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Math Help - Summation Help for Horse Racing Problem

  1. #1
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    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
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  2. #2
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    Grandad's Avatar
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    Hello Ian

    Welcome to Math Help Forum!
    Quote Originally Posted by Cowan5 View Post
    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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