Calculating odds on top3 positions

[Mofo]

Oh boy - my brain hurts. And I still can't work this out. I know you guys a pretty smart so hopefully you can help me out.


In a fixed odds event, if a horse pays $2 to win what does it pay to place? What if it pays $5 to win? How does the number of horses in the field affect the calculation?

What if you judge a horse to be more likely to get proportionally more 2nd and 3rds than 1sts? Does this mean that no calculation can be applied reliably, or does it just make it more complex?

I suppose basically all I really want to know is how the bookies work it all out.

Cheers,

[jfc]

http://us.geocities.com/possum_31415/place.htm

[Mofo]

Thanks for the link jfc! Interesting... I think I'll bookmark this one.

Do you know the calculation?

[jfc]

Apparently there is something called the Harville Formula for these classes of calculations.

I haven't bothered delving into that as I'd already derived the formula from first principles as follows:

The Trifecta probability is

abc/(1-a)/(1-a-b)

where a, b, and c are the win probabilities for runners A, B, C.


For every permutation instance A, B and C in your field calculate that probability and add it to slots A, B and C of an array.

When complete that array will have the required probabilities.

[Mofo]

Wow!

I'm not a mathematician but this is the kind of thing I was looking for. Thanks again. I'll do some work to find out what all that means.

Cheers,

[jfc]

In a fixed odds event, if a horse pays $2 to win what does it pay to place? What if it pays $5 to win? How does the number of horses in the field affect the calculation?

....


I suppose basically all I really want to know is how the bookies work it all out.

Cheers,

Bookies smart enough to work it all out are also smart enough to turn in their satchels and exploit the unprecedented opportunities now available with low-rake punting.

There is an extinct class of Bookies called Each-Way Bookies who typically offer 1/4 Win odds for the Place.

That oversimplification is wrong and has been well-known since at least WWII.

In fractional odds a 2/1 Win chance would pay 1/2 for the Place.

The new decimal equivalents are 3.0W and 1.5P.

But key in such a scenario into that nifty place calculator:

e.g this 100% market:

3
3
12
20
20
20
20
20

It calculates the fair place for the 3.0W as 1.233.

That is more than a double-overlay for the Place!