California for you. Also, depending on what form of input you are using, the takeout rate may or may not be needed (more on this later). The next item to the right is a breakage pull-down menu which will let you change between nickel, dime or no breakage. Generally you'll want to keep this set to Dime breakage. The last item on top of the Kelly tool is a box where you can enter your current bankroll, in the example pictured, we've set the bankroll to $200 and that number will be used to suggest wager amounts on the individual horses.

From left to right, the rest of the fields on the Kelly Tool are as follows:

Pools, Odds, % Pull Down Menu -- This menu for entering in the current track odds or pools. Set it to whatever info you'll be able to make use of before a race (generally win odds, but sometimes win pools).. Using Pools is the way to get the most accurate numbers, but you should be able to get similar results out of the Kelly Tool by setting this option to Odds and using the odds from the tote board. The % option will allow you to enter win percentages of specific horses instead. If you set this menu item to Odds or % then the takeout rate box will be ignored since it's assumed that the odds you'll be using will already have the takeout factored into them as they do at tracks across the country.

In Pool mode, the total value at the bottom of the column will reflect the total amount in the win pool. The example pictured is set to Pool mode and the total in the Win pool is $78,692 (the pools for the 1 and 2 horses obscured by the menu are $14,106 and $7,366 respectivly). In % or Odds mode, the total value at the bottom of the column will reflect the sum of the percentage chance all horses in the race have to win as reflected by the odds or %-line you've entered. Looking at it can help you quickly guage how accurate/balanced your the odds line you're using is. The value should be close to:

100 / (100 - takeout) * 100

So if the track you're following has a takeout rate of 15%, you'd want to make sure this value was close to 100 / (100 - 15) * 100 = 117.6. Because of the effect breakage can have though and the likelihood that some of the odds you are entering will actually be slightly off due to the rounding of odds. Anything within 5 is fairly close. If you see something signifigantly different, it's likely that you've made a mistake entering in your odds or are using a bad set of numbers. Note that the total for the % column,118.697, (3rd from the left) in our example also displays the same number and as we can see, it's close to the value we'd expect.

% To Win/Odds -- In this field, you need to enter the percentage chance you feel that each horse has to win the race either in the form of a % out of 100 or via an odds line you've created. After filling in fields for each horse, you'll see a total t the bottom of the column which represents the percentages to win for each horse.You should try to get this number as close to 100 as possible.

This is a key field becuase it's used to find overlays and underlays and leverage the odds. You'll need to create your own morning line to get the information for this field, or technically you could use the track morning line. To create you own line, you'll probably want to use the morning line tool and set the % Line to '100' or takeout to '0'. Once you've created your own line, the % fields displayed on the morning line are the fields you'll want to enter in the '% to Win' field in the Kelly Tool. For more information, refer to the example below. It's important to note that the total sum of all the percentages should add up to 100, no more, no less. If you see the total is greater or less than 100, you'll have to add or subtract from some horses to get it in line. In our example, we've given the #1 horse a 20% chance to win, the #2, a 10% chance, etc. Note that the total in the example adds up to 100% and we can quickly glance one column to the right to discern the % chance each horse has as suggested by the actual odds

% Field -- This field will display the percent chance each horse has to win as suggested by the odds on the horse. They may all add up to more than 100% since the takeout and breakage rate can affect this percentage. It's also a useful betting guideline, to ensure a profit in the longrun if you're only betting one horse per race, you want to make sure that you feel that the horse has a better chance to win the race than suggested by this field. For instance, if the % field shows that a horse has a 20% chance to win the race, you better be confident that the horse's chances are better than 20% otherwise you'll end up losing money in the long run.

Odds -- This field will show the exact odds in decimal form for the horse. It's the same number you see on the Win Tool and a more precise number than the track monitors or online toteboard systems will give you.

% Gain -- This field will only show up if you've filled out the % To Win field for the horse. It represents your expected ROI for a wager on this horse. A value of 100 means that over the long run, you'd expect to get all the money you wagered on this horse. A value of 50 would mean that over time, you should expect to lose half the money you wager on this horse. 200 would mean that you'd expect to double your money by wagering flat bets on this horse. Note that with the Kelly Criterion, you'll sometimes be asked to bet on a horse with a negative expected return. In our example, the #1 horse shows a negative extected return but the Kelly Tool suggests we place a small wager on it anyway.

Bet % -- This field will only show up if you've filled out the % To Win and it displays the recommended percentage of your bankroll you should wager on this horse. It's very possible that the tool will recommend that you wager on one or more horses (especially if there's a favorite you don't like) and it's possible that it'll recommend that you don't wager on any of the horses. In our example, the Kelly Tool recommends we bet about 0.5% of our bankroll on the #1 horse, 3.6% on the #4 horse and 4.2% on the #5 horse. The total percentage of your bankroll to bet is displayed at the bottom which is 8.32% in our example.

Bet -- This field will only display if you've entered the % To Win field. Before looking at the bet field, you should set the bankroll field to your available bankroll. After you've entered your bankroll, it'll display the suggested amount to wager (in dollars) on each horse. You'll need to round these numbers to the nearest dollar to make actual wagers. You'll often find that you'll need to round the numbers off to obtain bettable amounts. In the example, we'd probably bet $1 on the #1, $7 on the #4, and $8 on the #5.

An example:

The most critical part of making the Kelly Tool profitable is creating your own line and accuatly assesing the chance each horse has to win. So lets do an example. Consider a race with 3 horses and a takeout rate of 15.33%. Horse #1 has $100 bet to win on it, #2 $200, and #3 $300 and you have $40 available in your bankroll.

Entering those numbers into the Kelly Tool with the left menu set to pools and the right one set to % will yield the following numbers:

#Pools% To Win%Odds% GainBet %Bet

Now, it's time to enter the % To WIn you think each horse has. Let's say you think horse #1 has a 10% chance to win the race, horse #2 a 50% chance amd horse #3 a 40% chance. When you enter those numbers into the Kelly Tool you'll end up with the following:

#Pools% To Win%Odds% GainBet %Bet

So the Kelly Tool is suggesting that you wager about 17% of your bankroll on the #2 horse and suggests a wager of about $7 on that horse to maximize the groth of your bankroll over the long term.

A couple notes/issues. As mentioned on Josh's page, the Kelly Criterion has a couple small problems. The first is that it assumes that it's infinitly bad to lose your entire bankroll. While that may be true for some people, it also means that it gets harder and harder to bet if your bankroll is very small. If you only have a few dollars left, it may only suggest that you wager a few cents on a race. Since that's not practical, it doesn't work well for small bankrolls.

A good explanation of the Kelly Criterion (sort of)

(the following was taken from's Derby List FAQ -- a must read for people just getting involved in the game). The excerpt below mentions the Kelly Criterion, but there are some important differences and you should not confuse the math given below with that used by the Kelly Tool. More information about the method described below can be found on the Odds N' Edge Tool page..

Even though it's not the Kelly Criterion, the ideas and concepts about betting low odds horses or scaling back on the suggested optimal kelly bets are valid..

 Q: What is the "Kelly criterion"?
 It is a formula for calculating how much to bet. It assumes that
 your objective is long term capital growth (getting rich).
 The handicapper's choice of money management strategy is similar to
 the stock market choice between growth stocks and income stocks.
 Growth stocks tend to be more volatile, but in the long term return
 more profit. That is because the profits from growth stocks are
 reinvested rather than skimmed off. Every reinvestment is a
 calculated risk. Therefore, income stocks tend to fluctuate in
 value less, but also return less profit in the long term.
 Kelly betting is for growth. It reinvests profits, and thus puts
 them at risk. If your objective is to make small but consistent
 profits,it may be too aggressive a money management scheme. Kelly
 betting may also be too aggressive for the new player whose
 objective is to make many bets, (each one a learning experience),
 but who does not want to risk significantly depleting his bankroll
 in only a few losing bets.
 In fact, the Kelly formula defines a limit for any long term money
 management strategy: It is maximally aggressive. Betting more than
 the Kelly amount is an undue risk. Doing it habitually will slow
 long term growth.
 Here's how it works: Let's suppose you have worked out an odds
 line, and one of the horses is overlayed -- that is to say, the
 parimutuel odds being displayed are higher than the odds you
 calculated as fair. Assuming that you think the odds will "hold
 up", (that you will actually receive the posted odds if the horse
 wins), you will make a bet.
 Next question: How much?
 Assume that the object of the game is to increase the size of your
 bankroll at the maximum rate possible. If you bet too little, you
 make too little profit. But if you bet too much and lose, your
 bankroll will be reduced to the point that recovery will be
 severely delayed even if you start picking winners very
 Your intuition probably tells you to bet more when you have a
 bigger advantage, and to bet less on longshots. In a technical
 paper about data transmission(!), titled "A New Interpretation of
 Information Rate", Dr. John L. Kelly of AT&T proved that your
 intuition is absolutely correct. (see the bilbliography)
 To make your bankroll grow at the maximum rate, you should always
 bet a fraction of your bankroll, calculated as follows:
             fraction to bet (Kelly) = Edge / Odds
 The "edge" you have is the average amount of money you expect to
 win per unit wagered. For example, suppose you figure a horse would
 be a fair bet at even money (1-1), but the odds offered are 4-1.
 (This will almost never happen.) For every two times a similar race
 is run, you expect to lose once and win once, losing 1 unit and
 winning 4, for a profit of 3 units -- 1.5 units per unit wagered.
 Thus your edge is 1.5 (150%). The odds are 4, so the Kelly
 criterion says, bet 1.5/4 = 37.5% of your bankroll.If that sounds
 scary, don't worry. In the real world Kelly bets are almost always
 much smaller.
 Here is a convenient way to calculate the edge from the odds
 displayed on the tote board. Suppose you figure the horse's chance
 to be Lt/Wt ("lose-true" to "win-true") and the parimutuel tote
 board shows odds of Lp/Wp ("lose-parimutuel" to "win-parimutuel").
              Wt x Lp  -  Lt x Wp
       Edge =  ------------------   x Wp
                   (Lt + Wt)
       Odds = Lp/Wp
                (Wt x Lp - Lt x Wp)     1
       Kelly =  ------------------- x ------
                   (Wt + Lt)           Lp
 (Of course, these numbers need not be integers. For example, you
 could figure a horse's fair odds at (0.78)/1. Or you could work out
 the exact parimutuel payoff from the totals on the tote board,
 figuring in the track take and breakage, and derive the parimutuel
 odds from that. We will use integers in the examples that follow.)
 Let's try another example. Suppose you figure the horse at 4/5, but
 the parimutuel is offering 7/5.
         "True" odds     =  4/5, thus, Lt = 4, and Wt = 5
         Parimutuel odds =  7/5, thus, Lp = 7, and Wp = 5
        Substituting into the formula, we obtain,
                5 x 7  -  4 x 5
        Edge =  ---------------   = 15/45 = 1/3
                  (4 + 5) x 5
        Odds =  7/5
        Kelly = (1/3) x (5/7) = .238
 In a situation like this, you should bet 23.8% of your bankroll.
 -- Or should you?
 These calculations at short odds are very critical. (Try
 experimenting with changing the numbers very slightly.) You are
 therefore vulnerable to last minute changes in the parimutuel odds.
 You are also vulnerable to making a small mistake. How confident
 are you in that 4/5 you figured?
 Some authors recommend that you never bet on such short priced
 horses, even when you figure they are standouts to win. In that
 case, just "pass" the race, they say. That may be good advice. A
 minimum acceptable price to some handicappers is 5/2.
 Many authors also recommend scaling back on the Kelly amount,
 generally recommending betting half the indicated amount. I take a
 middle course: I think it's a good idea to scale back the Kelly bet
 when betting into short odds. In the situation above, you might
 want to give yourself a some leaway on the "true" odds. Try
 readjusting it to even money. (We are still assuming that the
 parimutuel payoff is 7/5).
                1x7 - 5x1    1         1
      Kelly =   ---------- x ---   =   ---   =   14.3%
                 (1+1)x1     7         7
 If the "true" odds are downgraded even more, down to 6/5, the Kelly
 bet is only 1.3% of bankroll.
 In his book _Winning Thoroughbred Strategies_, Dick Mitchell quoted
 William Quirin as having said that the ability to consistently make
 a profit betting low odds horses is the mark of an expert
 handicapper. The volatility of the Kelly formula at low odds
 demonstrates very graphically why that is.
        What's the different between a system, a method, and an angle.
        A system is a mechanical method of play, in general you always
 use    the same data as input (speed figs, money won, etc) to produce
 a rating for a runner.  Some systems suggest waiting for a
 particular price, or are only playable in a few races.  An angle is
 a spot play or a wager on a single factor that is usually positive.
 Two good angles are claiming race class drop w/ switch to a winning
 jockey. Allowance horse got clobbered in a stake last time out, now
 back where he was running before.  Methods are the tools used to
 put together your own style of play.  This faq covers quite a few.
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