How much can you wager?

[Dave Schwartz]

I am looking for a formula that addresses maximum wagers versus pool size and different odds levels. Is anyone aware of a resource with such a formula so that I do not need to re-invent the wheel?


Regards,
Dave Schwartz

[chickenhead]

I tried to figure out the point of diminishing returns based on pool size, edge, and odds. It was easy to write a script that solved it, but I never was able to deduce a simple formula for it. Please post if you do get it.

[Greyfox]

Interesting problem, for which I do not have the answer.

The following article points out the problem with knowing the pool size.
The majority of money (40 %) is coming in at the last minute and that
will impact the odds. Then even if you can drag it up and make the bet
exactly at post time (ideal), info is still coming in after the gates are open and betting has been shut off.
If you find the formula, how do you get around those difficulties?

( I tried to get the link up. It's in PDF and HTML at the following page
http://www.google.com/search?hl=en&lr=&as_qdr=all&q=optimal+maximum+bet+%3D+wagering+pool&btnG=Search
it's title is Efficiency and Arbitrage across Parimutuel Wagering Pools.
As you might suspect the authors are looking at Dr.Z and Kelly criterion applications.)

[Dave Schwartz]

My thought was to use an average for the track/race to get a handle on it rather than using the individual pool.

Of course, one could also use a multiplier that says, "Assume the pool iwill be 1.8 times what it is at the time I make my bet." (The multiplier could be stored per track and adjusted relative to the purse value of the race.)

I am hoping that either Game Theory (Where is he anyway?) or Mike N. will have some ideas as well.


Dave

[Vigors]

Barry Meadows....now that we really need him.

Knowing B.M.'s expertice in this field, he can come up with
the formula and the answer to the half-cent!

[banacek]

I seem to remember Fabricand having something like this in one of his books.

[Greyfox]

I'm wondering if this man would have an answer? ( I don't know him personally.)

Steven Skiena
Professor,
Computer Science Department
1411 Computer Science
Stony Brook University
Stony Brook, NY 11794-4400
http://www.cs.sunysb.edu/people/faculty/SteveSkiena.html

This man wrote a book in 2001 entitled
Calculated Bets: Computers, Gambling, and Mathematical Modeling to Win.
He applied models to jai-alai. But parimutuel betting was involved.
Excerpts from that book are at:
http://www.cs.sunysb.edu/~skiena/jaialai/excerpts/excerpts.html

He could only say no ( sort of like the rest of us.)
Or he might point you in the direction of someone who has investigated this question.

[Dave Schwartz]

Actually, I have that book somewhere.

I think I have seen a formula somewhere. Maybe in a Mitchell book or Hausch. I'll go looking.


Thanks.

Dave

[m001001]

I am looking for a formula that addresses maximum wagers versus pool size and different odds levels. Is anyone aware of a resource with such a formula so that I do not need to re-invent the wheel?


Regards,
Dave Schwartz

Yes the wheel has been invented already, at least for those using a fairly accurate probability model.

If you have access to the UNLV library for notes of seminars organized by their gaming study center, search for topics regarding "Maximum Expected Value" which is the term commonly used by computer teams for betting at pool size limits with very large bankroll (in relation to pool size.) Benter presented his version of the formula in one of the UNLV events. (Beware there is a typo in the notes that may throw your result off a bit.)

[Dave Schwartz]

Apparently it requests a password and login to get into that area.

Thank you for your effort.

If you have any further clues, please send them along.



Dave

[Cratos]

I am looking for a formula that addresses maximum wagers versus pool size and different odds levels. Is anyone aware of a resource with such a formula so that I do not need to re-invent the wheel?


Regards,
Dave Schwartz
I don’t believe that an exact formula could be derived for many of the reasons given in earlier posts in this thread about how money is added to the betting pools with respect to allotted time to wager.

However you might want to use a conditional probability method based on historical wagering for the racetrack in question (top tier or bottom tier), the type of race (stakes or general race), the day of the week, and the size of the field in the race; and you would probably come up with a 95% confidence of what you want.

[njcurveball]

However you might want to use a conditional probability method based on historical wagering for the racetrack in question (top tier or bottom tier), the type of race (stakes or general race), the day of the week, and the size of the field in the race; and you would probably come up with a 95% confidence of what you want.

You would also need to factor in field size and which race it was on the card. Traditionally the earlier races get less money.

Sounce like a complicated equation Dave, right up your alley! :ThmbUp:

[Cratos]

You would also need to factor in field size and which race it was on the card. Traditionally the earlier races get less money.

Sounce like a complicated equation Dave, right up your alley! :ThmbUp:

You are correct

[arkansasman]

I have the formula and will email to you.

John

[Dave Schwartz]

Thanks, John.

[arkansasman]

Dave,

Check your email at Horsestreet.

John

[Dave Schwartz]

Thank you.

May I ask the source of that formula?

Dave

[DanG]

Thank you.

May I ask the source of that formula?

Dave
That’s it?

The “formula” is private through e-mail. :rolleyes:

Wow…

It’s like a peck on the cheek form a call girl. :faint:

[Dave Schwartz]

It’s like a peck on the cheek form a call girl.

:lol:

I am sure John will be glad to post it for all (or I will do it with his approval).

Because of the math symbols (half of which I don't understand), it is a graphic. (But I have a math-guy for a son.)


Dave

[Greyfox]

That’s it?

The “formula” is private through e-mail. :rolleyes:

Wow…

It’s like a peck on the cheek form a call girl. :faint:

We agree.
The good news is that I searched the net and found a number of sites
talking about Harville formulas and Johansen

[Greyfox]

oops. Punched a wrong button.

The bottom line is that I searched the net and
read a lot of "abstracts".
(Banacek with his Economics background might be helpful here.)
But if arkansas "man" has a formulae....why not here?

[DanG]

We agree.
The good news is that I searched the net and found a number of sites
talking about Harville formulas and Johansen
Understood men…

I was really half kidding as my NJ education won’t help with the hieroglyphics that I’m sure are involved. I’m not as fortunate as Dave to have a son with a “beautiful mind” to interpret.

Appreciate the effort all the same. :ThmbUp:

[highnote]

Hey Arkansasman -- inquiring minds want to know! :)

May I have a copy of the formula? :ThmbUp:

[Dave Schwartz]

I’m not as fortunate as Dave to have a son with a “beautiful mind” to interpret.

Yes, but the medication helps.
:lol:

[highnote]

I am looking for a formula that addresses maximum wagers versus pool size and different odds levels.

Hi Dave,

I've been thinking about this, but I'm not sure I know what you're trying to find out.

The maximum wager one can make is infinite on the one hand. And on the other hand, the smallest bet allowable will affect the odds. But I know you know that.

So maybe you want to know what is the maximum amount you can bet without destroying some part of your edge?

[Dave Schwartz]

John,

So maybe you want to know what is the maximum amount you can bet without destroying some part of your edge?

Yes, that is my intent.


Dave

[cj]

I would think using the average pool size and your average win price would give you a good enough approximation for what you are looking to find.

If, for example, you know you have a 15% edge on maiden claimers and average an $8.40 payoff, it would be a pretty easy calculation. I'm not sure there would be much to be gained by going with specific odds ranges, especially since you never really know what the odds will be anyway. This is really true at the tracks where this is important.

However, since it is 11:34 here, I'll have to work on it tomorrow.

[Dave Schwartz]

CJ,

Yes, I was thinking of something like that but a little more robust.

Dave

[spilparc]

Hi Dave,

So maybe you want to know what is the maximum amount you can bet without destroying some part of your edge?

It's a calculus problem.

[thelyingthief]

i addressed this problem by accepting its intractible nature. to properly assess the impact of a wager, it is necessary to know the size of the pool at post--an impossibility, generally, greatly aggravated by internet wagering--so i broke down the average pool size by race number, day of week, and race condition. i bet southern california, which, as you know, has the largest pools in the country (along with CD, NY, and the other exceptions); on the basis of my pool study, and given the relative stability of the odds offered at one minute to post (i know, i know, there IS deterioration, and sometimes significant variation), i was able to limit my wagering impact to appreciable effect.

i realize this is not sufficiently "mathematical", but, again, the problem is intractible, because of insufficient information and number of variables involved.

another argument for off-shore wagering, i s'pose...

[Dave Schwartz]

Theif,

That is precisely what I want to do!


Dave

[Robert Fischer]

where do you guys get your pool feeds from? - serious question

The formula itself is pretty easy right? If that is the issue I could probably find it or come up with it...

The idea if I am reading this correctly is to not hurt your value with your impact while wagering a large amount. ?

Calculate the pool size and Make a safe estimate. You can check a bunch of examples "on paper" until you get your balance of large bet + Safe Bet.

The Danger in playing this game is another high roller in the same pool. = If this guy is betting the same horse and a.Doesn't use pool information to wager or b.Has Lower Value criteria or c. somehow bets with you between pool updates ... that can hurt your value estimates. It starts getting complicated

[cj]

I have come up with a spreadsheet I'll post once I get home in about 12 hours.

You enter expected pool size, odds, takeout, expected edge, and minimum acceptable edge, and it will give you the maximum bet size.

For example:

Pool: 10,000
Takeout: 17%
Odds: 3 to 1
Expected Edge: 15%
Acceptable Edge: 5%

It calculates the minimum payoff needed to achieve the 5% and calculates the maximum bet you can make to not get below that. In this case, the minimum payout would be $7.40 and you could bet $268.

Of course, if you are getting a rebate, you could go to 0% minimum edge, or even below. I have some other stuff built in to show profits at various bet sizes.

[cj]

What you say is true Robert, though I wouldn't consider it a danger. It will get you in the ballpark, which is better than having no idea how much you can and should bet. For everytime you get burned by another bettor, you will benefit on a different race I would think. It would have to even out over time.

[cj]

This kind of died out. I decided that rather than try to come up with a formula, the best thing to do was use brute force and just test all possible wager sizes. I was very surprised at the amount you can bet until your profit starts to shrink. Of course your ROI shrinks the more you bet, but profits continue to rise until you reach a saturation point and they begin to shrink, and eventually turn into a loss.

However, I would guess 99% of the players here cannot possibly bet too much if they truly have a genuine edge.

[MichaelNunamaker]

CJ wrote "I was very surprised at the amount you can bet until your profit starts to shrink. Of course your ROI shrinks the more you bet, but profits continue to rise until you reach a saturation point and they begin to shrink, and eventually turn into a loss."

Well, sure, the curve is essentially the same shape as the famous Laffer curve of tax revenue (except our curve can go negative). So, the trick is to find the peak. As far the the amount one can wager being high, it depends on how big the tracks are, and what type of horses one is wagering on. Longshots dramatically reduce how much you can wager. For example, say you have a 10% edge and say reducing that edge to 5% will push you to the maximum profit point. So, one can increase the amount of money on a horse by 5% (not exactly, but close enough). If a longshot only has a couple of hundred bucks bet on it, you could only wager $10 to reach maximum profit!

OTOH, say you have that 10% edge on the favorite and it has $40,000 wagered on it. Now you have to wager $2000 to reach your maximum profit point. This is one of the reasons why, IMHO, low odds overlays are so very much better than longshot overlays. You can bet far far more on them, and the total profit is potentially much much higher. I see this discussion has talked some about the math involved, I have not seen the equations you guys are talking about, but I can tell you that they darn well better take the odds into account on each horse. If the math uses average odds, it will wind up giving you answers that make you astonishingly overbet longshots. Other than that, I have no opinion since I haven't seen it.

Mike Nunamaker

[cj]

I was definitely considering odds. Of course you can't bet the same amount on a 40 to 1 that you can on a 2 to 1. Even so, the amount you can bet on the 40 to 1 and still maintain a nice profit was surprisingly high to me.

The key is you must have a very good idea what your edge is. The bigger your edge, the more you can bet and cut into it and while increasing profit.

[cj]

I did a little playing around. You are correct of course, there is a lot more money to be made in the lower odds ranges if you can find an edge.