How to divide a number into several, unequal, yet increasing numbers [ for sending a PlaceOrder( OP_BUY, lots ) contract XTO ]

Question

I try to create an MQL4-script (an almost C++ related language, MQL4) where I want to divide a double value into 9 parts, where the fractions would be unequal, yet increasing

My current code attempts to do it this way (pseudo-code) :

   Lots1 = 0.1;
   Lots2 = (Lots1 / 100) * 120;//120% of Lot1
   Lots3 = (Lots2 / 100) * 130;//130% of Lot2
   Lots4 = (Lots3 / 100) * 140;//140% of Lot3
   Lots5 = (Lots4 / 100) * 140;//140% of Lot4
   Lots6 = (Lots5 / 100) * 160;//160% of Lot5
   Lots7 = (Lots6 / 100) * 170;//170% of Lot6
   Lots8 = (Lots7 / 100) * 180;//180% of Lot7
   Lots9 = (Lots8 / 100) * 190;//190% of Lot8
   ...

or better :

double Lots = 0.1;   // a Lot Size
double lot  = Lots;
...
                   /* Here is the array with percentages of lots' increments
                                                         in order */
int AllZoneLots[8] = { 120, 130, 140, 140, 160, 170, 180, 190 }; // 120%, 130%,...

                  /* Here, the lot sizes are used by looping the array
                                         and increasing the lot size by the count */
for( int i = 0; i < ArraySize( AllZoneLots ); i++ ) {
                        lots = AllZoneLots[i] * ( lots / 100 ) *;
 // PlaceOrder( OP_BUY, lots );
}

But, what I want is to just have a fixed value of 6.7 split into 9 parts, like these codes do, yet to have the value increasing, rather than being same... e.g, 6.7 split into :

double lots = { 0.10, 0.12, 0.16, 0.22, 0.31, 0.50, 0.85, 1.53, 2.91 };
            /* This is just an example
                            of how to divide a value of 6.7 into 9, growing parts

Answer 1

Not sure I understood right, but probably you need total of 3.5 shared between all lots.

And I can see only 8 lots not counting initial one.

totalPercentage = 0;
for(int i = 0; i < ArraySize(AllZoneLots); i++) {
    totalPercentage += AllZoneLots[i];
}

double totalValue = 3.5;

// total value is total percentage, Lots1 - 100%, so:
Lots1 = totalValue / totalPercentage * 100.00;

Then you continue with your code.

If you want to include Lots1, you just add 100 to the total and do the same.

Answer 2

This can be done so as to make equal steps in the values. If there are 9 steps, divide the value by 45 to get the first value, and the equal step x. Why? Because the sum of 1..9 is 45.

x = 6.7 / 45

which is 0.148889

The first term is x, the second term is 2 * x, the third term is 3 * x etc. They add up to 45 * x which is 6.7, but it's better to divide last. So the second term, say, would be 6.7 * 2 / 45;

Here is code which shows how it can be done in C, since MQL4 works with C Syntax:

#include <stdio.h>

int main(void) {
    double val = 6.7;
    double term;
    double sum = 0;
    for(int i = 1; i <= 9; i++) {
        term = val * i / 45;
        printf("%.3f ", term);
        sum += term;
    }
    printf("\nsum = %.3f\n", sum);
}

Program output:

0.149 0.298 0.447 0.596 0.744 0.893 1.042 1.191 1.340 
sum = 6.700

Answer 3

Q : How to divide a number into several, unequal, yet increasing numbers [ for sending a PlaceOrder( OP_BUY, lots ) contract XTO ]?

A : The problem is not as free as it might look for a first sight :

In metatrader Terminal ecosystem, the problem formulation has also to obey the externally decided factors ( that are mandatory for any XTO with an ambition not to get rejected, as being principally incompatible with the XTO Terms & Conditions set, and to get filled ~ "placed" At Market )

These factors are reportable via a call to:

MarketInfo( <_a_SymbolToReportSTRING>, MODE_MINLOT  ); // a minimum permitted size
MarketInfo( <_a_SymbolToReportSTRING>, MODE_LOTSTEP ); // a mandatory size-stepping
MarketInfo( <_a_SymbolToReportSTRING>, MODE_MAXLOT  ); // a maximum permitted size

Additionally, any such lot-size has to be prior of submitting an XTO also "normalised" for given number of decimal places, so as to successfully placed / accepted by the Trading-Server on the Broker's side. A failure to do so results in remotely rejected XTO-s ( which obviously come at a remarkable blocking / immense code-execution latency penalty one would always want to prevent from ever happening in real trading )

Last, but not least, any such XTO sizing has to be covered by a safe amount of leveraged equity ( checking the free-margin availability first, before ever sending any such XTO for reasons just mentioned above ).

---

The code:

While the initial pseudo-code above, does a progressive ( Martingale-alike ) lot-size scaling:

>>> aListOfFACTORs = [ 100, 120, 130, 140, 140, 160, 170, 180, 190 ]
>>> for endPoint in range( len( aListOfFACTORs ) ):
...     product = 1.
...     for item in aListOfFACTORs[:1+endPoint]:
...         product *= item / 100.
...     print( "Lots{0:} ~ ought be about {1:} times the amount of Lots1".format( 1 + endPoint, product ) )
... 

Lots1 ~ ought be about  1.0        times the amount of Lots1
Lots2 ~ ought be about  1.2        times the amount of Lots1
Lots3 ~ ought be about  1.56       times the amount of Lots1
Lots4 ~ ought be about  2.184      times the amount of Lots1
Lots5 ~ ought be about  3.0576     times the amount of Lots1
Lots6 ~ ought be about  4.89216    times the amount of Lots1
Lots7 ~ ought be about  8.316672   times the amount of Lots1
Lots8 ~ ought be about 14.9700096  times the amount of Lots1
Lots9 ~ ought be about 28.44301824 times the amount of Lots1

the _MINLOT, _LOTSTEP and _MAXLOT put the game into a new light.

Any successful strategy is not free to chose the sizes. Given the said 9-steps and a fixed amount of the total-amount ~ 6.7 lots, the process can obey the stepping and total, plus, it must obey the MarketInfo()-reported sizing algebra

Given 9-steps are mandatory,
each one has to be at least _MINLOT-sized:

double total_amount_to_split = aSizeToSPLIT;

total_amount_to_split = Min(   aSizeToSPLIT,                 // a wished-to-have-sizing
                               FreeMargin/LotInBaseCurr*sFty // a FreeMargin-covered size 
                               );
int next = 0;

while ( total_amount_to_split >= _MINLOT )
{       total_amount_to_split -= _MINLOT;
        lot_size[next++]       = _MINLOT;
       }
/*
###################################################################################
------------------------------------------------- HERE, WE HAVE 0:next lot_sizes
                                                                  next NEED NOT == 9
If there is anything yet to split:
   there is an integer amount of _LOTSTEP-s to distribute among 'em

   HERE, and ONLY here, you have a freedom to decide about split/mapping
                                           of the integer amount of _LOTSTEP-sized
                                           additions to the _MINLOT "pre"-sets
                                                                     in lot_size[]-s
   YET, still no more than _MAXLOT is permissible for the above explained reasons
------------------------------------------------- CODE has to obey this, if XTO-s
                                                                         are to
                                                                         get a chance
###################################################################################
                                                  */