Summation Help for Horse Racing Problem

**Cowan5** · January 22nd 2010, 09:41 AM

Hi I have a problem regarding summation and the index numbers. It is from a formula used in the betting industry.

"Consider a race with n runners with starting prices (the odds of each horse) denoted by Si:1 such that there are ni (>0) horses at Si (i=1,2,3...,k) with S1<S2....Sk."

Let p = Σ ni/(1+Si)

I want to find p but I don't understand the terms ni and Si, help appreciated.

Regards,
Ian

**Grandad** · January 22nd 2010, 11:08 AM

Hello Ian

Welcome to Math Help Forum!

Originally Posted by Cowan5

Hi I have a problem regarding summation and the index numbers. It is from a formula used in the betting industry.

"Consider a race with n runners with starting prices (the odds of each horse) denoted by Si:1 such that there are ni (>0) horses at Si (i=1,2,3...,k) with S1<S2....Sk."

Let p = Σ ni/(1+Si)

I want to find p but I don't understand the terms ni and Si, help appreciated.

Regards,
Ian

Let me unpack this for you:

there are ni (>0) horses at Si (i=1,2,3...,k) with S1<S2....Sk.

means there are:

$n_1$ horses at odds of $S_1:1$

$n_2$ horses at odds of $S_2:1$

...

$n_k$ horses at odds of $S_k:1$

and the numbers $S_1, S_2, ..., S_k$ are in ascending order of size: $S_1<S_2<...<S_k$ .

Then the formula $p = \sum_{i=1}^k\left(\frac{n_i}{1+S_i}\right)$ means that:

$p = \frac{n_1}{1+S_1}+\frac{n_2}{1+S_2}+...+\frac{n_k} {1+S_k}$

Does that make it clearer?

Grandad

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