This actually does work as expected. If you choose random order, that order is not saved anywhere and the articles will be randomly sorted upon each loading of the page. If you want to have a random, but stable order, you would have to choose a different sorting method and set the data for that manually.

It might be how you expect it to work but its certainly not logical for anyone else to assume that. Think about it. All the other "order" options work across pages so there is no way that anyone could assume that "random" does not appear across pages.

Thanks for your answers. The topic is closed but i would like to comment further if possible.
With custom fields is now very easy to create directory websites. I more and more use joomla articles to create complex and vast websites.
Some of them contains lists of partners, employees, consultants, doctors, and so on that need to be listed somewhere. The problem is that the date order or the alphabetical order are always unfair because they always give more importance to someone instead of someone else.
In these cases the random order is perfect but if you have 50/100/200 or more entries have all of them in one single page is unpractical but splitting in more pages is now impossibile: some items can show in page 1 and page 3, or some items may not appear anywhere. The very concept of pagination falls apart because with random sorting it says 'page 1 of 8' but in reality it is not really 8 pages, it is 8 similar screens with X elements taken at random from a larger list.

Random is random.
When need a determined order, then it is not a random. Easy ?
What is not logical?

The issue is well known, it not joomla, but a nature of random behavior.

@PixedBo for your case, what you actualy can do is to make a plugin that change orderby_sec periodicaly, to one of these values

So let say, 1 hour order by "title", next hour order by "ordering", and another hour order by "title reveres" and so on.

Random is random. When need a determined order, then it is not a random. Easy ? What is not logical?

The issue is well known, it not joomla, but a nature of random behavior.

I'm not arguing about the nature of the "random" concept, my issue was about the whole pagination system of articles that falls apart if i want to display 200 articles in random orderd diveded in 10 pages. If I choose to see a list of items in random order and the system itself let me divide them by 10 i naively expet to see all 200 in 10 pages but in random order. Seeing 20 then going to page 2 and see agin some old items mixed with new items is counterintuitive imho. Browsing 10 pages with repetitions and the possibility of not seeing certain elements at all is not random, is chaos.

Anyway no problem, i get that this is how the system works and i'll live with it. I'm not a developer so i'll no try to develop a plugin (but thanks for the hint) I am just an enthusiast who wanted to express his point of view