kelly bet question

[formula_2002]

I ran a Kelly bet using a current data base that returned 1.10 win pool roi.
I set the edge at .05 and the odds at final track odds.
There were 562 plays
I seeded the Kelly bankroll with $1124.
At the end of the 562 plays, the Kelly bankroll was $2403.
Total Kelly bet was $41,869.
The profit =3%
The flat bets returned $1238 for a 10% profit.

Although a Kelly bet returned 214% more than the flat bet,
the investment was considerably more than a flat bet.

Is this the way Kelly bets work?

[formula_2002]

http://www.albionresearch.com/kelly/default.php
kelly calculator
with a starting br of $1124, betting on a .20-1 horse having a 5% edge, the calculator's bet size is $247.00.
I determined that a .20-1 odds at a 5% edge has a probability of winning equal to 1/(odds+1)*1.05. or an 87%.



I calculated the bet size as $281.

1124*edge/odds = 1124*(.05/.20)=$281

while the total bet may vary a bit, it seems the outcome may be of the same gender.

Kelly does not increase your roi, it increases you net worth

anyone agree or disagree?.

[Overlay]

I ran a Kelly bet using a current data base that returned 1.10 win pool roi.
I set the edge at .05 and the odds at final track odds.
There were 562 plays
I seeded the Kelly bankroll with $1124.
At the end of the 562 plays, the Kelly bankroll was $2403.
Total Kelly bet was $41,869.
The profit =3%
The flat bets returned $1238 for a 10% profit.

Although a Kelly bet returned 214% more than the flat bet,
the investment was considerably more than a flat bet.

Is this the way Kelly bets work?

Dick Mitchell also noted the risk associated with full Kelly bet sizing when he wrote on page 96 of Commonsense Betting, "It can be proved mathematically that by using this edge-to-odds ratio for a very large number of races (approaching infinity), your bankroll will be larger than it would be if you used any other betting scheme. Unfortunately, this optimum percentage doesn't guarantee safety. If you want to improve the safety factor dramatically while preserving a steep rate of growth, it's best to choose a 'fractional Kelly strategy'. For parimutuel wagering, 50 percent Kelly is adequate. (This percentage depends upon your win percentage and average mutuel.) A very good rule of thumb is to never let a single win bet exceed 5 percent of your capital and never let a place or show bet exceed 10 percent of your capital."

[formula_2002]

Dick Mitchell also noted the risk associated with full Kelly bet sizing when he wrote on page 96 of Commonsense Betting, "It can be proved mathematically that by using this edge-to-odds ratio for a very large number of races (approaching infinity), your bankroll will be larger than it would be if you used any other betting scheme. Unfortunately, this optimum percentage doesn't guarantee safety. If you want to improve the safety factor dramatically while preserving a steep rate of growth, it's best to choose a 'fractional Kelly strategy'. For parimutuel wagering, 50 percent Kelly is adequate. (This percentage depends upon your win percentage and average mutuel.) A very good rule of thumb is to never let a single win bet exceed 5 percent of your capital and never let a place or show bet exceed 10 percent of your capital."
Thanks, I'm going to take that as a yes. :)
Now I'll adjust the net worth for a 3% rebate and see what happens.

[Dave Schwartz]

I ran a Kelly bet using a current data base that returned 1.10 win pool roi.
I set the edge at .05 and the odds at final track odds.
There were 562 plays
I seeded the Kelly bankroll with $1124.
At the end of the 562 plays, the Kelly bankroll was $2403.
Total Kelly bet was $41,869.
The profit =3%
The flat bets returned $1238 for a 10% profit.

Although a Kelly bet returned 214% more than the flat bet,
the investment was considerably more than a flat bet.

Is this the way Kelly bets work?


Formula,

Yes, it is precisely the way Kelly works.

I have been saying this for years and the supposedly smart guys laugh at me:

Kelly lowers your ROI!


That is why I use the HorseMarket Investing strategy. If you read the marketing piece you will see whay Kelly does that.

http://www.horsestreet.com/products/hmi/index.html



Try this - look at the average bet size on the wagers you won and average bet size on your losers.

The short version of "why" is that you wind up betting more money on your losers than your winners.


It is possible to reverse that trend.

You do not make MORE money, but you bet substantially less winning about the SAME amount.


Imagine if you could actually RAISE your ROI! That is what HMI does. (The Opponent Method also raises your ROI but is a bit too anti-Kelly for most people.)


Regards,
Dave Schwartz

[formula_2002]

Thanks, I'm going to take that as a yes. :)
Now I'll adjust the net worth for a 3% rebate and see what happens.
that puts the final br $4056, 328% better than a flat bet, no rebate return.

average bet size was $100. largest bet was $1020 on a .20-1 horse

[Dave Schwartz]

Doesn't matter what percentage you set it to. Kelly will ALWAYS reduce your ROI from the flat bet ROI.

[GameTheory]

Yes, that's the effect, but to really do Kelly wagering properly you don't "set your Kelly percentage" and that's that -- you adjust it to the conditions of EACH bet. If you can't do that, then you can use a percentage for a group of bets taken together, but even that is different than just taking some average and applying it to every race. (The wrong average, usually.) That is "fixed percentage of bankroll" betting. Kelly uses a percentage, but it is anything but fixed, unless every one of your bets carries the same probability of winning and pays the same odds. Varying it the conditions of the each proposition is sort of the point. The misunderstanding and misapplication of Kelly has given it a reputation worse than it deserves, but nevertheless "full Kelly" betting will take you on a ride with high peaks and subsequent huge drawdowns. Part of the problem, of course, is that the original formula from which "Kelly" gets its name was actually based on a fixed-edge proposition, like a coin toss, but when applied to something where the size of the payoffs varies, it gets more complicated.

[formula_2002]

the data base contains only favorites and second choices (thats where all the profit is)
even at that, the odd swings can be large, say .20 -1 through 4-1, but, and its a big but, they are profitable in somewhat small increment.
>0<1
>=1<2
>=2<3
>=3<4
ofcourse if I could have it my way, the increments would be in one percentage points.!
I must admit I didn't realize Kelly gained wealth and lowered the roi until I did the work (only recently possible :) )

[DJofSD]

http://en.wikipedia.org/wiki/Kelly_criterion

[JeremyJet]

Is this the way Kelly bets work?

In its simplest form, betting on only one proposition, it reduces to edge divided by odds . The general formula is considerably more complex, and provides for
wagering on multiple, mutually exclusive propositions.

Regards,

JeremyJet

[formula_2002]

In its simplest form, betting on only one proposition, it reduces to edge divided by odds . The general formula is considerably more complex, and provides for
wagering on multiple, mutually exclusive propositions.
Regards,

JeremyJet

thanks, I think I'm going to stay away from that for the moment and concentrate on making the model find the inclusive plays :)

[JeremyJet]

Dave's approach is a martingale betting system. The problem with that approach is that it doesn't consider how good the bet is. It's only based on if you won or lost your previous bet.

Regards,

JeremyJet

[formula_2002]

Dave's approach is a martingale betting system. The problem with that approach is that it doesn't consider how good the bet is. It's only based on if you won or lost your previous bet.

Regards,

JeremyJet
I think he assumes a GOOD bet.
Given a positive roi and small deviation in the odds with relative high probability, can martingale beat kelly? that is increase wealth and increase ROI.
Under those those conditions, positive roi and small deviation in the odds with relative high probability, its not so much martingale, but perhaps figuring out bet size using the normal curve. If you know you should end up in the tail of the curve, bet it that way..incease bet size as you lose!!! :)

[Overlay]

Yes, that's the effect, but to really do Kelly wagering properly you don't "set your Kelly percentage" and that's that -- you adjust it to the conditions of EACH bet....Kelly uses a percentage, but it is anything but fixed, unless every one of your bets carries the same probability of winning and pays the same odds. Varying it the conditions of the each proposition is sort of the point.

I believe that adjusting bet size based on degree of edge in individual races (rather than on a longer-term basis) is what Mitchell referred to as "hyper-Kelly". He commented, "From a theoretical point of view, the hyper-Kelly method is the absolute best way to do things. The problems associated with it are the accuracy of your probability estimates, and last-minute changes in odds....The ability to estimate [a horse's chances] is the essential skill required for consistent winning....The way to approach the problem of estimating probabilities is stochastically. We'll keep track of our win percentage for a large group of 'typical' races. We'll use that number as an estimator. We'll choose a very conservative range around that estimator and build in a huge error factor. This will assure us of a minimum-boldness strategy."

He further said that the hyper-Kelly approach satisfies the Ziemba and Hausch listing of desirable characteristics of a money-management system, where bet size is influenced by 1) current bankroll size; 2) the likelihood of winning the bet; 3) the difference between the public probability of winning the bet and the actual probability (that is, the degree of "edge"); and 4) the relative importance placed by each individual on achieving bankroll growth versus avoiding bankroll loss.

[GameTheory]

I believe that adjusting bet size based on degree of edge in individual races (rather than on a longer-term basis) is what Mitchell referred to as "hyper-Kelly". He should have called it "Kelly", and the averaged version "dumbed-down Kelly" or possibly more accurately "losing Kelly". It is not individual races so much that is important, but individual PROPOSITIONS -- you define the proposition. It could involve a whole group of races, but then you need to treat the whole group as a SINGLE wager, and whatever percentage of bankroll you come up with is for the whole group, presumably with a fixed flat dollar amount for each component wager that is determined before the first race is run.

But when you take a group of wagers, determine the overall edge, and then average it as if each wager has the same edge and use that to compute your "optimal fraction" which you are going to bet on every race from now until forever, you are doing it all wrong. That is what most people call Kelly betting, and it isn't. (If you do insist on using a fixed percentage based on an average, at least compute the correct average -- use the geometric mean instead of the usual arithmetic mean.)

[CBedo]

As was stated before, one issue with Kelly is knowing the true edge. Given the possible catastrophic results from overbetting your bankroll, this is why most go to a "fractional" Kelly. One interesting way to look at it is to graph your results for the same type of bet by the percentage bet size (use your Kelly percentage as the midpoint of the range and graph it plus/minus a number of percentage points on either side. You should see a graph that to some extent is that starts a some point, rises to a peak, and then falls off again (inverse parabolic). The interesting information to be gained should be a) where the peak is (which hopefully should be roughly the kelly number), and b) the sensitivity of the results. If the graph rises to s steep peak and then falls dramatically, be careful. This means that if you get the percentage wrong, you could have some serious problems. What you would hope to see would be a nice flat curve with not much change in results for changes in the bet size.

[Dave Schwartz]

Dave's approach is a martingale betting system.

This would be absolutely false.

There is nothing even remotely close to doubling up any more than Kelly is a parlay method.

[robert99]

Yes, that's the effect, but to really do Kelly wagering properly you don't "set your Kelly percentage" and that's that -- you adjust it to the conditions of EACH bet. If you can't do that, then you can use a percentage for a group of bets taken together, but even that is different than just taking some average and applying it to every race. (The wrong average, usually.) That is "fixed percentage of bankroll" betting. Kelly uses a percentage, but it is anything but fixed, unless every one of your bets carries the same probability of winning and pays the same odds. Varying it the conditions of the each proposition is sort of the point. The misunderstanding and misapplication of Kelly has given it a reputation worse than it deserves, but nevertheless "full Kelly" betting will take you on a ride with high peaks and subsequent huge drawdowns. Part of the problem, of course, is that the original formula from which "Kelly" gets its name was actually based on a fixed-edge proposition, like a coin toss, but when applied to something where the size of the payoffs varies, it gets more complicated.

Agree with that description of Kelly.

To philosophise - the objective of Kelly is to leverage every bet to maximise the edge for that bet so that a given bank increases at its optimum rate.
ROI is a bogus and misleading metric for that purpose.
If you want to double your bank as quickly as possible then how much your bank is churned in the process is irrelevant.

For optimum returns you have to know the edge accurately. Too high or low an estimation and returns drop. Horse racing has a different edge each bet but over the long term you can consider this a several sets of say 5%, 10%, 15% etc edges and the original theory of a fixed edge each bet holds but volatility will be a mix of all these edges in whatever sequence they come in.

A long term Kelly betting management scheme is extremely volatile - a roller coaster ride. Peaks of high current bank size are quickly followed by troughs. The advantage, if you keep going, are that the subsequent troughs gradually show an increase in total bank. So ROI can rise or fall at any point depending where in the sequence it is measured but, long term, wealth grows slowly as total investment mounts up.

The bank can never go to zero but at every bet at full Kelly there is a 90% chance that 10% of the original bank can subsequently be lost and a 10% chance that 90% can be lost. If you lose 90% early on it takes a very long time for the bank lost to rise back up to its original level.

Betting half the theoretical stake reduces volatility considerably at a cost of reducing the bank growth by 25%. It just take longer on average to increase the bank to the size full Kelly would. However, it can take a shorter period if you were to lose 90% of bank early, say, using full Kelly. You can also look at half Kelly as reducing your edge estimate by 50% so you are tending towards a safer side.

PMU betting has the added problem of not knowing the return price as well as the problem of estimating the edge. Once Kelly stakes grow large and they do so quite rapidly, you are winning your own back in an ever larger part.

[formula_2002]

The data base generates a number, that for years I was not quite sure what to do with it.
It is generated prior to the closing odds and is not even adjusted for scratches.
I think I have found a use for it in determining bet size in a positive roi game.

Br*(.1/(1/number))=bet size.

Starting with a $1124 br,the data base returned a flat bet total of $1238 for a roi of 1.10.

Using the calculated bet size, the $1124 br evolved into $6619.
In 562 plays total bet was $68746 and generated a wealth index :) of $6619/$1124=5.89

[formula_2002]

THE FILE IS TOO LARGE TO POST HERE ON PA.
I POSTED IT ON MY WEB SITE.
I WOULD APPRECIATE COMMENTS.

CLICK ON WEALTH BET DATA

THANKS


The data base generates a number, that for years I was not quite sure what to do with it.
It is generated prior to the closing odds and is not even adjusted for scratches.
I think I have found a use for it in determining bet size in a positive roi game.

Br*(.1/(1/number))=bet size.

Starting with a $1124 br,the data base returned a flat bet total of $1238 for a roi of 1.10.

Using the calculated bet size, the $1124 br evolved into $6619.
In 562 plays total bet was $68746 and generated a wealth index :) of $6619/$1124=5.89

[JeremyJet]

This would be absolutely false.

There is nothing even remotely close to doubling up any more than Kelly is a parlay method.

On your wesite, HMI "The most powerful overall approach to money management and wagering ever devised"

http://www.horsestreet.com/products/hmi/index.html

Kelly, in it's simplest form, outperformes your money management system. Your knock against Kelly is how much money was wagered with said methodology campared to your system. But aren't you on PaceAdvantage advocating the world of rebates? Why would a player, looking for a rebate, look to cut down on his action? Or is this "overall approach to money management" not for everyone?

Regards,

JeremyJet

[Robert Goren]

I think that most people miss apply Kelly. I think they miss figure the edge. I have seen people use the ROI as the the edge. THIS IS WRONG. The correct way to figure it is to figure the percentage chance form the sample of the odds. For instance 3-2 is 0.40, 2-1 is 0.33 ect. You average these percentages to get your expected win percentage. You then take your actual win %- your expect win% to get your edge. I know the ROI is easier figure but you get skewed result. The higher the ROI the more skewed . Lets say your ROI was $1.90 per dollar wagered. The ROI edge would be 0.9. On an even money shot you wager 90% of your bank roll. If the win % was 0.30% and the average expected win % was 0.16% the edge would be 0.14 and you wager 14% of your bankroll on an even money shot.

[Dave Schwartz]

Mr. Jet,

Rebate players are a special breed. The goal is to put as much money through the window as possible. If you are flat bet profitable without the rebate then you should add more horses or bet more money so that you are not profitable.

My belief is that the goal is NOT to JUST grow the bankroll. If Kelly would grow my bankroll from (say) $1,000 to $5,000 over some number of bets, I believe it would be superior to grow that same bankroll from $1,000 to $4,900 while betting only half as much money.

If I can accomplish that, then, of course, I could use HMI and bet the money more agressively - theortically almost doubling the wager sizes (to be equal with Kelly handle) and win far more money.

The quote from your prior post has me wondering...

Dave's approach is a martingale betting system. The problem with that approach is that it doesn't consider how good the bet is. It's only based on if you won or lost your previous bet.

These two bold sentences apply precisely to Kelly as well. Do you see that?


Regards,
Dave Schwartz

[GameTheory]

These two bold sentences apply precisely to Kelly as well. Do you see that?
How so? To figure your optimal (Kelly) percentage, you need to know your current bankroll, and the probability of winning and potential payoff of the bet you are about to make. That's the "how good the bet is" part. As far as whether you won or lost your last bet, that is not part of the equation, and in fact wouldn't matter if you had never made a bet before and never intend to again (after this one). Kelly, done properly, uses no history and has no memory. It doesn't care if you are in the red, black, or whatever. Bankroll, probability, odds -- that's it. If those parameters are the same, the bet is the same. I won't speak for HMI because my memory on that is fuzzy on that and I don't feel like looking it up, but many other systems have you betting different amounts in exactly the same scenario for the upcoming wager because of what happened previously in the sequence and whether you or up or down relative to some starting point. Which has its psychological uses, but makes no mathematical sense.

[JeremyJet]

These two bold sentences apply precisely to Kelly as well. Do you see that?

No, I don't see that.

Regards,

JeremyJet

[formula_2002]

Dave, the 562 play data base and a $1124 starting bankroll produced the following results;

$1238 for a flat bet. A ratio of 1.10. (which is of course the roi)
$2403 for a Kelly bet, based on a 5% edge. A ratio of 2.14
$4094 for a JCM BET, based on a 5% edge. A ratio of 3.64

JCM BET = EDGE/ PROGRAM GENERATED NUMBER, INDEPENDENT OF FINAL ODDS.

using a 10% edge, a Kelly bet returned a loss
using a 10% edge, a JCM bet returned $6619. A ratio of 5.89.

If you like, I will e-mail the data base in excel format to you.
Perhaps we can compare your "Ratio" to the above.

Thanks
JCM :)

[Dave Schwartz]

In order to easily compare apples to apples, I would need the data where you are betting the same percentage in each race.

We can then compare to that.

Send it with a single column of payoffs (including zeroes for losers).

[formula_2002]

In order to easily compare apples to apples, I would need the data where you are betting the same percentage in each race.

We can then compare to that.

Send it with a single column of payoffs (including zeroes for losers).
on its way,, thanks

[Dave Schwartz]

It appears from the file that you sent, that you are wagering fractional dollar amounts. Could we please work in the real world?

I can make this work but nobody can play with that kind of precision - unless you know of a place that allows you to wager $6.73 in the win pool.


Dave

[formula_2002]

It appears from the file that you sent, that you are wagering fractional dollar amounts. Could we please work in the real world?

I can make this work but nobody can play with that kind of precision - unless you know of a place that allows you to wager $6.73 in the win pool.


Dave
dave, disregard my feable attemps.
Base on the information presented in the table i.e final odds and win position and a starting bankroll of $1124 what is your final bank roll ( if needed i'll accept fractional bets from you and use my commonn sense to interpert your results) :) you know like x100

[Dave Schwartz]

I will try to get to this before the day is up. I have a big programming day today.


In order to do a fair comparison we will need to know some other info about your results, so please post this:

1. Biggest drawn down.
2. Return on investment (i.e. advantage)


Remember that the PURPOSE of HMI is to raise ROI.

Also, HMI is a "session" tool. Thus, the goal will be to "win a session before losing it." This becomes important to any true professional. As an example, suppose your BR hit $100,000 and your optimum bet is 5% of bank. You simply cannot wager that much.

IMHO, anyone who wagers (say) 5% of a professional-sized bankroll would have to be nuts. I mean, imagine if you had built your BR up to (say) $10,000 and you lost 10 in a row - your BR has dropped 40%!


Dave

[lansdale]

I ran a Kelly bet using a current data base that returned 1.10 win pool roi.
I set the edge at .05 and the odds at final track odds.
There were 562 plays
I seeded the Kelly bankroll with $1124.
At the end of the 562 plays, the Kelly bankroll was $2403.
Total Kelly bet was $41,869.
The profit =3%
The flat bets returned $1238 for a 10% profit.

Although a Kelly bet returned 214% more than the flat bet,
the investment was considerably more than a flat bet.

Is this the way Kelly bets work?

Formula 2002,

This is, in general the way that Kelly works, but this is a very crude approach which, as many have suggested in this thread, needs major tweaking. First of all, ignore what Dave Schwartz is saying about Kelly and listen to Game Theory.

Kelly has been proven beyond doubt to be superior to all other investing techniques in compounding wealth assuming an investor edge. It was crucial to the success of William Benter and Alan Woods ('entropy' on this site), who made hundreds of millions in the Hong Kong betting pools, and even moreso to Edward Thorp, who pioneered its use in one of the earliest hedge funds, making billions in the process, and continues to use it to this day.

If you decide to continue in this direction, and I think you should, I strongly suggest you do some reading.

'Fortune's Formula' by William Poundstone, which is basically the story of how Thorp and his MIT colleague Claude Shannon, famed for his contribution to information theory, learned to apply Kelly as a gambling and investing tool.

'Efficiency of Racetrack Betting Markets' - Ziemba and Haush. This volume of academic monographs contains the seminal paper of Benter on his method, including material on his use of fractional Kelly bet-sizing. It's clear that one of the big advantages of using logit regression was that the 'modular' component of factor-weighting provided him with a very precise estimate of a horse's wager value.

'Blackjack Attack' - Don Schesinger. I realize that the relationship between blackjack and handicapping may seem remote, but the efficacy of Kelly in all forms of wagering unites them. Maybe worth noting that Benter, Woods, and Thorp all began by understanding the power of Kelly by doing very well as card counters before moving on to other pursuits. Don Schlesinger is the guru of blackjack mathematics, a brilliant man who although retired from running the derivative-trading desk at Morgan Stanley, continues to train their traders. Reading his book will give you a good idea of the concept of optimal bet ramping and how Kelly bet-sizing works in the real world.

Don't have more time right now, but if you have an edge - and it seems you do - Kelly is the answer.

Cheers,

lansdale





'Blackjack Attack' - Don

[lansdale]

I ran a Kelly bet using a current data base that returned 1.10 win pool roi.
I set the edge at .05 and the odds at final track odds.
There were 562 plays
I seeded the Kelly bankroll with $1124.
At the end of the 562 plays, the Kelly bankroll was $2403.
Total Kelly bet was $41,869.
The profit =3%
The flat bets returned $1238 for a 10% profit.

Although a Kelly bet returned 214% more than the flat bet,
the investment was considerably more than a flat bet.

Is this the way Kelly bets work?

Forumula,

This is a pretty good summary, by an investor, of the way Kelly works.

http://www.lmcm.com/pdf/sizematters2.pdf

[GameTheory]

Formula 2002,

This is, in general the way that Kelly works, but this is a very crude approach which, as many have suggested in this thread, needs major tweaking. First of all, ignore what Dave Schwartz is saying about Kelly and listen to Game Theory. Formula listen to me? That'll be the day. I certainly wouldn't ever tell anyone "Don't listen to Dave Schwartz", but when it comes to Kelly, be very careful about listening to *anyone* as it is widely misunderstood. We should probably start saying "optimal betting" or "bet sizing for maximum growth" instead as the normally understood definition of Kelly in the gambling world is just plain wrong. I've seen lots of articles, papers, and reports that are anti-Kelly, but the problem with all of them is that they aren't talking about what Kelly is (or is supposed to be), although the discussions I've seen in the mathematically-inclined sports betting forums are much more astute on the subject than in the horse-racing world so maybe people are getting the picture.


'Fortune's Formula' by William Poundstone, which is basically the story of how Thorp and his MIT colleague Claude Shannon, famed for his contribution to information theory, learned to apply Kelly as a gambling and investing tool. Great book for those interested in this sort of thing -- mainly non-technical.

'Efficiency of Racetrack Betting Markets' - Ziemba and Haush. This volume of academic monographs contains the seminal paper of Benter on his method, including material on his use of fractional Kelly bet-sizing. It's clear that one of the big advantages of using logit regression was that the 'modular' component of factor-weighting provided him with a very precise estimate of a horse's wager value.Large portions of this are now available online:

http://books.google.com/books?id=HX2xapyqENsC&lpg=PP1&dq=Efficiency%20of%20Racetrack%20Betting%20Markets&pg=PP1#v=onepage&q=&f=false

[formula_2002]

Formula 2002,
'Fortune's Formula' by William Poundstone, which is basically the story of how Thorp and his MIT colleague Claude Shannon, famed for his contribution to information theory, learned to apply Kelly as a gambling and investing tool.

'Efficiency of Racetrack Betting Markets' -

We are on the "same page"
All the above have made it to the status of being on my night table!! :)
For some time I might add.
What has sunk in recently it the concept of disregarding roi as a measure of success in a positive edge enviorment.
My own figure, if it can stand the test of time, would bring Kelly to another level.

[formula_2002]

I will try to get to this before the day is up. I have a big programming day today.


In order to do a fair comparison we will need to know some other info about your results, so please post this:

1. Biggest drawn down.
2. Return on investment (i.e. advantage)


Remember that the PURPOSE of HMI is to raise ROI.

Also, HMI is a "session" tool. Thus, the goal will be to "win a session before losing it." This becomes important to any true professional. As an example, suppose your BR hit $100,000 and your optimum bet is 5% of bank. You simply cannot wager that much.

IMHO, anyone who wagers (say) 5% of a professional-sized bankroll would have to be nuts. I mean, imagine if you had built your BR up to (say) $10,000 and you lost 10 in a row - your BR has dropped 40%!


Dave
Dave, I dont understand why 1 and 2 are important.
I start out with $1124, bet a total of $68,746 and got a return of $6619.
What's your total bet and return?
Hey, I'm happy for you if it's more!!!

Disregard pool size. Adjustments can be made..

[CBedo]

What has sunk in recently it the concept of disregarding roi as a measure of success in a positive edge enviorment.From a business standpoint, we misinterpret the term roi in horse racing probably. Really what most are calliing their roi (or their edge) is a profit margin per transaction. In business terms your return on assets is your profit margin multiplied by your asset turnover ratio, which in horseracing is a measure of how much money you can jam through the window. If you think about it, it makes perfect sense. I think most of us could raise our edge dramatically by only playing our best race of the week (maybe, lol), but what good is a huge edge if you can only make one bet a week? The other side of that is the "grocery store" model. Most grocery stores live off razor thin margins, but they are very efficient with inventory turning it over many times. Small margins, but still nice returns (two horse win betting comes to mind as a possible application).

So you are on the right track to not put "roi" on a pedastel; you have to think about it in terms of the bigger picture.

And just like there are tradeoffs with differing profit margin models, there are issues with turnover as well, usually relating to working capiital liquidity and safety.

[Dave Schwartz]

See, we have different goals. You function in the theoretical world.

My goal is raising ROI. Yours is most money.

I find your goal impractical. Sounds good on paper but nobody (including Benter) EVER bet his Kelly of TOTAL bankroll.

They may well use Kelly to size their wagers proportionately for risk purposes... That means they should wager 10 units on a horse at 2/1 with a 40% hit rate and 4 units if they have a 5/1 horse with 20% hit rate.


See, Kelly is, and always has been theoretical.


I repeat, the goal is to raise (rather than lower) your ROI. You have experienced a lowering of ROI - which is what I have said all along that Kelly does.

If you and others are only concerned with growth then HMI serves you no purpose.

Again, in my opinion winning (say) 90% as much money but betting only 50% as much money is a better place to be.


Disregard pool size. Adjustments can be made..

LOL - What "adjustments?" When your bankroll reaches $500,000 and you're supposed to bet $25,000 how are you going to do that?


Betting "fractional" Kelly is not "Kelly." It is no longer Kelly at all. It is just "betting percentage of bankroll. This is also known as "increasing after a win."



I have no desire to get into a pissing match here... I have seen this before. Like the guy that sends me a sample where he gets 73% winners at 8/5. If anyone has a system THAT good, you simply go out and bet the money anyway you want and wait for the money to engulf you.

HMI was designed for the player that is marginally profitable with a reasonable hit rate who is looking to play a session-type approach. (That is, they are not trying to put their ENTIRE BR at risk VERY day.)


Regards,
Dave Schwartz

[Dave Schwartz]

Chris,

You are absolutely correct. However, when you can have an 65% drawdown on total bankroll with 20 consecutive losers, (at 5% of bank) one simply does not play that way in the real world when they are playing 5-figure bankrolls.

I certainly understand that the goal is to grow the bankroll. However, I contend that in the real world my bankroll will grow faster+safer if I can increase my flat-bet ROI as opposed to seeing it decrease.

Now, perhaps not everyone agrees with that position. So be it. Please let me know how that turns out for you.



Dave

[formula_2002]

See, we have different goals. You function in the theoretical world.

My goal is raising ROI. Regards,
Dave Schwartz

Excellent..

Dave, what a great oppurtunity you have here.
I've given you enough data for you to show your stuff.
(the same kind of same data you present on your web site)

SHOW ME THE MONEY ALREADY!! :(

[formula_2002]

Chris,

You are absolutely correct. However, when you can have an 65% drawdown on total bankroll with 20 consecutive losers, (at 5% of bank) one simply does not play that way in the real world when they are playing 5-figure bankrolls.

I certainly understand that the goal is to grow the bankroll. However, I contend that in the real world my bankroll will grow faster+safer if I can increase my flat-bet ROI as opposed to seeing it decrease.

Now, perhaps not everyone agrees with that position. So be it. Please let me know how that turns out for you.



Dave


In the 500+ plays, it appears there were never more than 6 win bet losses in a row...

[CBedo]

Chris,

You are absolutely correct. However, when you can have an 65% drawdown on total bankroll with 20 consecutive losers, (at 5% of bank) one simply does not play that way in the real world when they are playing 5-figure bankrolls.

I certainly understand that the goal is to grow the bankroll. However, I contend that in the real world my bankroll will grow faster+safer if I can increase my flat-bet ROI as opposed to seeing it decrease.

Now, perhaps not everyone agrees with that position. So be it. Please let me know how that turns out for you.



DaveI think we are saying the same thing in a different way. The bottom line is we want to grow our bankroll as fast as possible within a certain comfortable risk threshold. My point was that roi or edge or margin or whatever you want to call it is only half the story.

[Dave Schwartz]

I am working on your data now... will post the results in a short while.


Dave

[Dave Schwartz]

Okay, I did this with no tweaking...

I actually just accepted the settings I had in the last time I ran the system in a demo.

This sample was absolutely perfect for HMI because of your low runouts/high consistency. It worked out better than even I am used to seeing against Kelly.


http://www.horsestreet.com/BBSImages/Formula-01.png

I used 5% as the Kelly Bet% because I was thinking that was what you said. Perhaps it should be higher? (My flat bettor says it should be 7.1%.) Let me know and I will plug that in.

Advantage
11.7% HMI
8.4% Flat
4.8% Kelly

Total Profit
$4,713 HMI
$2,980 Kelly
$ 528 Flat

[Dave Schwartz]

This time I did it with the 7.1% optimum suggested by the falt bettor.

It works out even better.

http://www.horsestreet.com/BBSImages/Formula-02.png


Oh, I added arrows to note the biggest drawdown, another important point.


Next, I will tweak a little...

[Dave Schwartz]

Here are what I think are the optimal settings for HMI.

http://www.horsestreet.com/BBSImages/Formula-03.png


Interestingly, not too far from what the "standard" settings were. Because of the high hit rate relative to runouts, I was able to raise the high side to 122%.

I really liked the low drawdown percentage. You can do what you do with almost no chance of going broke!

By the way... see that number next to the Kelly P&L? Since HMI was able to be more agressive, that number represents what Kelly would have made had you adjusted the bet size equal to HMI.


Rarely do I see a sample which fits HMI so well that HMI actually bets more money than Kelly. Of course, the reason is that the bankroll grew so much larger.



Dave

[GameTheory]

All of the Kelly results are exactly the same. Thought you changed the % after the first one. And how do you compute the optimal Kelly %?

[Dave Schwartz]

Hmmm... I thought I did too.


Just looked it up. The Kelly ALWAYS uses the optimum from the flat sample. In other words, it always uses the precise optimum.

[Dave Schwartz]

I manually changed the bet% to 5%.

http://www.horsestreet.com/BBSImages/Formula-04.png

This is another fact about Kelly... rarely is the optimum actually the optimum.

[Dave Schwartz]

http://www.horsestreet.com/BBSImages/Formula-05.png

It appears that "optimum" (for this sample) is almost precisely 1/2 Kelly: 3.6%.


Dave

[LottaKash]

Would someone be so kind, and summarize these findings a bit....I got a little lost in all of this..... fascinating endeavor however....

Advantages for each set, session and method. ?....Disadvantages ?

Please....:jump:

[GameTheory]

The problem, as I have been getting at, is that you can't compute the true optional Kelly percentage using the average mutuel. You get the wrong answer. You're not taking into account the variety of payoff amounts, and that matters. So your 7.1% is not correct unless every winner pays exactly $4.37. (The true optimum will be lower than that optimum found using the average.) Which explains why your "optimum is rarely the optimum".


For instance, you (and most everyone else) would compute the optimal percentage from these two series of bets as the same ($2 payoffs):

0
6
0
6
0
6
0
6

win% = 50%
avg mutuel = $6
opt % = 25%

0
3
0
3
0
6
0
12

win% = 50%
avg mutuel = $6
opt % = 25%

Except 25% for the second series is wrong -- the true answer is 18.92%, which is the number that maximizes the geometric mean of the returns. The standard Kelly formula of edge/odds ONLY applies when the winners all win the same amount and the losers all lose the same amount (odds-wise). In horse racing, the losers do all lose the same, but the winners pay different amounts. And the more disparity you have in your win prices, the greater the disparity in your true optimal percentage to the untrue-but-usually-used-anyway percentage computed using the average payoff.

When you assume all the payoffs are going to be the same, that is an idealized scenario that gives you the optimal risk for the given win% and total return. But since that is never the case in reality, you always will compute an optimal % that is too high, and you'll be overbetting. So in your head-to-head tests vs Kelly you are always stacking the deck somewhat.

That's if you insist on using a fixed fraction. If you REALLY want to do it right, you compute that fraction for each individual bet, if possible.

[formula_2002]

Here are what I think are the optimal settings for HMI.

http://www.horsestreet.com/BBSImages/Formula-03.png


Interestingly, not too far from what the "standard" settings were. Because of the high hit rate relative to runouts, I was able to raise the high side to 122%.

I really liked the low drawdown percentage. You can do what you do with almost no chance of going broke!

By the way... see that number next to the Kelly P&L? Since HMI was able to be more agressive, that number represents what Kelly would have made had you adjusted the bet size equal to HMI.


Rarely do I see a sample which fits HMI so well that HMI actually bets more money than Kelly. Of course, the reason is that the bankroll grew so much larger.



Dave
Impressive stuff Dave, thanks for your efforts.
A few questions;
1. is bet size determined by final odds? (no would be a good answer)
2. what is the cost for this program?
3. do you have a free online instruction manual?
4. in the above example, the br never goes below 88%, or $989?

[lansdale]

The problem, as I have been getting at, is that you can't compute the true optional Kelly percentage using the average mutuel. You get the wrong answer. You're not taking into account the variety of payoff amounts, and that matters. So your 7.1% is not correct unless every winner pays exactly $4.37. (The true optimum will be lower than that optimum found using the average.) Which explains why your "optimum is rarely the optimum".


For instance, you (and most everyone else) would compute the optimal percentage from these two series of bets as the same ($2 payoffs):

0
6
0
6
0
6
0
6

win% = 50%
avg mutuel = $6
opt % = 25%

0
3
0
3
0
6
0
12

win% = 50%
avg mutuel = $6
opt % = 25%

Except 25% for the second series is wrong -- the true answer is 18.92%, which is the number that maximizes the geometric mean of the returns. The standard Kelly formula of edge/odds ONLY applies when the winners all win the same amount and the losers all lose the same amount (odds-wise). In horse racing, the losers do all lose the same, but the winners pay different amounts. And the more disparity you have in your win prices, the greater the disparity in your true optimal percentage to the untrue-but-usually-used-anyway percentage computed using the average payoff.

When you assume all the payoffs are going to be the same, that is an idealized scenario that gives you the optimal risk for the given win% and total return. But since that is never the case in reality, you always will compute an optimal % that is too high, and you'll be overbetting. So in your head-to-head tests vs Kelly you are always stacking the deck somewhat.

That's if you insist on using a fixed fraction. If you REALLY want to do it right, you compute that fraction for each individual bet, if possible.

Game Theory,

I'll try to return when I have more time, but briefly: everything you say here is right, everything Dave posts on the issue of Kelly is wrong. He truly has no understanding of how it works. As you say, Kelly bet-sizing cannot use averages. For this reason Formula 2002's bets were also not Kelly bets, so to apply that word to any of this is simply wrong.

You were also right about why HMI is false as a money-management technique - it violates the the law of independent trials. This is a common gambler's delusion, and I'm surprised that Dave would fall for it, but there is no relationship between between the outcomes of any two bets. This completely invalidates HMI. Any legitimate money-management technique treats each bet as a separate event. In the same way, the notion of 'sessions' is a canard. In reality all wagering is one big 'session'.

Got to run now, but I'm going to try to get in touch with Schlesinger or his friend Stewart Ethier to get more material on this. Keep in mind this isn't a matter of opinion - you're right.

Cheers,

lansdale

[ryesteve]

there is no relationship between between the outcomes of any two bets.I don't know enough about HMI to understand how that would relate to its effectiveness, but this statement isn't necessarily true. Depending upon one's methodology, success or failure can be dependent on track conditions, track biases, or for the multi-track player, which track(s) he's currently playing. Under those circumstances, winning streaks and losing streaks don't necessarily occur randomly.

[formula_2002]

GT, Landsdale, the data is on my web site.
its an excel file.
add a column with your bet size. what results do you get?

Thanks

[formula_2002]

GT, Landsdale, the data is on my web site.
its an excel file.
add a column with your bet size. what results do you get?

Thanks
let me make this easier.
Say I have a very long history of betting 2.00-1 odds. Exactly 2-1.
I win 36% of the time
my current br is $1000.
What would you suggest as my bet size?

[Dave Schwartz]

A few questions;
1. is bet size determined by final odds? (no would be a good answer)
2. what is the cost for this program?
3. do you have a free online instruction manual?
4. in the above example, the br never goes below 88%, or $989?

1. "No" is the correct answer. The bets are sized by betting percentage of the "current" bankroll, which is being changed based upon the current trends.

2. There is a printed manuscript which explains the "how" for $29.95 and a video "seminar" (which includes the spreadsheets) for $64.97. The two, bundled together, are $88.97.

3. No. That would defeat the purpose of selling the manuscript.

4. Correct.

[GameTheory]

GT, Landsdale, the data is on my web site.
its an excel file.
add a column with your bet size. what results do you get?

ThanksI don't see it -- what link would that be exactly?

[formula_2002]

I don't see it -- what link would that be exactly?


WEALTH BET DATA

[GameTheory]

WEALTH BET DATAWas looking for an excel file -- LTCPN228.TXT is correct?

[GameTheory]

Dave seems to have lost $20 in winnings somewhere -- I get the same number of bets, the same number of winners, but a total $2 return of 1238.10 rather than 1218.10. So on that basis, I get an "averaged" (i.e. incorrect) Kelly percentage of around 8.3% and a true optimal fixed percentage of around 6.3%. In order to mimic Dave's results, I randomly shaved a dollar here & there off the prices to get down to 1218.10, in which case his averaged Kelly % remains the same at around 7.1%, and the true number being around 5.8% (which is not totally precise because of me randomly shaving those prices). But something like that.

And of course using the optimal percentage performs better than the averaged number because the averaged number is too high. But all of this is quite suspect because we are using the results of the bets in question to determine all these optimal numbers, something you can't do in real life. But as an estimate going forward, that's all you can do.

I can't comment on the HMI results without seeing the whole sequence, and there is the question of where the extra $20 in mutuels went and whether they are in fact included in the actual workout even if not in the top section original summary.

(I notice only two prices above $10.00 -- maybe Dave shaved off that digit in conversion?)

[formula_2002]

Was looking for an excel file -- LTCPN228.TXT is correct?
Yep.

[formula_2002]

Kelly or not to Kelly aside, when the table is held to the follwoing constrants;

val(n228)>=.5.and.val(n202)>=2.or.val(n228)<.5.and.val(n202)<2;

then
starting br =$1124
final br=$6152 1.24 roi
total bet = $20813
185 plays
71 wins 38%
$2 flat bet return =$392 (.94 roi)
bankroll never went below $931 83%

where n202= final odds
and n228 is a computer generated number independent of the odds

[Dave Schwartz]

Not sure about $20, but I can tell you that all bet sizes are rounded to whole numbers. In other words, there are no bets in the amount of $16.21.

I do not recall if the rounding scheme is up, down, or closest but it is consistent.

[formula_2002]

these results were based on a slightly different treatment
n193=bet zize =.05/(1/n228)*n192
rather than
n193=bet zize =.1/(1/n228)*n192
where n192=br

Kelly or not to Kelly aside, when the table is held to the follwoing constrants;

val(n228)>=.5.and.val(n202)>=2.or.val(n228)<.5.and.val(n202)<2;

then
starting br =$1124
final br=$6152 1.24 roi
total bet = $20813
185 plays
71 wins 38%
$2 flat bet return =$392 (.94 roi)
bankroll never went below $931 83%

where n202= final odds
and n228 is a computer generated number independent of the odds

[formula_2002]

THANKS TO ALL

TIME TO TAKE THIS BACK TO THE "SELECTIONS" FORUM

http://www.paceadvantage.com/forum/showthread.php?t=61232

[lansdale]

I don't know enough about HMI to understand how that would relate to its effectiveness, but this statement isn't necessarily true. Depending upon one's methodology, success or failure can be dependent on track conditions, track biases, or for the multi-track player, which track(s) he's currently playing. Under those circumstances, winning streaks and losing streaks don't necessarily occur randomly.

ryesteve,

For the purposes of handicapping what you say is certainly true, but for the purposes of money management and bet-sizing, it's not. Also, for the hypothetical purpose of this thread, we're not talking about success and failure, but optimal money managment for a player who is already assumed to be playing with an edge - is already successful. Re streaks, in fact they are a random phenomenon, but because of the natural tendency of the human mind to misjudge probability, it overvalues their meaning. One of the best-known forms of this is the 'gambler's fallacy' - the belief that because you've lost a few bets you're due for a win or vice versa. There's also the 'hot hand fallacy' - I've linked a well-known article below on this subject.


Although real-world betting isn't as completely random as a casino game, there's still far too much variance in outcomes to make the size of your next bet dependent on whether or not you won your previous bet. To make this a feature of a money-management scheme is to play into the delusions of gullible gamblers.

http://wexler.free.fr/library/files/gilovich%20(1985)%20the%20hot%20hand%20in%20basket ball.%20on%20the%20misperception%20of%20random%20s equences.pdf

Cheers,



lansdale

[lansdale]

Kelly or not to Kelly aside, when the table is held to the follwoing constrants;

val(n228)>=.5.and.val(n202)>=2.or.val(n228)<.5.and.val(n202)<2;

then
starting br =$1124
final br=$6152 1.24 roi
total bet = $20813
185 plays
71 wins 38%
$2 flat bet return =$392 (.94 roi)
bankroll never went below $931 83%

where n202= final odds
and n228 is a computer generated number independent of the odds

formula,

If you can get this kind of ROI with a number you don't even understand, why worry about money-managment? :)

Cheers,

lansdale

[formula_2002]

formula,

If you can get this kind of ROI with a number you don't even understand, why worry about money-managment? :)

Cheers,

lansdale.

Sorry, I hoped you had more understanding of what you were saying, than I of what I was saying. :)
So your bet size would be?
PS. I did not mean to mislead you, I know how I constructed the number, I just could not find the "nail" that I could hammer it with, until, perhaps now.

[ryesteve]

Re streaks, in fact they are a random phenomenon, but because of the natural tendency of the human mind to misjudge probability, it overvalues their meaning. One of the best-known forms of this is the 'gambler's fallacy' I'm fully aware of the gambler's fallacy, and I'm not falling into that trap. I still maintain that a streak can be self-induced, rather than a random phenomenon, for the reasons I already stated, even if a player does have a long-term edge.

And to be honest, I really can't grasp exactly what your position is on this when you say that "for handicapping purposes" what I say is true, and yet you follow it up with a complete contradiction to what I said, as quoted above.

[lansdale]

.

Sorry, I hoped you had more understanding of what you were saying, than I of what I was saying. :)
So your bet size would be?
PS. I did not mean to mislead you, I know how I constructed the number, I just could not find the "nail" that I could hammer it with, until, perhaps now.

formula,

If you're still interested in betting Kelly, you still don't seem to understand that you need to know your edge for every race, not just your average edge. If you have been reading Benter, he lays out this method pretty clearly. I'm assuming you know the weighting of the factors that provide your edge. If you do this for each race, the formula for bet size is edge/odds-1. And I would recommend using fractional Kelly to minimize variance, as Benter did, and as every successful blackjack player and team that I know does - 1/2, and 1/3 are typical, although I know of one very successful team that uses 1/4.

Just to backtrack, I have a difficult time interpreting the charts you post, which makes it difficult to answer some of your questions, although I do get that you are playing with an edge. If you have any doubts about your model, as Benter mentions, you want to get as large a database as you can, and most of the charts he uses were derived from samples of about 2k or 3k races. This was enough for his purposes. Since you posted an 8k sample, I think you have that covered. The one thing I would suggest, which you may already have done, is to get some smaller of 'out-of-sample' estimates using unrelated races, to check on the model's accuracy. I think Game Theory has discussed this in other threads, and could give you much better advice on this than myself.

If this seems unclear, let me know.

Cheers,

lansdale

[lansdale]

I'm fully aware of the gambler's fallacy, and I'm not falling into that trap. I still maintain that a streak can be self-induced, rather than a random phenomenon, for the reasons I already stated, even if a player does have a long-term edge.

And to be honest, I really can't grasp exactly what your position is on this when you say that "for handicapping purposes" what I say is true, and yet you follow it up with a complete contradiction to what I said, as quoted above.

ryesteve,

I don't know whether you read my link, but obviously you reject notion that the 'hot hand' is an illusion although numerous studies bear this out. I won't try to persuade you otherwise.

When I say 'for handicapping purposes' I'll try to use an example.
Say I'm playing blackjack. The shoe is hot - there is a bias. Accordingly I make a max bet. I lose the bet. Since the shoe is still hot my next bet size is identical. I don't lower my bet because I lost the last one.

Cheers,

lansdale

[formula_2002]

formula,

If you're still interested in betting Kelly, you still don't seem to understand that you need to know your edge for every race, not just your average edge. If you have been reading Benter, he lays out this method pretty clearly. I'm assuming you know the weighting of the factors that provide your edge. If you do this for each race, the formula for bet size is edge/odds-1. And I would recommend using fractional Kelly to minimize variance, as Benter did, and as every successful blackjack player and team that I know does - 1/2, and 1/3 are typical, although I know of one very successful team that uses 1/4.

Just to backtrack, I have a difficult time interpreting the charts you post, which makes it difficult to answer some of your questions, although I do get that you are playing with an edge. If you have any doubts about your model, as Benter mentions, you want to get as large a database as you can, and most of the charts he uses were derived from samples of about 2k or 3k races. This was enough for his purposes. Since you posted an 8k sample, I think you have that covered. The one thing I would suggest, which you may already have done, is to get some smaller of 'out-of-sample' estimates using unrelated races, to check on the model's accuracy. I think Game Theory has discussed this in other threads, and could give you much better advice on this than myself.

If this seems unclear, let me know.

Cheers,

lansdale


ok, edge/odds-1..nothing has changed in paradice.

Benter ultimately adjust his analysis using the public's odds. A combination of his odds line and the public's odds.
There is a standard deviation in all the above to contend with.
They are nothing more than guide lines.

So we are left with many thing to assume. Its like trying to catch a bubble.
Your chances improve if you can find out where all the bubbles are!!
Hope I didn't break anyone's bubble :)

[m001001]

I had made similar comments in speculus' thread...
http://www.paceadvantage.com/forum/showpost.php?p=727366&postcount=321


I believe lansdale has pointed out correctly that using a "universal" edge/advantage is NOT how Kelly betting meant to work. It works when you can estimate accurately your edge in each race for each horse.

And please don't forget that Kelly is to maximize wealth growth, not ROI. HMI on the other hand tries to increase ROI. They are different animals, for different people.

If you cannot estimate your edge accurately for each race, you cannot use Kelly. If you can make the estimations fair accurately, you are better off go with Kelly.

[Dave Schwartz]

If you cannot estimate your edge accurately for each race, you cannot use Kelly. If you can make the estimations fair accurately, you are better off go with Kelly.

m001001,

Thank you for so succinctly saying what many of us have been trying to say in this thread and others for years.


Regards,
Dave Schwartz

[Red Knave]

I have been following this thread with great interest. Yet another example of what can be discovered if you give people an open forum.
I have learned a few interesting bits about Kelly that I didn't understand correctly before.

I still have a question, though, and maybe there is no perfect answer, but, How does one determine their edge for the next race?

[GameTheory]

m001001,

Thank you for so succinctly saying what many of us have been trying to say in this thread and others for years.
But that is also true in general for any money management system, or simply for betting at all. (You think you have an edge, maybe you don't.) You have to estimate your future performance whether you are using Kelly, HMI, or flat betting. There is not any additional problem with this when Kelly is involved, it just means you shouldn't be maximally aggressive based on an estimate which may be flawed. Same is true of any other way of betting.

Which is why you leave yourself a margin for error with fractional Kelly, etc. (You leave a margin for error with any system, right? What's different about Kelly?) Then your bets are still "Kelly-sized" IN RELATION TO EACH OTHER, even if they aren't at full magnitude. So I don't really understand why people say fractional Kelly "isn't really Kelly". Sure it is. It is not full Kelly, but the Kelly percentages still inform all of your bets. Again, you really want to calculate your edge for each bet if possible. Sometimes it is not possible -- the real point is to BRING TO BEAR ALL THE INFORMATION YOU KNOW. A lot of the time we throw out useful information because of convenience, and it hurts us. For example, if you cannot estimate your edge for each individual bet, which is often the case, then go ahead and use a fixed fraction (but calculate it correctly -- taking the standard average of the odds is always wrong). Or take a group of wagers where you CAN estimate edge for the whole group, and then determine an optimal percentage to bet ON THE WHOLE GROUP AS A SINGLE BET (presumably with the whole amount split equally between the wagers). But you can estimate your edge for each bet, at least somewhat, as formula_2002 can do here if he is watching the odds, then calculate that percentage for each bet and you'll do better. You can't do it precisely, obviously, but you can tell the difference between a horse at 4-1 and 3/2 and adjust accordingly. You could even just use odds rank or morning line as a guide to tweak your probabilities in a rough way. Every little bit helps -- use that information. (Or bet in groups where the differences between groups would be less dramatic -- figure out your kelly percentage for an typical group of 10 or 20 races -- it might be like 40%. Then allocate 40% (or some fixed fraction thereof) of your bankroll for that group, divide by the number of bets and flat-bet that amount for those 10 or 20 races (only then is this "wager" completed) and then move on to the next group.

Or use HMI! I've got no problem with it, although some of the explanation and justification of it compared to Kelly is incorrect. Unlike lansdale, I think there are some good reasons to use systems like HMI or Opponent Method (which I use myself often) -- but they are psychological reasons rather than mathematical ones. And I do think a proper understand of Kelly, or optimal wagering, is helpful, because it puts ALL betting systems into proper perspective and you have a true benchmark and you can see exactly what they are achieving for you. Simply put, you can't really make "optimal" decisions about your wagering if you don't know what the "optimal" thing to do in a given situation is. If you are going to make an exception to the rule, you ought to know what the rule is.

I think many people find Kelly very mysterious because of the math involved, but it is simpler than any other system other than flat betting because it only deals with the situation in front of you. If you have X amount of money, Y probability of winning the upcoming bet, and that bet will pay Z amount -- you get the same answer every time. Where with a lot of other methods, X,Y,& Z could be identical to some previous situation but the system is telling you to bet a different amount this time because of something else that has already happened in the past. It should be obvious that doing that MAKES NO SENSE WHATSOEVER from a mathematical perspective. The situation is identical! Why would your bet be different? Well, for psychological reasons to make you feel better...

[JeremyJet]

I still have a question, though, and maybe there is no perfect answer, but, How does one determine their edge for the next race?

Your odds compared to the odds on the board.

Regards,

JeremyJet

[JeremyJet]

Here's a quick example of how I use Kelly. I gotta run.

Regards,

JeremyJet


Tote odds

1. 5/2
2. 15
3. 3/2
4. 6
5. 8
6. 4
7 13

Your odds

1. 9/5
2. 12
3. 5/2
4. 6
5. 30
6. 10
7. 99

Bets - Edge

1. $122 (.25)
2. $31 (.384)
4. $24 (0)

Full Kelly
Bankroll: $1000
Total Wager: $178
Expected Profit: $42.42

[formula_2002]

Here's a quick example of how I use Kelly. I gotta run.

Regards,

JeremyJet


Tote odds

1. 5/2
2. 15
3. 3/2
4. 6
5. 8
6. 4
7 13

Your odds

1. 9/5
2. 12
3. 5/2
4. 6
5. 30
6. 10
7. 99

Bets - Edge

1. $122 (.25)
2. $31 (.384)
4. $24 (0)

Full Kelly
Bankroll: $1000
Total Wager: $178
Expected Profit: $42.42


here is another good example
from todays posted plays on the selections forum.
day is not over..


Monmouth Park - Race 9 [ Chart ]
# Win Place Show
11 $3.40 $2.60 $2.40

pid r1 # 1 ran out


Hoosier Park - Race 4 Chart
# Win Place Show
6 $8.80 $4.20 $3.40
that was a double down bet

[formula_2002]

days finals;
4 wins in 8 plays
flat bet roi=1.13
structured bet roi =.933

[formula_2002]

After a short three days of real money testing here are the results;

Paper results:
Each day was a positive flat roi day.
11 wins in 23 plays for a 1.21 roi.
Using a structured % of bankroll bet size, we turned $500 into $492.
Total structured bet was $1714, for a .99+ roi.
But as you might be aware, some of the bet sizes were too large, and would have impacted payouts.

Real world play.
Did not flat bet, used a modified % of BR w/o impacting bet size.
I was able to turn $500 into $390 for a .78 roi.
Because I had to monitor the pools I missed a few good bets. Things like dinner, shopping, working, seem a distraction.

Even if the structured bets beat the flat bet roi, in the end, its not how I would choose to live.

So I will continue on in the flat bet world (size of $15 to $50. Larger at NY tracks), hope to get close to breaking even and getting 20% off on my Bris account and be :jump: .

[formula_2002]

After a short three days of real money testing here are the results;

Paper results:
Each day was a positive flat roi day.
11 wins in 23 plays for a 1.21 roi.
Using a structured % of bankroll bet size, we turned $500 into $492.
Total structured bet was $1714, for a .99+ roi.
But as you might be aware, some of the bet sizes were too large, and would have impacted payouts.

Real world play.
Did not flat bet, used a modified % of BR w/o impacting bet size.
I was able to turn $500 into $390 for a .78 roi.
Because I had to monitor the pools I missed a few good bets. Things like dinner, shopping, working, seem a distraction.

Even if the structured bets beat the flat bet roi, in the end, its not how I would choose to live.

So I will continue on in the flat bet world (size of $15 to $50. Larger at NY tracks), hope to get close to breaking even and getting 20% off on my Bris account and be :jump: .
A CORRECTION, THE STRUCTURED PAPER BETS RETURNED A 1.15 ROI.
FINAL BR WAS $749