Optimal Bankroll Growth in the Racetrack Betting Market

[Magister Ludi]

Prerequisite: You are investing profitably in a racetrack betting market. [Note: some of the following is cut and pasted from an earlier thread. Please excuse the redundancy].

If you are investing profitably in the racetrack betting marketplace as a member of the order Cetacea, you should already be very familiar with the Cournot-Nash equilibrium for timing your bets and how to calculate the simultaneous nonlinear equations for sizing them. But what if you’re a smaller investor who’s met with limited success and you want to grow your bankroll?

If you do have an edge, there is no faster way to attain optimal geometric growth for your assets than the Kelly Criterion. I’m not going to debate or belabor that point. Given, that the Kelly Criterion-sized investments yield optimal geometric asset growth, what are the best investments to make in a racetrack betting market to grow your bankroll as quickly as possible?


Firstly, let’s look at a win bet:

Example: horse with 5:1 odds and an expected 3% edge

BR = bankroll = $100,000
p = expected win probability
q = expected loss probability
A = net odds
e = (A+1)p-1>0
f* = fraction of BR to invest = e/A
f*BR = amount invested
EV = expected value = ef*BR

p = .1717
A = 5
e = (5+1)*.1717-1 = .03
f* = .03/5 = .006
f*BR = $100,000*.006 = $600
EV = $600*.03 = $18

The short form:

edge = 3%
odds = 5
edge/odds = 3%/5 = .6%
optimal bet = .6% * $100,000 = $600
EV = $600*3% = $18

With a 3% edge and a $100,000 bankroll, your optimal bet on a 5:1 horse is $600. Your expected value is $18.




Secondly, let’s look at an exacta.

Example: If Horse 1 is 4:1 and horse 2 is 3:1, then the probability of a 1/2 exacta is 0.2*(0.25/(1-.2))=.05. The probability of a 2/1 exacta is 0.25*(0.2/(1-0.25))=.067.

[I know about Henery, Stern, Lo, Bacon-Shone, et alii. I’m trying to keep it simple].

Let us assume that we have a 3% edge with the 1/2 exacta.

edge = 3%
p = .05
odds = (1/p) – 1 = 19
edge/odds = 3%/19 = .158%
optimal bet = .158% * 100,000 = $158
EV = $158 * 3% = $4.74
Our expected value for the 1/2 exacta is about 25% of that of the win bet.


Lastly, let us look at a place bet. We’ll take the 3:1 place horse in the 1/2 exacta above. The probability of it placing is 1-.2=.8. We’ll further assume a 3% edge.

edge = 3%
p = .8
odds = (1/.8) – 1 = .25
edge/odds = 3%/.25 = 12%
optimal bet = 12% * 100,000 = $12,000
EV = $12,000 * 3% = $360.00

Our expected value for the place bet on the 2 horse is $360, 20 times that of the win bet and 76 times that of the exacta.

[DeltaLover]

Kelly Criterion is not applicable to horse betting.

- Final odds are never known in advance

- The winning percent of a starter is never known to a sufficient pressision

- The bet size is limited by minimum unit bet

- As the bankroll grows the suggested Kelly bet size will affect the payout.

For these reasons any discussion about applying Kelly criterion to horse betting presents only academic interest and cannot be applied to real word.

[Magister Ludi]

Originally Posted by DeltaLover

Kelly Criterion is not applicable to horse betting.

- Final odds are never known in advance

- The winning percent of a starter is never known to a sufficient pressision

- The bet size is limited by minimum unit bet

- As the bankroll grows the suggested Kelly bet size will affect the payout.

For these reasons any discussion about applying Kelly criterion to horse betting presents only academic interest and cannot be applied to real word.

http://eprints.soton.ac.uk/51683/

Note the author. Mr. Benter, Drs. Ziemba, Hausch, Thorpe, and countless others have all sized their racetrack investments with the Kelly Criterion.

[thaskalos]

Originally Posted by Magister Ludi

http://eprints.soton.ac.uk/51683/

Note the author. Mr. Benter, Drs. Ziemba, Hausch, Thorpe, and countless others have all sized their racetrack investments with the Kelly Criterion.

It occurs to me that the Kelly Criterion would only have limited applicability in our game...seeing that bet sizes in this country can only be elevated to a certain extent before they begin hurting the player's cause.

Comparing the horseplayer to Edward Thorp -- as you have done several times -- is unfair and terribly inaccurate. He didn't play the same game that we are playing.

[Magister Ludi]

Originally Posted by thaskalos

It occurs to me that the Kelly Criterion would only have limited applicability in our game...seeing that bet sizes in this country can only be elevated to a certain extent before they begin hurting the player's cause.

Comparing the horseplayer to Edward Thorp -- as you have done several times -- is unfair and terribly inaccurate. He didn't play the same game that we are playing.

Mr. Thaskalos,

There is plenty of room in larger pools/smaller bankrolls to make Kelly-sized bets, especially in exotic pools.

Dr. Thorpe used to go to the track with Drs. Ziemba and Hausch.

[DeltaLover]

Originally Posted by Magister Ludi

http://eprints.soton.ac.uk/51683/

Note the author. Mr. Benter, Drs. Ziemba, Hausch, Thorpe, and countless others have all sized their racetrack investments with the Kelly Criterion.

I do not think that this is addressing the issues I have described above...

In the abstract it is clearly mentioned that this is a theoretical calculation.

I would like to see a clear inductive answer to the described issues rather than an argument from authority.

Tell us for example what are you going to do if Kelly is dictating a $2K bet to a $15K pool ?

Or to take the other extreme, what are you going to do if Kelly is dictating a $0.25 bet to a specific exacta bet?

How you can use Kelly if you have no clue if your 5-2 shot while the horses are boarding is going to finally be 8-5 or 3-1 ?

You really think that these examples are not realistic?

[Robert Fischer]

Nothing wrong with looking at the premise of this thread(different wager types ?) with the given assumption that Kelly works in horseplaying.

If the premise is proved to be correct or incorrect, you may substitute a different bet-sizing strategy, and see if it continues to hold true.

[Magister Ludi]

Originally Posted by DeltaLover

I do not think that this is addressing the issues I have described above...

In the abstract it is clearly mentioned that this is a theoretical calculation.

I would like to see a clear inductive answer to the described issues rather than an argument from authority.

Tell us for example what are you going to do if Kelly is dictating a $2K bet to a $15K pool ? If you think that you're going to exceed the optimal bet for that pool size, you calculate the optimal bet with Isaacs' equations and the Kelly Criterion. The smaller bet prevails.

Or to take the other extreme, what are you going to do if Kelly is dictating a $0.25 bet to a specific exacta bet? No bet.

How you can use Kelly if you have no clue if your 5-2 shot while the horses are boarding is going to finally be 8-5 or 3-1 ? If you have no clue as to what the final odds are going to be, you have no clue as to what or how much you should be betting. No bet.

You really think that these examples are not realistic?

see above

[thaskalos]

Originally Posted by Magister Ludi

Mr. Thaskalos,

There is plenty of room in larger pools/smaller bankrolls to make Kelly-sized bets, especially in exotic pools.

Dr. Thorpe used to go to the track with Drs. Ziemba and Hausch.

Mr. Ludi,

Thorp wrote an introduction to Ziemba's book...and has admitted to testing and using that method only briefly. Do you suppose that Ziemba's method can still be applied for profit in this country?

Did Benter make his vast fortune by betting in the USA?

Do you think that the horseplayer in this country is on a never-ending journey towards ever-increasing bet sizes and never-ending bankroll growth?

You say that "there is still plenty of room..."

And that's what I said: Limited applicability!

The bankroll grows to a point...and then there is "no more room...".

It is not in the cards for the horseplayer of this country to be the next Edward Thorp...regardless of what wagering method he uses. So why continue bringing up Thorp's name, when we need to make a point about this game?

[DeltaLover]

Originally Posted by Magister Ludi

If you have no clue as to what the final odds are going to be, you have no clue as to what or how much you should be betting. No bet.

I think this summarizes our discussion.

In today's game we never know what the final odds are going to be so we never bet.

[thaskalos]

Originally Posted by DeltaLover

I think this summarizes our discussion.

In today's game we never know what the final odds are going to be so we never bet.

Know the final odds?

We cannot even know ahead of time who the race favorite will be...in many -- if not most -- cases.

[thaskalos]

Originally Posted by DeltaLover

I think this summarizes our discussion.

In today's game we never know what the final odds are going to be so we never bet.

And if anyone out there DOES know what the final odds will be, ahead of time...how could we possibly persuade you for a demonstration?

[Robert Fischer]

so much for the premise of the thread.....

[thaskalos]

Originally Posted by Robert Fischer

so much for the premise of the thread.....

If I was rude, I apologize.

I just happen to think that claims should be backed up by substance...not only theory.

[lansdale]

Hi DL,

The objections you raise to using Kelly are easily solved by the measures in my subject line - ML refers to the latter in this thread and Benter also discusses his risk-aversion technique for dealing with pool-size limits in his well-known article, which I know you've read. Re the former problem - dropping odds, conditional betting solves this.

The prime obstacles for horseplayers attempting to use Kelly are not these superficial issues but facts: 99% of players have no edge and those who do have an edge (presumably winning, non-database players) don't know what their edge is. The only players who can even attempt to use Kelly are database players who have built a profitable betting model - a very difficult task, which some here, however, have accomplished.

I believe the best way to think about Kelly is as a tool for the latter elite few. But just because everyone can't and shouldn't use it doesn't mean no one can or should.

Cheers,

lansdale

Originally Posted by DeltaLover

I do not think that this is addressing the issues I have described above...

In the abstract it is clearly mentioned that this is a theoretical calculation.

I would like to see a clear inductive answer to the described issues rather than an argument from authority.

Tell us for example what are you going to do if Kelly is dictating a $2K bet to a $15K pool ?

Or to take the other extreme, what are you going to do if Kelly is dictating a $0.25 bet to a specific exacta bet?

How you can use Kelly if you have no clue if your 5-2 shot while the horses are boarding is going to finally be 8-5 or 3-1 ?

You really think that these examples are not realistic?