Random Magic Paths - is it truly random?

[PvK]

Alneyan said:
...
- Murphy's Law, obviously. If you need a fire random badly, you will never get that random. Ever. Your neighbours, of course, will have their hands full of Garnet Amazons, sages with a pick in fire, and things of the like. Should you attempt to "convert" their mages, you will end up taking their non-fire mages away.

I just really desperately needed a one-in-eight random magic path pick on a new mage... and I got it.

So, obviously the real explanation is ... I stole your luck!

PvK

[alexti]

The_Tauren13 said:
You are determined to think me the fool, simply by my choice of wording, when your English is not so perfect either. Lets just say, for it to not be 'poor', in my eyes, I should be able to observe the results of the RNG and accumilate reasonable statistical results.

I don't claim the perfect knowledge of English, it's not even my native language, but I don't see any other possible meaning of your over half of all PC games have poor random number generators, but to think that you have either found somewhere a research that studied in details RNG in more than a half of PC games or you've conducted such a study yourself. Considering amount of time and effort required to perform such a task I find it hard to believe that your statement was based on facts and not on a wrong expectations from RNG. Another doubt comes, because RNG for uniformly distributed numbers is included in CRT and most games are likely to use it. Those RNG are not perfect, but you won't find their faults without collecting massive amounts of data.

The_Tauren13 said:

Perhaps your Dom II experience differs greatly from mine, but I have noticed many examples of random magic paths following odd distributions. Allow me to look at my current games: King of the Hill: 32 sages, no astral. So... (5/6)^32 ≈ .00293, .00293 * 6 magic paths ≈ .0176 = 1.76%... quite a low probablitity. Now we are looking at nearly 6 tails in a row, which is of course still believable...

Now, am I missing something? Sages have complete random, right? So the probability of never getting one particular path in sequence of 32 sages is (7/8)^32=0.014 and the probability of never getting unspecified path in sequence of 32 sages is 0.11 - 11%. (That is 10.8% rounded to 11, not 0.014*8, because possibility of 2 missing paths needs to be taken into account). I assume that you would have made a similar observation if your 32 sages were missing some other path. So the probability of making your observation is any particular game is 11% (it's close to the probability of getting 3 tails in a row).

The_Tauren13 said:
Unfortunately I am now forced to finish this message on another computer, so when I get home I can look at Borrowed Time as well and see the distribution of my Sauromancers' paths. If that isn't enough data for you, I could run a test game and recruit a hundred random mages... Hell, you could run a test game if youre not too busy. If I come up with more reasonable results,

That again goes back to my question of your usage of "poor". What do you expect as "reasonable results"? Any particular result that you'll get has quite low probability of happening. However, when you play the game, some result *has* to happened. There isn't any "highly probable" result. RNG would start looking suspicious if you were repeatedly getting the same lowly probable results. (For example, missing astral in 32 sages in every game you've played).

The_Tauren13 said:
I may concede the point that Dominions II is not another example of a poor RNG. But it would take much more for me to concede my other examples... but those games aren't half as good as Dom II, so who cares . If you give me your email I could send you my turn files and you can check my mage counting...

I don't doubt your counting and I don't suspect your data, I just questioning the conclusion you make from those observations...

The_Tauren13 said:

Perhaps, which is why I am attempting to further testing. But I dont have Dominions II installed here so you will have to wait.

This is well intended effort, but you need to understand what you're looking for. Let's say you look into some saved game and do the count. You can find some "unique feature" there (like 32 sages without astral). By itself, that doesn't indicate anything (because some result had to happen). However, if you can find the same "unique feature" in many other games, that will start to look suspicious. So I suggest you to list "unique features" you want to consider, then I will look for the same features in my games (I have few dozen of saved games I can check).

The_Tauren13 said:

Indeed. If you dispute my deterministic view of the universe and my claim that everything in the universe comes down to gravitational, nuclear, electromagnetic, etc. (which are not random) forces acting on atomic particles, go ahead, and we can argue that as well .

No... I'm disputing your ability to know every aspect of the universe To my knowledge deterministic/stochastic nature [of nearly anything] have not been established by the science and I haven't heard about anybody getting anywhere closer to understanding of those things. It is not even clear what kind of methods one can use to reliable establish deterministic/stochastic nature of something.

[alexti]

Bummer_Duck said:
I totally agree that 8 smiths is too small of sample. I believe I stated 14+ earlier, but perhaps not.

Here calculations are getting more complicated.
Probability of 14 smiths missing one of the paths is 80.8%.

Bummer_Duck said:
In my current game, I will be recruiting my 15th drawf this year, and I am still missing representation of 2 magic paths. 3 paths represent 71.4% of the mages, with 3, 3, and 4 mages per magic path, respectively (3 magic paths have 1 representative each). This is the widest distribution of paths I can remember in all my tests. So...turn those equations around for me. How likely is it that in each game or test, that ~3 paths would represent +71% of the mages?

It seems to be even more complicated to calculate (Probability that 10 or more smiths out of 14 will be concentrated in 3 paths). It seems to be around 40-45%, but I had to drop the tail of the sequence, so I'm not sure about accuracy. I will try to calculate it precisely later.

Bummer_Duck said:
shouldn't it approach 3/8? or 37.5% the larger the sample is? What am I missing here?

You mean number of mages concentrated in 3 paths should approach 37.5% of total number of mages? - No it should not, what are you saying would effectively mean that the equal number of mages in each path, which is very unlikely event. On the large samples peak of probability will probably be somewhere in 45-60% range (that's very rough estimate, I will try to calculate it precisely some time later)

[The_Tauren13]

alexti said:
Now, am I missing something? Sages have complete random, right?

Indeed. I must have been smoking something, for I was basing my probabilities off of there being only 6 magic paths

alexti said:
However, when you play the game, some result *has* to happened. There isn't any "highly probable" result.

Yes, I have not been too terribly clear. What I am specifically looking for is: large numbers of random mages of the same type being recruited, and a particular path having been unrepresented. So to refute my hypthesis, simply find several games in which all paths of magic are represented. The reason I was thinking a test game, though, is that in normal games (or at least my games) don't tend to have enough mages of one particular type to really formulate any conclusion. What I was thinking is just playing several games and recruiting 100+ mages, perhaps Vanheim dwarves as in the origional situation, and observing if frequently only 7 paths will be represented in the set.

alexti said:
I don't doubt your counting and I don't suspect your data, I just questioning the conclusion you make from those observations...

Which I do not deny are questionable, which is why I am making the attempt to gather somewhat more concrete data.

alexti said:
To my knowledge deterministic/stochastic nature [of nearly anything] have not been established by the science and I haven't heard about anybody getting anywhere closer to understanding of those things.

There is no reliable evidence, either way. In quantum machanics, effective observation is impossible. You cannot observe particle behavior without interfering with it. Also, simply because we do not have the means of predicting the exact behavior of such particles does not mean it is not possible to do so.

Yes, the general trend these days is to believe in Quantum Indeterminacy. This may have much to do with why I don't. I prefer to follow the less beaten paths. For example, I am currently working on an astrophysical project with the purpose of providing evidence to support Modified Newtonian Dynamics, an alternative theory to the widely supported Dark Matter Theory. Science requires disbelievers in order to continue its advancement. Where would we be if nobody ever questioned that the world was flat?

[Graeme Dice]

The_Tauren13 said:
Where would we be if nobody ever questioned that the world was flat?

About the same place we are now, since very few people ever believed that the world was flat.

[alexti]

The_Tauren13 said:
The reason I was thinking a test game, though, is that in normal games (or at least my games) don't tend to have enough mages of one particular type to really formulate any conclusion. What I was thinking is just playing several games and recruiting 100+ mages, perhaps Vanheim dwarves as in the origional situation, and observing if frequently only 7 paths will be represented in the set.

You're right about the need to do it in testing game. I've started counting randoms in some finished game and noticed how few spectres have water. Then I've realized that I was using spectres with water as mini-SC for raiding, and obviously I've lost quite a few of them.

[alexti]

About the tests. I suggest to take Jotuns or C'tis or Ermor with death mage pretender, research to Well of Misery and then set couple of mages on summon spectres monthly. After 24 hosting 24 turns you'll get 96 random picks (I was choosing multiplication of 8, so that Bummer_Duck's number (may I call it duck number?), which is max percentage of picks concentrated in 3 paths, can reach its ideal value.
Move all non-spectres out and count results in F1 screen. It seems to be doable under 10 minutes (unlike buying mages which can not be queued). I've just run 2 test games:

Game 1.
F-13,A-12,W-13,E-13,S-11,D-11,N-11,B-12. Duck number is 41%.

Game 2.
F-12,A-12,W-9,E-15,S-9,D-14,N-14,B-11. Duck number is 45%.

[Ivan Pedroso]

alexti said:

You mean number of mages concentrated in 3 paths should approach 37.5% of total number of mages? - No it should not, what are you saying would effectively mean that the equal number of mages in each path, which is very unlikely event. On the large samples peak of probability will probably be somewhere in 45-60% range (that's very rough estimate, I will try to calculate it precisely some time later)

Hmmmmmm, why shouldn't it approach 3/8 ?!?

Let us assume that the distribution behind the scenes is uniform. Then the observed frequencies will approach 1/8. Of cause getting a sequence that actually results in an observed frequency of exactly 1/8 for every path will be highly unlikely, but they WILL approach 1/8 as the sample grows. I mean: if you use a uniform distribution to generate some values, then the distributed values will look more and more uniform. And therefor adding the frequencies of the three highest represented paths will tend towards 3/8 (from above obviously). I concede that getting the result 3/8 in a test sample will "never" happen.

[atul]

Ivan Pedroso said:
Hmmmmmm, why shouldn't it approach 3/8 ?!?

Let us assume that the distribution behind the scenes is uniform. Then the observed frequencies will approach 1/8.

What you're missing here, assuming I've managed to follow the debate, is that they're talking about 3 most common random result. As there's selection based on how the randoms have turned out, the distribution is altered.

Gah, talking hard, let me give an example.

Two random numbers, x1 and x2, both with uniform distribution from zero to one. Each have an expected value of 0.5. But if you're asking what's the expected value of the _greater_ of two, that's 2/3!

Same thing told in the universal language of love (mathematics):
x1,x2 ~ U(0,1)
E(x1)=E(x2)=1/2
E(max(x1,x2))=2/3

My language or notation may be a bit off, but I hope the general idea is clear.

Of course, same applies to discrete case with magic randoms and so on, but is a bit harder to calculate.

[alexti]

Ivan Pedroso said:

Hmmmmmm, why shouldn't it approach 3/8 ?!?

Do you talk about convergence? Like lim(percentage, N->inf)= 3/8?

Ivan Pedroso said:
Let us assume that the distribution behind the scenes is uniform. Then the observed frequencies will approach 1/8. Of cause getting a sequence that actually results in an observed frequency of exactly 1/8 for every path will be highly unlikely, but they WILL approach 1/8 as the sample grows.

not WILL, only likely. For example, for any sample size, you have positive probability of getting all picks in one path. For samples of large size the distribution function will be getting more or more condensed, which you may call "approach". But you can't provide N for some small value x such that percentage of picks concentrated in 3 paths will deviate from 3/8 by no more than x.

Ivan Pedroso said:
I mean: if you use a uniform distribution to generate some values, then the distributed values will look more and more uniform. And therefor adding the frequencies of the three highest represented paths will tend towards 3/8 (from above obviously). I concede that getting the result 3/8 in a test sample will "never" happen.

The resulting process (the percentage of picks concentrated in 3 paths) is also a random process. That means that for different samples of the same size will produce different results.

The chances of getting 3/8 are getting smaller as you increase the sample size. The root of the issue is that the more your sample size is, the more possible outcomes can happen. That makes every particular outcome less and less likely to happen.

This random process also has a certain distribution. Which will roughly look like:
Code:

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   xxx

  xxxxxxx

 xxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxx

3/8                            1

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If we pick the range [x1,x2] that covers 99% of possible outcomes, then we could show that lim (x1, N-> inf) = lim (x2, N-> inf) = 3/8 (well, I think we can show), which intuitively seems as "approach", but unlike convergence, this "approach" has a stochastic character, like the difference between *will* and *most probably will*