I have added function to controller class:

class ServiceHolder_Controller extends Page_Controller 
{   
    public function RandomBackgroundNumber() {
        return rand(1,4);
    }
}

        <% loop $Children %>
            <a href="$Link" title="$Title" class="serviceBox <% if $First %>firstService<% end_if %>" 
               style="<% if $RandomBackgroundNumber == 1 %>
                        background-color: #19b5f0;
                      <% else_if $RandomBackgroundNumber == 2 %> 
                        background-color: #00adef;
                      <% else_if $RandomBackgroundNumber == 3 %> 
                        background-color: #59d1ff;
                      <% else_if $RandomBackgroundNumber == 4 %> 
                        background-color: #14ade5;
                      <% end_if %> " >
                <span style="display: block; text-align: center;">
                    <img src="$ServiceHolderIcon.URL" alt="$Title" style="max-width: 130px; max-height: 130px; margin: 0px; border: none; background: transparent;" />
                </span>
                <span style="display: block; text-align: center;">$Title</span>
            </a>
        <% end_loop %>   

The loop is working nice, but I cannot set background this way... Could Anyone tell me why "style" attribute in my anchor is always empty?

EDITED

When I add additional else to the if-else statement I get the color but every anchor is the same blue color from "else" statement:

                      <% else  %> 
                          background-color: blue;
                      <% end_if %> " >

So it looks like the rand(1,4) do not return correct values to compare?

It's one of the basic methods used in many many CMS all around the world?
No one knows? :(

Hi Sebastiankozub

Is RandomBackgroundNumber a function on your child pages or just your parent?

If it is just on the parent, you may need to call $Top.RandomBackgroundNumber instead.

-helenclarko

I think you mean $Up, not the $Top, but whatever way still no working... Could anyone reproduce it?
ServiceHolder.ss

<div class="content-container unit lastUnit serviceHolder">
    
        <% loop $Children %>
            <a href="$Link" title="$Title" class="serviceBox <% if $First %>firstService<% end_if %>" 
               style="<% if $Up.RandomBackgroundNumber == 1 %>
                        background-color: #19b5f0;
                      <% else_if $Up.RandomBackgroundNumber == 2 %> 
                        background-color: #00adef;
                      <% else_if $Up.RandomBackgroundNumber == 3 %> 
                        background-color: #59d1ff;
                      <% else_if $Up.RandomBackgroundNumber == 4 %> 
                        background-color: #14ade5;
                      <% else %> 
                        background-color: #14ade5;
                      <% end_if %>" >
                <span style="display: block; text-align: center;">
                    <img src="$ServiceHolderIcon.URL" alt="$Title" style="max-width: 130px; max-height: 130px; margin: 0px; border: none; background: transparent;" />
                </span>
                <span style="display: block; text-align: center;">$Title</span>
            </a>
            <!--$ProductHolderIcon-->
            <!--img src="$ProductHolderIcon.URL" alt="" style="max-width: 60px; max-height: 60px; margin: 20px;" /-->
            <!--img src="$ProductHolderIcon.Link" alt="" style="max-width: 60px; max-height: 60px; margin: 20px;" /-->
        <% end_loop %>       

</div>

ServiceHolder.php

<?php

class ServiceHolder extends Page 
{
    private static $allowed_children = array('ServicePage');
}


class ServiceHolder_Controller extends Page_Controller 
{
    public function init() {
        //RSSFeed::linkToFeed($this->Link() . "rss");    
        parent::init();
    }
    
    private static $allowed_actions = array( 
        //'rss'
    );
    
    public function RandomBackgroundNumber() {
        return rand(1,4);
    }
}
?>

The problem was in " == ". Strange that PHP Framework takes Pascal syntax to template syntax and I think I see "==" in Template Syntax documentation also ;)
Moreover to get values from parent we need $Up variable, not $Top (not sure but I think Top goes to top level page: SiteTree?).