# Summation Help for Horse Racing Problem

• Jan 22nd 2010, 09:41 AM
Cowan5
Summation Help for Horse Racing Problem
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
• Jan 22nd 2010, 11:08 AM
Hello Ian

Welcome to Math Help Forum!
Quote:

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:
Quote:

there are ni (>0) horses at Si (i=1,2,3...,k) with S1<S2....Sk.
means there are:
$\displaystyle n_1$ horses at odds of $\displaystyle S_1:1$

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

...

$\displaystyle n_k$ horses at odds of $\displaystyle S_k:1$
and the numbers $\displaystyle S_1, S_2, ..., S_k$ are in ascending order of size: $\displaystyle S_1<S_2<...<S_k$.

Then the formula $\displaystyle p = \sum_{i=1}^k\left(\frac{n_i}{1+S_i}\right)$ means that:
$\displaystyle p = \frac{n_1}{1+S_1}+\frac{n_2}{1+S_2}+...+\frac{n_k} {1+S_k}$
Does that make it clearer?