Kelly Horse Race or Ziemba Roulette

[jfdinneen]

In the spirit of the New Year, I offer the following thought-provoking argument:

Betting is often described as a competition between you and the "Crowd" (i.e. Pari-Mutuel) on which of you can better estimate the true distribution of odds in a particular sporting event. In that context, a good starting point is to ask Bill Benter's fundamental question of handicapping: what additional variables (if any) explain a significant proportion of the variance in results to date that is not already accounted for by the public odds (Wisdom of Crowds)? By keeping records, it is possible to determine whether or not you have been successful over time in so doing. However, it is not possible to know (in advance) if you have an overlay in an upcoming event. This is the fundamental flaw of handicapping and, eo ipso, the flaw of fundamental handicapping.

The alternative approach is technical trading and an often underestimated strategy is "Bold Play" and its variants. Bold play is recommended for subfair games (i.e. p < 0.5, assuming even money bet; see SEER to calculate p for other prices) and, given the high-level of taxation, one can argue that horse-racing qualifies. Without going into the mathematical details and assuming a little "poetic licence", bold play reduces to an algorithm comprising two rules:
__a) Bet amount to reach target bankroll in single event (e.g. one race); or
__b) Bet amount in current event to reach bankroll level from which it is possible to attain target bankroll in next event.
You will no doubt immediately recognize that it is possible to iterate rule b) over many events (e.g. complete racecard) but, ideally, you want to minimize the number of iterations. This technical trading approach only requires information on current bankroll, target bankroll, number of remaining events, house limits, and access to the public odds.

In summary, the advice to use fundamental handicapping to find overlays which you then exploit using edge-based staking (Kelly, 1956) assumes a superfair game but if, in fact, the game is essentially subfair then technical trading is recommended using bold play (Ziemba, 2002) or one of its variants in as few iterations as is feasible given whatever constraints are in place (e.g. maximum stakes).

John

[Dave Schwartz]

John,

Is this your blog?
http://vendire-ludorum.blogspot.com/...-roulette.html


I find your post both illuminating and timely. At the very moment of refreshing PA and seeing your post, I had just completed an hour-long brainstorming session with my wife. (I lecture, she listens until I understand the solution.)

The topic of this session, as well as many recent sessions is, "How to make a value assessment when final odds do not exist[/i]" coupled with a good dose of "How to overcome the whales when they are right so often."

What I have been working on for the last several months (though it seems like decades) is to find a way to use the whales rather than be used by them. A lesser but not altogether bad alternative is to nullify the impact of the whales on my selection process.

The strength of my own handicapping is that it picks great contenders. Not good, but great. So great, in fact, that I can wager 3-4 of them per race flat and come within 4.5% of even. When all is said and done, one finds that profit begins with the 3.5th public choice.

Of course, that is all hindsight - as one cannot truly discern which horses will be what odds with any degree of certainty before the race is run.


In the very end of my lecture I had just reached the point of targeting which contender(s) to bet - the point of the whole exercise I am sure you will agree. (One can only assume how much love it takes to listen to MY lectures willingly on a regular basis.)

That was when it hit me... Pick the contender that you need in order to put yourself in the best position to win the "game!"


The approach you are outlining here is - effectively - a due column approach to wagering. Yes?


Regards,
Dave Schwartz

PS: Thanks for the great links.

[Overlay]

I agree that a "maximum boldness" betting strategy is optimal in an unfair game. But if pari-mutuel wagering on horse racing were unfair in the same sense that casino games of pure chance are unfair, I would cease all handicapping activity today.

I disagree with the basic premise that it's not possible to predict (in terms of probabilities of occurrence, rather than with absolute certainty) the various outcomes of future events in racing. Are you saying that horse racing does not contain detectable performance patterns that repeat themselves over and over? Or what would be the use of keeping the records to which you refer, if not as a means, not just of knowing to what degree you have achieved overall success in the past, but of being able to improve performance through distinguishing handicapping/betting actions that produce positive results, or that offer an edge to the player, from those that do not?

[Robert Fischer]

Originally Posted by Overlay

If pari-mutuel wagering on horse racing were unfair in the same sense that casino games of pure chance are unfair, I would cease all handicapping activity today.

I disagree with the basic premise that it's not possible to predict (in terms of probabilities, rather than with absolute certainty) the likelihood of various outcomes of future events in racing.

Exactly.


the OP starts out strong including:

Originally Posted by jfdinneen

In the spirit of the New Year, I offer the following thought-provoking argument:

Betting is often described as a competition between you and the "Crowd" (i.e. Pari-Mutuel) on which of you can better estimate the true distribution of odds in a particular sporting event. In that context, a good starting point is to ask Bill Benter's fundamental question of handicapping: what additional variables (if any) explain a significant proportion of the variance in results to date that is not already accounted for by the public odds (Wisdom of Crowds)? By keeping records, it is possible to determine whether or not you have been successful over time in so doing.

[jfdinneen]

Originally Posted by Dave Schwartz

John,

Is this your blog?
http://vendire-ludorum.blogspot.com/...-roulette.html
...
In the very end of my lecture I had just reached the point of targeting which contender(s) to bet - the point of the whole exercise I am sure you will agree. (One can only assume how much love it takes to listen to MY lectures willingly on a regular basis.)

That was when it hit me... Pick the contender that you need in order to put yourself in the best position to win the "game!"
...

Dave,

Happy New Year!
__a) Yes, that is my blog.
__b) You are absolutely correct that winning war is what counts, not any specific battle. That is why you should set goals (interim targets) and then project how to reach those goals as quickly as possible.
__c) Not recommending system betting, simply reflecting two basic conceptual approaches (i.e. fundamental and technical) to same end result.

John

[gm10]

Originally Posted by jfdinneen

In the spirit of the New Year, I offer the following thought-provoking argument:

Betting is often described as a competition between you and the "Crowd" (i.e. Pari-Mutuel) on which of you can better estimate the true distribution of odds in a particular sporting event. In that context, a good starting point is to ask Bill Benter's fundamental question of handicapping: what additional variables (if any) explain a significant proportion of the variance in results to date that is not already accounted for by the public odds (Wisdom of Crowds)? By keeping records, it is possible to determine whether or not you have been successful over time in so doing. However, it is not possible to know (in advance) if you have an overlay in an upcoming event. This is the fundamental flaw of handicapping and, eo ipso, the flaw of fundamental handicapping.

I don't think I agree with the last two sentences - unless I misunderstood. Why would you not know whether you have an overlay or not? Your input variables must be known at the time of the race, so you can calculate your own odds and compare with the public's odds.

There is the problem of getting fixed odds, but that is definitely a local, American problem - and not an insurmountable one either.

As a side remark: Benter mixes his own probabilities with the crowd's probabilities. This is not the best way to measure how much variance you are explaining. This measures how much variance you and the public combined, can explain.

The alternative approach is technical trading and an often underestimated strategy is "Bold Play" and its variants. Bold play is recommended for subfair games (i.e. p < 0.5, assuming even money bet; see SEER to calculate p for other prices) and, given the high-level of taxation, one can argue that horse-racing qualifies. Without going into the mathematical details and assuming a little "poetic licence", bold play reduces to an algorithm comprising two rules:
__a) Bet amount to reach target bankroll in single event (e.g. one race); or
__b) Bet amount in current event to reach bankroll level from which it is possible to attain target bankroll in next event.
You will no doubt immediately recognize that it is possible to iterate rule b) over many events (e.g. complete racecard) but, ideally, you want to minimize the number of iterations. This technical trading approach only requires information on current bankroll, target bankroll, number of remaining events, house limits, and access to the public odds.

In summary, the advice to use fundamental handicapping to find overlays which you then exploit using edge-based staking (Kelly, 1956) assumes a superfair game but if, in fact, the game is essentially subfair then technical trading is recommended using bold play (Ziemba, 2002) or one of its variants in as few iterations as is feasible given whatever constraints are in place (e.g. maximum stakes).

John

I wasn't familiar with the concept of Bold Play. Thanks for the post.
Can you post a link that contains more mathematical details?

[jfdinneen]

Originally Posted by Overlay

...Are you saying that horse racing does not contain detectable performance patterns that repeat themselves over and over? Or what would be the use of keeping the records to which you refer, if not as a means, not just of knowing to what degree you have achieved overall success in the past, but of being able to improve performance through distinguishing handicapping/betting actions that produce positive results, or that offer an edge to the player, from those that do not?

Overlay,

Happy New Year!
You are correct that, using fundamental handicapping, one can detect repeatable performance patterns and make reasonable estimates of the probability of the future occurrence of those same patterns. The problem is that, as more handicappers acquire knowledge of these patterns, you lose the advantage (mutual information as measured by Kullback-Leibler distance) with respect to the public odds (semi-strong market efficiency).

John

[Dave Schwartz]

John,

I have tried to reconcile that with Tsun Tsu's Art of War where he discusses retract while losing and advance when winning. However, that is based upon the idea that you can make/conscript more soldiers while retracting.

It would seem that with a finite number of soldiers a better plan is to constantly put your enemy in the position of fearing a total loss, or as you have eluded to, two losses in a row cost the enemy his kingdom.

This is especially true in a skirmish-within-a-battle-within-a-war. That is, a session that one can play very aggressively, knowing that there are many more sessions to be played.

Are you aware of any warfare strategies that effectively "parlay?"

Are you familiar with http://vptruth.com/?


Dave

PS: Happy New Year to you. How's the weather?

[jfdinneen]

Robert,

Happy New Year!
Not sure if you had a specific question?

John

[jfdinneen]

Originally Posted by gm10

I don't think I agree with the last two sentences - unless I misunderstood. Why would you not know whether you have an overlay or not? Your input variables must be known at the time of the race, so you can calculate your own odds and compare with the public's odds.
There is the problem of getting fixed odds, but that is definitely a local, American problem - and not an insurmountable one either.
As a side remark: Benter mixes his own probabilities with the crowd's probabilities. This is not the best way to measure how much variance you are explaining. This measures how much variance you and the public combined, can explain.
I wasn't familiar with the concept of Bold Play. Thanks for the post.
Can you post a link that contains more mathematical details?

gm10,

Happy New Year!
__a) I agree that you can make necessary calculations (see reply to Overlay).
__b) Benter and Variance: You are inadvertently mixing two separate issues, identifying valid variables (fundamental law of handicapping) and aggregating one's own odds distribution with that of public, Benter did both. Maybe, I misunderstood your point!
__c) Mathematical background
_____1) Classic: L. E. Dubins and L. J. Savage (1965). How to Gamble If You Must: Inequalities for Stochastic Processes. McGraw-Hill.
_____2) Recommended: S. N. Ethier (2009). The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer.
_____3) Various: Kulldorff (1993), Ziemba (2002)

John

[Robert Fischer]

Originally Posted by jfdinneen

Robert,

Happy New Year!
Not sure if you had a specific question?

John

Happy New Year

[jfdinneen]

Originally Posted by Dave Schwartz

...Are you aware of any warfare strategies that effectively "parlay?"

Are you familiar with http://vptruth.com/?
...

Dave,

__a) Not sure I fully understand your question on Parlay. Can you clarify or give example?
__b) Not familiar with Rob Singer - does not appear to respect mathematical rigor so I should probably avoid comment!
__c) Respectable 0C / 32F, but no snow for last few days.

John

[Overlay]

Originally Posted by jfdinneen

Overlay,

Happy New Year!
You are correct that, using fundamental handicapping, one can detect repeatable performance patterns and make reasonable estimates of the probability of the future occurrence of those same patterns. The problem is that, as more handicappers acquire knowledge of these patterns, you lose the advantage (mutual information as measured by Kullback-Leibler distance) with respect to the public odds (semi-strong market efficiency).

John

John,

Happy New Year to you as well!

I certainly recognize what you say. It's especially prevalent in cases where betting decisions are made on the basis of an individual variable or angle that is designed to isolate a single horse, and that then gets overbet into unprofitability on a stand-alone basis as public awareness of the effectiveness of the variable or angle increases. The same could theoretically happen to full-field odds-lines based on a properly weighted and balanced/distributed mix of fundamental factors, but I regard it as much less likely that the public (despite having more aggregate information than any individual) would ever reach the point of sending every horse in every race off at odds that offered no discernible value to the bettor on any entrant.

[jfdinneen]

Overlay,

I agree that the doomsday scenario is not very likely but the golden rule is that once you have a discernible advantage you must both NOT share it with others and exploit it to the hilt until the market assimilates the pattern (which it will, eventually). Then, you must just as quickly drop it and move on!

I disagree with those who claim to religiously follow any particular, publicly available strategy (e.g. speed, pace, form cycles, trainer patterns) as these approaches will most likely be baked into the public odds. Yes, they can successfully predict winners but it is very unlikely they will be profitable long-term.

John

[sjk]

I have been doing the same thing for 15 years and have not seem any degradation of my results.

The only thing I use is the information in the charts I download daily.