# Math Help - Dutching Maths

1. ## 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.

2. 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:

$Gain = Stake*(Odds - 1)$

$Profit = Gain - Stake$

3. Originally Posted by markoone
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

4. ## 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.

$
S1 = \frac{(o2 * P)}{(o1 * o2) - (o1 + o2)}
$

$
S2 = \frac{(o1 * p)}{(o1 * o2) - (o1 + o2)}
$

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?