Dutching - a maths problem

[cosmicway]

Everyone knows what dutching is.
I divide my money in two or more selections so the return is the same whatever the outcome, provided one of my selections wins.

If horse no 1 pays the (decimal) price A1 and horse no 2 pays the (decimal) price A2 then the dutched price is:

A(1-2) = 1 / ( 1 / A1 + 1 / A2 )

and the fraction I have wagered on the 1 is A(1-2) / A1 while the fraction I have wagered on the 2 is A(1-2) / A2.

This is simple when the prices are announced in advance (fixed odds betting). Sometimes there is a special designator on the ticket for dutching selections so you don't have to use a calculator.

Question: Is there a formula for this in pool betting ? If I say I want 1 and 2 dutched (or 1 and 2 and 3 dutched) is there an algorithm the betting pool operators can use to work out the fair price ?

[Ray2000]

CXWong's book

"Precision: Statistical and Mathematical Methods in Horse Racing"

has a chapter on hedging with those formulas and Kindle edition is around $30

PACE discussion here
http://www.paceadvantage.com/forum/s...ad.php?t=83545


Wongs Excel files are here but you probably need the book to see how to use them


http://www.maxabet.com/precision/




also see

http://www.dmtc.com/handicapping/tools/

[cosmicway]

Originally Posted by Ray2000

CXWong's book

"Precision: Statistical and Mathematical Methods in Horse Racing"

has a chapter on hedging with those formulas and Kindle edition is around $30

PACE discussion here
http://www.paceadvantage.com/forum/s...ad.php?t=83545


Wongs Excel files are here but you probably need the book to see how to use them


http://www.maxabet.com/precision/




also see

http://www.dmtc.com/handicapping/tools/

Does he solve the problem ?
I mean I want to dutch two horses for the win but there is no fixed price.
Only the pool price counts. The toteboard may show 2.65 and 3.65 momentarily and this may well be how they end up, but could the totalizator handle it and do it for me ?

[cosmicway]

Suppose the money to be divided is T.
The money on the winner is X from simple win bets and Y from various dutched bets:

Y = Sum of (Fi . Yi)

Where Fi are the fractions of the dutch type bets that should be allocated on the winner.

Price = T / ( X + Y ) = T / ( X + Sum of (Fi . Yi) )

But we have unknowns on both sides of the equation.

In the simple case when it's only me who did that with two horses 1 and 2 it becomes:

Price 1 = A1 = T / ( X + Y . A2 / ( A1 + A2) )
Price 2 = A2 = T / ( X + Y . A1 / ( A1 + A2) )

It's a quadratic system and it can be solved (for A1 and A2).
What about the general case though ?

[Ray2000]

Both Wong's Excel file and the Del Mar tool require manual entry of real time odds and give the proportion to bet on x horses to produce the same return.

If your looking for the formulas to use in a tote scrapping program, it's beyond me..

Here's Wongs generalized solution

[thespaah]

Originally Posted by cosmicway

Everyone knows what dutching is.
I divide my money in two or more selections so the return is the same whatever the outcome, provided one of my selections wins.

If horse no 1 pays the (decimal) price A1 and horse no 2 pays the (decimal) price A2 then the dutched price is:

A(1-2) = 1 / ( 1 / A1 + 1 / A2 )

and the fraction I have wagered on the 1 is A(1-2) / A1 while the fraction I have wagered on the 2 is A(1-2) / A2.

This is simple when the prices are announced in advance (fixed odds betting). Sometimes there is a special designator on the ticket for dutching selections so you don't have to use a calculator.

Question: Is there a formula for this in pool betting ? If I say I want 1 and 2 dutched (or 1 and 2 and 3 dutched) is there an algorithm the betting pool operators can use to work out the fair price ?

Looks complicated. Or am I reading too much into it?

[cosmicway]

Originally Posted by Ray2000

Both Wong's Excel file and the Del Mar tool require manual entry of real time odds and give the proportion to bet on x horses to produce the same return.

If your looking for the formulas to use in a tote scrapping program, it's beyond me..

Here's Wongs generalized solution

That looks useful, thanks.
I 'm looking for formula to suggest to the company tote operators, if exists.

[Ray2000]

Originally Posted by cosmicway

I 'm looking for formula to suggest to the company tote operators, if exists.

Ahhh OK, It does exist.

One of my ADWs allows you to set up Dutch Wagering based on Win Pool, or Win/Double(Exacta/Quinella) and pull the trigger when/if ROIs are acceptable.

GL

[Robert Fischer]

nice feature

[cosmicway]

Originally Posted by Ray2000

Ahhh OK, It does exist.

One of my ADWs allows you to set up Dutch Wagering based on Win Pool, or Win/Double(Exacta/Quinella) and pull the trigger when/if ROIs are acceptable.

GL

He gets to know the tote price and does it afterwards for you.
In this way he sometimes overpays you and sometimes underpays you.
It's not exact.

[HKHandicapper]

Hey all

long time reader to the forum and love a lot of what you all post.

I'm looking for Wong's files, but he took down the link it seems.

In particular, 7.1 Kelly Win. If anyone has this file would they mind sharing it with me? I'd greatly appreciate it.

His book is a great read, I enjoyed it.

Thanks

HKH

[lamboguy]

Originally Posted by HKHandicapper

Hey all

long time reader to the forum and love a lot of what you all post.

I'm looking for Wong's files, but he took down the link it seems.

In particular, 7.1 Kelly Win. If anyone has this file would they mind sharing it with me? I'd greatly appreciate it.

His book is a great read, I enjoyed it.

Thanks

HKH

personaly, I am not a dutcher, but I would love to know how you are doing with Hong Kong racing.

[paulbenny]

Amwest has had the dutching formula built in on win and some other bets for years. The calculation is at the point in time you make your wager. The pools are constantly changing so it is just like any other wager you make before the pools close in terms of the expected return. Things change.

[cosmicway]

Originally Posted by paulbenny

Amwest has had the dutching formula built in on win and some other bets for years. The calculation is at the point in time you make your wager. The pools are constantly changing so it is just like any other wager you make before the pools close in terms of the expected return. Things change.

I had figured there are ways.
The Europeans don't like.
It's the companies' traders they say who don't like (that is the people who burn money).
It's not really a threat to them but they don't like.

[Robert Fischer]

Originally Posted by cosmicway

I had figured there are ways.
The Europeans don't like.
It's the companies' traders they say who don't like (that is the people who burn money).
It's not really a threat to them but they don't like.

It comes down again to First; having a significant opinion of value (like a 3rd outside-of-Dutch horse who will be falsely favored), as well as Secondly; also properly estimating a rough final odds by a combination of reading will-pays, knowing the circuit and current markets etc...

The absence of these things is an even bigger problem than the general problem of a 'moving target' as mentioned in this thread.