DUTCH BET Exchange Formula

[rosseaux]

Good evening, my name is Giuseppe and I have just registered for your forum.

I'm Italian Boy and this Topic Is translated from help of Google Translate.

I need Mathematical help regards an excel file of Sports Trading .. Soccer in this case ..
My problem is related to finding numbers to multiply according to certain conditions.

I don't know much about it but I think it's used in the right way CRAMER ..

If I have a Profit Target (€ 5 for example) .. I would like to make it equalize it between the profit of the Back and the Lay.

Now I graphically expose the whole:

Profit target = 5 €

-----------------------Back-------Lay
P.Back/P.Lay------??------------??--
Price------------2,1-----------1,9--
Clear Gains----??------------??--
Liability-------------------------??--
Profit---------------??------------??--

We come to the point.

I already know the formulas to get the whole thing:

Target = 5 €

First of all, the difference in profits must be obtained by subtracting the price of the Lay (Q.Lay) from that of the Back (Q.Back).

∆ Gains = Q.back - Q.lay.. so.. 2,1 - 1,9 = 0,2

Then it is necessary to derive the percentage of Profit by dividing the Back Price with the Price of the Lay ..

% Gains = Q.Back / Q.Lay ... so.. 2,1 / 1,9 = 1,10526

So we get the Back Stake..

P.Back = ((Target * Q.Lay) / (∆ Gains)) .. so .. ((5 * 1,9) / 0,2) = 47,5 €

Now we get the amount of the Bank ..

P.Lay = (% Gains * P.Back) .. so.. (1,10526 * 47,5) = 52,5 €

So..

Profit Back = Back Clear Gains - Liability .. so.. ((47,5 * 2,1) - 47,5) - (52,5 * (1,9 - 1)) ... That is (52,25 - 47,25) = 5 €

Profit Lay = Lay Clear Gains - Q.Back .. so .. (52,5 - 47,5) = 5 €

Graphically it turns out like this:

-----------------------Back-----------Lay
P.Back/P.Lay-----47,5----------52,5---
Price-------------2,1-----------1,9---
Clear Gains---52,25---------52,5---
Liability------------------------47,25--
Profit--------------5----------------5------


.. it works perfectly .. because as you can see in both cases .. both win the Back .. and both win the Lay .. I would earn equally € 5 profit .. which is My Equalized Target .. also called DUTCH BET ..

Too bad that then comes the damn 5% commission on winnings that ruins everything.

What I ask is: what formula can I use to integrate even 5% commission in order to get the same result shown above?

In my case... the 5% commission applies only to the winnings of the bet .. which then becomes:

Back Clear Gains = ((P.Back * Q.Back) * (1 - 0,05)) - P.Back

.. and also applies to winning the bank .. which then becomes:

Lay Clear Gains = (P.Lay) * (1 - 0,05)

Instead it does not apply to losses .. therefore neither on the LIABILITY of the Lay or even on the loss of the Back ..

Let's take an example:

Profit Target = € 5,00
Q.Back of home team "1" = 2,1
Q.Lay in live home team "1" = 1,9
Commission = 5%
Back Stake = ??
Lay Stake = ??

How much should I Back (Back Stake) on the home team "1" to Q.Back 2.1 to obtain in the case of Victory a profit of € 5.00 making sure that it is the same profit derived from the possible winning of the Lay (Lay Stake) on the home team "1" at Q.Lay 1,9 ??

I hope I made myself understood because it is not easy to explain my goal of obtaining both if the home team "1" wins and if it loses home team "1" the same and identical profit of € 5.00.

I would add that I think I have found a way to integrate the Commission with 5% at least in LAY STAKE ..

It turns out like this:

P.Lay (LAY STAKE) = ((Q.Back * (1 - Comm.)) / (Q.Lay - Comm.)) * P.Back) ..

The Commission in the formula is expressed in decimal .. so 5% becomes 0.05 ...

Only the problem is precisely in finding the Right Stake of the Back (P.Back) .. That is My Big Rock ...

Let's be clear .. I already know the result of my example .. but I reached it with hours and hours of attempts .. manually changing the values ​​.. It is not Sustainable to reach it with attempts if the Mathematics can come to my rescue ...

If so it can be helpful to communicate the result:

P.Back = 204,4199 (And I don't know how it's possible to derive it)

P.Lay = 220,442 (Derived from the Formula that I just wrote above)..

In practice, I miss only that of Back STAKE (P.Back) ..

I hope that I have clarified all the concepts .. but if it were not so .. just ask what I was not good at explaining ..