AstralSoul
Illusionist
A fellow got a Magic House, and I got 50 diamonds from the 1st-floor boss. Today, I got a Magic WS from the 2nd-floor boss. They don't drop often, but they drop.
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Discussion Gathering of the Phoenix Cults
- Thread starter Silmaril
- Start date
Sir Derf
Adept
Wow, it's almost like outcomes of stated random events conform to those stated random events, if only in a loose form...
Seriously, second level, fist section, PP at 15% offer from the 4th chest.
So, in 20 chests so far, 3 opportunities at 15%*30%*15% = 0.625% chance at getting all three.
And, for all those concerned about clustering...
When we were looking at only the first 2 chests, that had odds of 4.5% to get both, a cluster of 2.
With three chests, there are three ways to have gotten 2 out of 3 PPs, PPx, PxP, and xPP, with individual odds of 3.8%, 1.6% and 3.8%. Combined, that means that you had a 7.7% chance of getting a 2-cluster with 3 chests, up from 4.5% in 2 chests.
Additionally, the earlier stated 0.625% chance of getting all three in 3 chests is up from the 0% chance of getting a cluster of 3 in only 2 chests, and represents the additional 15% chance after having already received the 4.5% chance in the first 2 chests.
And, for those who need explicit statements of universal truths, 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.
Seriously, second level, fist section, PP at 15% offer from the 4th chest.
So, in 20 chests so far, 3 opportunities at 15%*30%*15% = 0.625% chance at getting all three.
And, for all those concerned about clustering...
When we were looking at only the first 2 chests, that had odds of 4.5% to get both, a cluster of 2.
With three chests, there are three ways to have gotten 2 out of 3 PPs, PPx, PxP, and xPP, with individual odds of 3.8%, 1.6% and 3.8%. Combined, that means that you had a 7.7% chance of getting a 2-cluster with 3 chests, up from 4.5% in 2 chests.
Additionally, the earlier stated 0.625% chance of getting all three in 3 chests is up from the 0% chance of getting a cluster of 3 in only 2 chests, and represents the additional 15% chance after having already received the 4.5% chance in the first 2 chests.
And, for those who need explicit statements of universal truths, 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
Adept
Second level Final Boss - 30% chance at PP
So, 2 Levels, 32 chests, 15%*30%*15%*30% = 0.2025% chance, or 1:500, to get all 4 PPs in the first 2 Levels of the Spire on any particular run on the Spire.
At 99.8% that you won't get all 4, that's (99.8%)^52 or 90.11% that you won't get all 4 ever in a year (yes, it's only been 9 months, but let's look at round numbers). Which means you have a 9.89% chance that you will get all 4 PPs at least once in a year Or, roughly 1 in 10 people will see this once in a year.
The odds will be slightly lower to have it happen only once in a year, at 52*0.2%*(99.8%)^51, or 9.39%. The remaining 0.5% represents possibilities that you will get all 4 twice or more in the year.
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.
So, 2 Levels, 32 chests, 15%*30%*15%*30% = 0.2025% chance, or 1:500, to get all 4 PPs in the first 2 Levels of the Spire on any particular run on the Spire.
At 99.8% that you won't get all 4, that's (99.8%)^52 or 90.11% that you won't get all 4 ever in a year (yes, it's only been 9 months, but let's look at round numbers). Which means you have a 9.89% chance that you will get all 4 PPs at least once in a year Or, roughly 1 in 10 people will see this once in a year.
The odds will be slightly lower to have it happen only once in a year, at 52*0.2%*(99.8%)^51, or 9.39%. The remaining 0.5% represents possibilities that you will get all 4 twice or more in the year.
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.
Laurelin
Sorcerer
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).
@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.
@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.
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