ETA : tl;dr Summary (this beccame very long!). The question, I think, is not 'can computer-generated random occurrences appear
not to be random' (yes), but rather 'are Elvenar's computer-generated random occurrences
actually random, or do they just appear to be?' (unknown/unknowable).
Obligatory Disclaimer: All of the above computations on expected outcomes are just that, expected. Real world observations can vary from exactly reproducing the expected results to the least likely outcome, but will most likely fall within standard deviations of the peak possibility.
@Sir Derf : Thank you for taking the time and trouble to explain how randomness works. Maths dunces like myself appreciate your hard work!
However, I think the real point here is not 'how does randomness actually work in Real World mathematics?'. As I say, I am no high mathematician, but I have enough basic knowledge to understand how extreme outcomes (whether favourable or not) do occur, even in truly random systems.
The debate is not, either, whether or not computers can truly mimic Real World randomness - that debate has rumbled on for decades, and in the end, as you probably already know (and it's been mentioned on the Forums before, too - perhaps even by you yourself, although I can't actually recall), has been solved in
practice, even if not in
theory, since 1996, by Fourmilab's
HotBits service, which generates true random numbers [and I quote from the Fourmilab website] "... by timing successive pairs of radioactive decays detected by a Geiger-Müller tube interfaced to a computer".
It seems to me that the real debate here is whether
any computer game which needs to make a profit, especially one which is consistently moving further and further towards the typical mobile-style F2P game model (in many ways with which I may one day bore the Forum, but not in this thread, as it's completely off-topic) - with all the very well-known intentional lack of randomness and/or
exploitation of randomness (e.g. the much-disliked 'scratchcard-style' Event Reward system) which such games almost all employ, usually in order to influence consumer spending.
Although I do see other players discussing other games by name here, I believe that it's disallowed, but I will say that - just for example - one mobile game I play features a so-called 'random' system whereby, when you complete a specific in-game objective which 'earns' a difficult-to-obtain item, the game will 'randomly' generate a second version of this item, but you need to pay real money to obtain this second item. These 'randomly generated' items
never (in the experience of any player, for over three years, in a game with several million players) appear unless the item in question is both in the upper reaches of difficulty to obtain (some days or even weeks of gameplay required), and also in the upper levels of cost (over £5.00, in a game where the minimum microtransaction amount is £0.99).
That particular game doesn't even try very hard to 'fool' its audience, since not only does one never see the 'randomly generated' bonus items if they would be worth less than £5.00, which is more than a slight indicator of whether or not they truly appear 'randomly', but - with enormous lack of subtlety, and frankly with the attitude that the players must be either stupid or desperate - the bonus items
always appear (100% chance) when the item
IS worth more than £5.00 - even to the extent that they actually become a nuisance and take up valuable space on the very limited-size playing board (which one can, of course, pay real money to increase in size in order to accommodate these 'bonus' items...).
And one reason why I mention this is because whenever these not-random guaranteed 'bonus items' appear, the game even puts up a message boldly (and, as I say, patronisingly) declaring: "You are LUCKY! A rare extra item has appeared BY CHANCE! Grab it before it disappears forever!".*
* Yes, of course this breaches most marketing laws. But when does anyone challenge, let alone prosecute, a mobile game company on such grounds?!
Now, I know Elvenar doesn't sink to such depths... but I also know that Elvenar, like so many other large Freemium games, employs psychologists as well as programmers and mathematicians. The psychologists are not there just for decoration, and so one wonders whether the programmers, in constructing their random number-generating algorithms, may or may not be influenced by others who are employed (amongst other reasons, of course) to ensure that 'random' events end up, when averaged across the entire playerbase (again, millions of people), falling at least to some extent into the bracket of 'random in InnoGames's favour' - while still
appearing genuinely random enough to be both psychologically acceptable to players
and, even when non-randomness is suspected
, explicable by maths experts such as yourself, thanks to the odd behaviour of randomness in Real Life anyway, plus the nigh-impossible task of ever
proving whether any player's particular results are unfavourable (or favourable, of course - if, in my example, one
wants to buy non-random 'bonus items'?) due solely to random chance or, at least in part, by design.
I doubt we will ever know this, of course, but mobile gaming (and F2P gaming in general) isn't the most famously 'fair' [or conspicuously moral] commercial environment. In fact, it falls not far short of the average Vegas Casino in terms of usually, if not always, ensuring that 'the house always wins in the end'. And maybe that
is random... but maybe not so much, if we really
did get to see (say) a year's worth of
actual random (?) results across the entire playerbase, not just the tiny percentage who ever comment on game Forums. Now
that would be interesting.