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Math Help - Dutching Maths

  1. #1
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    Dutching Maths

    ok, I'm not a student of sorts, but I need some help with maths as its my worst subject - one of my vices is gambling and is not to be encouraged, but even so, I still do it. Here's my question:

    we have a 5 horse race and I want to bet on 2 of the horses in order to give me a set profit whichever horse wins.

    So Horse1 has odds of 4.5 and horse2 has odds of 7.6 and I have a target profit of 20 if either of these horses win. I do have a dutch calculator to give me the figures, but the author will not reveal the maths to me and I am sure it must be simple. Now i know that I need to stake 6.88 on horse1 and 4.07 on horse2.

    Horse1 odds = 4.5, stake = 6.88 - if wins, gain 24.08
    Horse2 odds = 7.6, stake = 4.07 - if wins, gain 26.86

    If horse1 wins, profit = 24.08 - 4.07 = 20.01
    If horse2 wins, profit = 26.86 - 6.88 = 19.98

    so what I need here is the maths for working out the stakes - can anybody help please? Many thanks.
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  2. #2
    Super Member Aryth's Avatar
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    I can't say that I know the math involved, but I did find something peculiar, say we divided gain by the initial stakes, we get this:

    \frac{24.08}{6.88} = 3.5

    \frac{26.86}{4.07} = 6.6

    It's easy to see that these two numbers are exactly 1 less than the initial odds. Meaning that there might be a pattern here:

    Gain = Stake*(Odds - 1)

    Profit = Gain - Stake
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by markoone View Post
    ok, I'm not a student of sorts, but I need some help with maths as its my worst subject - one of my vices is gambling and is not to be encouraged, but even so, I still do it. Here's my question:

    we have a 5 horse race and I want to bet on 2 of the horses in order to give me a set profit whichever horse wins.

    So Horse1 has odds of 4.5 and horse2 has odds of 7.6 and I have a target profit of 20 if either of these horses win. I do have a dutch calculator to give me the figures, but the author will not reveal the maths to me and I am sure it must be simple. Now i know that I need to stake 6.88 on horse1 and 4.07 on horse2.

    Horse1 odds = 4.5, stake = 6.88 - if wins, gain 24.08
    Horse2 odds = 7.6, stake = 4.07 - if wins, gain 26.86

    If horse1 wins, profit = 24.08 - 4.07 = 20.01
    If horse2 wins, profit = 26.86 - 6.88 = 19.98

    so what I need here is the maths for working out the stakes - can anybody help please? Many thanks.
    This seems an odd way of doing things and in my opinion you are doing the wrong calculation (or rather basing you betting strategy on the wrong principles), but:

    Let s1 and s1 be the two stakes and o1 and o2 be the odds expressed in the way you imply from your post, then:

    s2=\frac{20(o1+1)}{o1(o2+1)-(o1+1)}

    s1=\frac{o2+1}{o1+1}~s2

    RonL
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  4. #4
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    Mathematics for dutching two outcomes

    Hi,
    I am a software developer interested in the same subject as this, and would like to post the algorithm that I use for my software. I am not an expert at math myself but eventually worked this out. Normally I use programming languages that allow me to assign variables and run loops etc, which makes it easier, but i finally got it down to one line (or two).
    I know this is an old post but it may help someone along the line anyway.

    <br />
S1 = \frac{(o2 * P)}{(o1 * o2) - (o1 + o2)}<br />

    <br />
S2 = \frac{(o1 * p)}{(o1 * o2) - (o1 + o2)}<br />

    Where:
    S1 is the stake on the first outcome
    S2 is the stake on the second outcome
    o1 is the odds of the first outcome
    o2 is the odds of the second outcome
    P is the profit that you intend to make


    What I was looking for on here was how to do this with 3 or more outcomes? any suggestions?
    Last edited by camjohnson95; March 17th 2009 at 06:27 AM.
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