Random Magic Paths - is it truly random?
 

Hi!

So...I'm in my first real game. I have played a bunch of test beds, and sims to get familiar with the combat system, and what to research when. I have been concentrating on Vanheim for now, and I have noticed that the random magic picks don't seem to be that random. Each game is different, though. In one testbed/game, I may be flush with earth3, blood1 and earth3, Death1 Drawfs, and never get Fire or Astral. In the next game, I don't get any Blood or Death, but get earth3, air1 and earth4. I'm talking about a fairly good sample, of 14+ dwarf mages. While it isn't a huge sample, IMO it shows a pattern of non randomness.

Above and beyond this, the Sages that I recruit seem to follow the same sort of nonrandom distribution that the Dwarfs share per game. Is this a known bug? or is it just me. :-)

Re: Random Magic Paths - is it truly random?
 

There are three types of random picks: Elemental, Sorcery, and totally random. Otherwise chances should be equal.

Re: Random Magic Paths - is it truly random?
 

Random paths are as random as they came, at least in the examples you give. Only the following characteristics can alter the distribution of random paths:

- Some units have Sorcery (Nature, Astral, Death, Blood) randoms, others have Elemental randoms, while most randoms are full randoms. A few units have both randoms (the Celestial Master among them, if memory serves).
- A few units do not have two randoms, but instead a random +2 level in the same path. This random could also be Sorcery, Elemental or a full random. Atlantis has a mage with this pattern: 3 water, and 2 randoms in the same path.
- 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.

Re: Random Magic Paths - is it truly random?
 

Well, it is an obvious fact that over half of all PC games have poor random number generators. I'm sure this is just another example of that.

Re: Random Magic Paths - is it truly random?
 

I don't see any pattern in your examples, it looks totally random (I assume that you know that earth3 is fixed and only one path is random). As you said in each game you've got different sequence of randoms which is the right behaviour for randoms. I would get concerned if you've observed something like Astral-Death-Blood-Earth-Air-... pick in every game.

Re: Random Magic Paths - is it truly random?
 

I assume that you talk about pseudo-random number generators (because all software RNG are totally deterministic), But then that is some statement. Obvious why and to whom? Over half - where this number comes from? poor - how do you define "poor"?

To find a fault in most current pseudo-RNG (usually they have one fault or another) one needs to do quite a bit of research, which doesn't look possible by observing game's behaviour, because it would take too much time to collect meaningful statistics.

Re: Random Magic Paths - is it truly random?
 

Oh I quite disagree; it doesn't take long to realize. Examples of incredibly poor games: Disciples II: The hit percentages never worked well. Most notably paralyziation; you would frequently hit 10 in a row, and then miss 10 in a row. Warlords IV: A low combat creature is fighting a high combat creature and the weaker hits, nearly every time the high combat creature would then miss his next attack. Odd behavior like that is hard to miss.
The use of the term pseudo-random is pointless; there is no randomness in our universe. None. It is similar to when people argue that everything humans do is also natural because we are natural; the term becomes meaningless by its own definition.

By 'poor' I simply mean they simulate statistical results with less accuracy than one would expect. Perhaps I should say: 'less accuracy than I would expect', since you seem to be argumentative. Perhaps that was not meant as a flame against my intelligence, but it sure sounded like it.

Re: Random Magic Paths - is it truly random?
 

Er, so you are saying quantum mechanical probabilities are pre-determined?

Re: Random Magic Paths - is it truly random?
 

It's also an obvious fact that 76.45% of all statistics are made up on the spot.

Re: Random Magic Paths - is it truly random?
 

Here. Take this atom of U-238. Please tell me exactly when it will decay.

Re: Random Magic Paths - is it truly random?
 

I'm not familiar with those games, but generall I doubt that you can distinguish RNG problem from the bug in the code. For example, Dom2 had a bug with mind duel, where it was OE D6 instead of simple D6. By monitoring statistics you could have thought that the problem is in RNG.

RNG are not designed to simulate statistical results. They're simulating stochastic processes. Statistics are result of observation of the stochastic process. Any statistics resulting from the observation of stochastic process is a stochastic process itself. That's what make it hard to make reliable conclusions about stochastic process from the statistics.

Consider the original post with those dwarven smiths. Assuming that randoms are uniformly distributed, probability that 2 particular paths won't appear in a sequence of 14 smiths is (6/8)^14 = 0.0178. There 7+6+...+1 = 28 different pairs of 2 paths. So probability of not getting some 2 paths in a sequence of 14 smiths is 0.0178*28=0.4989. Just about like flipping that famous two-sided coin. So the examples that the poster has shown falls well within expected results. So after doing these calculations, original example looks like: "I've flipped coin and got tails 4 times in a row. Is it a buggy coin or am I missing something?" Now consider that there're few hundreds people playing Dominions here (some of them are quite familiar with probability theory, so we exclude them from this consideration) who do our "flips". It is very probable that few of them will get quite a few tails in a row. So one of them has posted his question (remember that in the actual case it is not immediately obvious that the probability of that outcome is 50%)

It was meant to question your knowledge of probability theory. You've jumped on Bummer_Duck hyphotesis/question claiming absolute knowledge (please reread your post) without any kind of backing. On top of that after closer examination Bummer_Duck's example is likely to be observed with ideal RNG. Of course, that doesn't prove that there's no problems with RNG, but this test, it passes very well.

Btw, I've noticed that you were not losing time meanwhile and have expanded your knowledge from over a half of PC games to the whole universe http://forum.shrapnelgames.com/images/smilies/wink.gif

Re: Random Magic Paths - is it truly random?
 

Graeme, I read it was 95%.
Tauren, even just using rand() is pretty damn good. It's not perfect; if you look closely, you can tease out a little bit of structure from it... But it's nothing that you'd notice by playing a game.
What IS noteworthy is the human brain's ability to find structure and pattern... even when it's not there, or when it's there only by chance. Once we've convinced ourselves it's there, another one of our great skills is disregarding evidence to the contrary.
To make it concrete: there's an enormous amount of variability and complexity in Dominions (and, to some extent, most video games). Just by chance, sometimes things that look like patterns emerge (just like, if you flip a coin long enough, you'll see a run of ten heads; if you flip a thousand coins, you'll probably see such a run pretty frequently). Those tend to stand out, and we look for them. When we see them again, the tendency is to say "See? This isn't random!", while missing (because they're not salient) all the times we could have seen them but didn't.

Re: Random Magic Paths - is it truly random?
 

I once thought I had a random thought, but then it turned out to be improbable...


That aside, I have felt the same way as Bummer Duck. However, I suspect that's just a perception thing, rooted in my own desperation to get whatever I'm not getting. When I get what I'm looking for the first time, I spend a lot less time thinking about how unlikely that was--I just pack up my army and march out to whip whatever booty I can find nearby!

Re: Random Magic Paths - is it truly random?
 

Yes, I realize the earth3 is standard, and drawfs only get 1 random.

It could very well be a perception thing. It is true that I have probably gotten a complete random distribution, if I add all the test bed games together.

However, I find it strange that in each game I tested, the majority of the dwarves random picks are in 2 paths. I have testbeded at least 8 games, and have *never* gotten representation of all magic paths in 1 game. I find this, in and of itself, questionable. Perhaps I just don't understand RNG?

Re: Random Magic Paths - is it truly random?
 

How many smiths (or any mages with randoms you had)? For example, probability that you'll get every random path in a sequence of 8 smiths is 7/8*6/8*...*1/8 = 7!/8^7 = 5040/2097152=0.0024 - not that likely to happen, isn't it? With more smiths the chances obviously grow, so the question is how many of them you had.

Re: Random Magic Paths - is it truly random?
 

That's what I belive. I can recall quite a few games, where I deliberately waited for a fire random and only ended up with a lot of earth picks, and other games where I just needed a single earth pick and only got fire...

I do believe that pseudo-random number generation is generally good enough for games like Dom2. I also believe that "Murphys Law" is mostly due to the fact that oddities and failures are far easilier remembered than average things. I also recall a newspaper report about traffic-jams on multi-lane motorways and lane-hopping: People will always believe that they are in the one wrong lane which is progressing slowest. The report said that this is due to the fact that people who are waiting will notice each car that overtakes them, whereas overtaking others is far less memorizable. Generally, each car that you overtake gives much less satisfaction than the annoyance pereceived by each other car that overtakes oneself...

Re: Random Magic Paths - is it truly random?
 

Whether or not the bug is in the code of the implementation of the random number algorithm used or that algorithm itself, it still comes to the same effect: the randomess for that game is bugged.

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.

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... 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, 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 http://forum.shrapnelgames.com/images/smilies/happy.gif. If you give me your email I could send you my turn files and you can check my mage counting...

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

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 http://forum.shrapnelgames.com/images/smilies/happy.gif. And while the subject may be considered philosophical, please don't bring religion into it... I'm a hardcore atheist. And thanks for adding the smiley this time so I know you're not just trying to be insulting.

Re: Random Magic Paths - is it truly random?
 

I totally agree that 8 smiths is too small of sample. I believe I stated 14+ earlier, but perhaps not. 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? shouldn't it approach 3/8? or 37.5% the larger the sample is? What am I missing here?

Re: Random Magic Paths - is it truly random?
 

And hardly outside of the realm of possibility either.


So you are telling me that the moment when a particular atom of a radioactive element will decay can be determined before it decays? Because that's what you're claiming when you claim a deterministic universe. Of course people dispute your claim, because it's known to be false.

Re: Random Magic Paths - is it truly random?
 

Here is some data for you number crunchers:

First game (three types of mages with randoms)

A: 0,3,0 - 3
E: 2,6,2 - 10
W: 2,8,0 - 10
F: 2,6,0 - 8
D: 1,1,0 - 2
S: 0,3,0 - 3
N: 1,4,0 - 5
B: 2,3,2 - 7

Looks pretty random to me.

Second game: (three types of mages with randoms)
A: 0,0,1 - 1
E: 2,3,8 - 13
W: 1,6,2 - 9
F: 2,3,2 - 7
D: 2,2,2 - 6
S: 4,4,2 - 10
N: 4,0,1 - 5
B: 2,3,2 - 7

A bit light on air... and frankly, I had not noticed, because I am Vanheim in both games (the mage types are smith, vanadrott and sage, of course)

Speaking of things I just realized, I guess I am hurting for cash in the first game http://forum.shrapnelgames.com/images/smilies/frown.gif

Re: Random Magic Paths - is it truly random?
 

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! http://forum.shrapnelgames.com/image...ies/tongue.gif

PvK

Re: Random Magic Paths - is it truly random?
 

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.

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).

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).

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

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).


No... I'm disputing your ability to know every aspect of the universe http://forum.shrapnelgames.com/images/smilies/wink.gif 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.

Re: Random Magic Paths - is it truly random?
 

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

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.

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)

Re: Random Magic Paths - is it truly random?
 

Indeed. I must have been smoking something, for I was basing my probabilities off of there being only 6 magic paths http://forum.shrapnelgames.com/images/smilies/shock.gif

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.

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

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? http://forum.shrapnelgames.com/images/smilies/smirk.gif

Re: Random Magic Paths - is it truly random?
 

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

Re: Random Magic Paths - is it truly random?
 

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.

Re: Random Magic Paths - is it truly random?
 

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%.

Re: Random Magic Paths - is it truly random?
 

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.

Re: Random Magic Paths - is it truly random?
 

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.

Re: Random Magic Paths - is it truly random?
 

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

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.

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:
<font class="small">Code:</font><hr /><pre>
xxx
xxxxxxx
xxxxxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxx
3/8 1
</pre><hr />

If we pick the range [x1,x2] that covers 99% of possible outcomes, then we could show that lim (x1, N-&gt; inf) = lim (x2, N-&gt; 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*

Re: Random Magic Paths - is it truly random?
 

Ok, the math you guys are throwing out is just beyond me. I would, however, dispute lumping all mages into the same catagory for a test, though. There could be a problem with 1 particular unit type. If I have some time this weekend, I'll try a few Drawf recruiting tests too.

Thanks for the responses!

Re: Random Magic Paths - is it truly random?
 

You should at least be accurate here. The correct wording of your last sentence ought to be "Of course some people dispute your claim, because many believe it to be false."

Just because some scientists believe that radioactive decay is totally random does not make it so. I work at a nuclear weapons research facility in the field of radiation detection, and I can assure you that this question is far from settled.

In fact, I personally believe that if the means to observe a single nucleus WITHOUT interference were to ever be developed, one would likely be able to predict when a particular radioactive atom is about to decay. But Heisenberg has a theorum which makes this a very difficult thing to achieve, even in a Gedanken experiment. http://forum.shrapnelgames.com/image...s/confused.gif

Be very careful with making sweeping judgements about the universe. It will likely bite you in the end.



On the subject of random paths for your mages, I used to think it seemed biased towards elemental over sorcery. I still do, but less severe than I used to think.

I also think that my opinion of seeing bias in my mages can perhaps be traced to such things as in my current Atlantis game, where I was REALLY wanting an earth King of the Deep, and had none after about 30 mages had been recruited. I then used my first earth mage to chain summon troll kings and now I have all the earth commanders I need.

Of course, I have since bought several Kings of the Deep with earth skill at a significantly higher rate now that it is less important to me. This may just be yet another emample of Murphy's Law! http://forum.shrapnelgames.com/image...es/biggrin.gif

Re: Random Magic Paths - is it truly random?
 

All right, I just went back in this thread and added up the four cases where people posted details with a decently high total to give us some meaningful statistics. On the conjecture of a bias of elemental over sorcery, here are the totals of elemental vs. sorcery picks.

Yvelina Game 1 : 31-17
Yvelina Game 2 : 30-28
Alexti Trial 1 : 51-45
Alexti Trial 2 : 48-48
Elemental seems favored in this to the first level.

This matches many of my own earlier trials on this subject. In fact, I can't seem to rcall of a decent-sized trial where the total sorcery randoms exceeded the total elemental randoms. The Alexti Trial 2 above is the first one I have seen where they were even equal.

Random or bias? I have no idea at this point, for one can argue either way based on the sparse data.

Later today, I will add up my Atlantis King totals and post that. I know I have not lost one as yet, so it will be a fair total. However, the game is early enough that I do not have as many Kings as any of the above four cases.

Re: Random Magic Paths - is it truly random?
 

Another sample if you want, rather small, but I should be able to increase the number of these mages if my neighbours leave me in peace (those are my sages in the Yarnspinners game):

Air and Blood: 4
Astral and Fire: 5
Death and Nature: 7
Water: 9
Earth: 10
Total: 51 sages, 28 in Elemancy and 23 in Sorcery.

Re: Random Magic Paths - is it truly random?
 

Well, I must say your test game results show none of the odd distributions mentioned in this thread; they don't appear to be more concentrated into 3 paths, and certainly aren't lacking any one path. If Im less busy today I might actually run some tests myself, and we could even look at the elemental/sorcery ratio for hundreds of mages.

For your test games, let me combine the two:
F-25,A-24,W-22,E-28,S-20,D-25,N-25,B-23
the 'duck number' is 41%
the elemental/sorcery ratio is 1.0645

Looks good to me. Hopefully I can make some more tests today.

Re: Random Magic Paths - is it truly random?
 

Duck: The random generated paths use the same function for all units with randoms odf the same kind. So if a unit has any random paths it will not have more or less of a problem than any other unit using the same allocation of randoms.

Panther: All randomly generated numbers in the game are derived from a large set of pregenerated numbers. These numbers are cycled through. While it is possible that there might be a very slight weight in the numbers towards the lower or higher range of a die, it is not a weight that should be readily perceptible.

Edit: I reread my post and realised it wasn't very clear what the point of my response to panther was, so here comes the explanation. A weight of the numbers to the lower or higher half of the distribution would be by far the likeliest cause for a predomince of either elemental or sorcery. If this was the case it would also mean that all other 'random die rolls' in the game would show similar tendencies, ie the bottom half of the distribution would show up more htan the tophalf, obviously most of those 'rolls' are not quite as readily accessible to the player though.

Re: Random Magic Paths - is it truly random?
 

Another test, with Spectres this time (there are 97 of them). Here are the results:
Fire:22
Air:22
Water:25
Earth:28
Astral:22
Death:31
Nature:17
Blood:27

It gives 97 elemental picks against 97 sorcery picks. Hmm, I guess I will run another time to try to get more Sorcery than elemancy.

*Grumbles* 110 for elemental picks, 86 for sorcery. The elements win once more.

Re: Random Magic Paths - is it truly random?
 

I took the sceptre test as well, 99 spectres.
Air 22 (3)
Fire 24 (0)
Earth 28 (3)
Water 26 (2)
Death 19 (2)
Nature 29 (2)
Astral 26 (1)
Blood 24 (2)
The first number is the total of results, the second is how many times that path appeared twice on the same spectre.
I find it interesting that no double fires came along, but with a chance of around 4% (Im not sure I did the math right) that's quite acceptable.
Total Sorcery: 98
Total Elemental: 100
Elemental wins, but by a very small margin.
I'd say there's no bias towards Elemental, atleast according to my tests, but with all the other tests...

Re: Random Magic Paths - is it truly random?
 

You a right that if I roll a number of dies (in this case eight-sided) and then only write down the largest value every time, then the average of this "highest-value-thrown" will indeed be higher than the usual 4.5 that is the average value of a standard eight-sided die. But that is (if understand it correctly) not the situation at hand.

As I see it, we are dealing with:
Some dude rolls a bunch of eight-sided dies, and then write down how many ones he got, how many twos he got and so on. He then adds the numbers of the three most common results, and divides this number with the total number of dies rolled.

An example:
100 eight-sided dies are rolled, and the following is written down:
#1 : 15
#2 : 12
#3 : 19
#4 : 10
#5 : 9
#6 : 12
#7 : 10
#8 : 13
The three highest are added (i.e. #3,#1, and #8) and we get:
19+15+13 = 47
And get (the Duck_Number): 47/100 = 0.47

The observed frequencies of the different values of the above example are:
P(x=1) : 15/100 = 0.15
P(x=2) : 12/100 = 0.12
P(x=3) : 19/100 = 0.19
P(x=4) : 10/100 = 0.10
P(x=5) : 9/100 = 0.09
P(x=6) : 12/100 = 0.12
P(x=7) : 10/100 = 0.10
P(x=8) : 13/100 = 0.13
Which are not all that close to the 1/8 = 0.125 value that where used to generate this sample.

If you increase the number of rolled dies to a much larger number than 100, then these frequencies will be closer to 1/8. (Well the probability of getting a sample using say 1.000.000.000.000.000 dies that results in frequencies that deviate greatly from 1/8 will be extremely unlikely - that is why I say that they "will approach" 1/8)

In fact you could choose any two small positive numbers, epsilon &gt;0 and delta &gt;0, (could be 0.00000001 and 0.000000001) and it will then be possible to find a laaaarge number N that insures that:

If N dies are rolled then the probability of getting an observed frequency that deviates from 1/8 with more than the small number epsilon, is smaller than delta.

That is:
Probability( |"observed frequency" - 1/8| &gt; epsilon ) &lt; delta

And then adding up the three largest observed frequencies will then result in a value that is in the interval
[3/8 - 3*epsilon ; 3/8 + 3*epsilon]
with as close to one hundred percent certainty as you want (just choose epsilon and delta to be very small)

So yes - I do in fact claim that given N = some extremely large number, then the Duck_Number will (most most most likely) be (ever ever ever so close to) 3/8.

Sorry for all this dry boring stuff http://forum.shrapnelgames.com/images/smilies/wink.gif

Re: Random Magic Paths - is it truly random?
 

Or maybe we can not... I feel really rusty. Does anybody know how to prove (or disprove) that lim (x2, N-&gt; inf) = 3/8? I did few attempts, and didn't manage it http://forum.shrapnelgames.com/images/smilies/frown.gif

Re: Random Magic Paths - is it truly random?
 

No.

Think about it: it's actually impossible for the total allocation of the three most-picked paths to be anything less than 3/8. If it were, at least one of those three paths would necessarily be underrepresented (below 1/8) and at least one of the five "rarer" paths must be overrepresented (above 1/8), which is a contradiction because then they wouldn't be the three most-picked paths.

Re: Random Magic Paths - is it truly random?
 

F-46;A-36;W-35;E-37;S-30;D-32;N-34;B-42
292 total...

Elemental: 154
Sorcery: 138

Duck number: 43%

Well, from our accumulated statistics, I would say Panther's Elemental/Sorcery ratio hypothesis may be fairly accurate.
No other conjectures show any consitancy. So much for my origional hypothesis http://forum.shrapnelgames.com/image...es/redface.gif

Re: Random Magic Paths - is it truly random?
 

This is elementary probability.

With p=.5 and 292 trials, there is about a 16% probability that you would get 154 (or more) of one outcome. You cannot reject the null hypothesis that Pr(elemental) = Pr(sorcery).

[I used the BINOMDIST function in Excel to calculate that]

Re: Random Magic Paths - is it truly random?
 

Okay, you are the undisputed king of the hill when it comes to these things, I grant you that. Unless someone like Alexti wishes to disagree, I'll leave that dispute to you. ;p

Anyway, I was mostly worried by the way some people seemed to think that 20 or so instances would be a amount enough for representative statistics. With 100 or so randoms the distribution is hardly yet uniform, I'd call a test for a lot larger sample before anyone makes any hasty decisions...

...although that disrepancy between elemental and sorcery picks seems interesting, not all of the results are statistically significant but there's a trend forming.

Re: Random Magic Paths - is it truly random?
 

31-17
30-28
51-45
48-48
28-23
99-93
97-97
110-86
98-100
154-138

Total of all statistics posted on this thread:
Elemental: 746
Sorcery: 675

Re: Random Magic Paths - is it truly random?
 

Using the BINOMDIST function that is only a 3% chance... make of that what you will.

Re: Random Magic Paths - is it truly random?
 

Do you know how to proof it? I don't see any obvious one. Let us consider frequency of death picks.
<font class="small">Code:</font><hr /><pre>
Probability to roll exactly k out of n P(k,n) = C(k,n)*p0^k*(1-p0)^(n-k). (p0 = 1/8)

For simplicity, let's consider overrunning your range up. Probability of that P(m+,n) = sum[k=m..n]{P(k,n)},
where m is smallest that satisfy m/n &gt; p0 + epsilon.
Ignoring rounding effects we can write m=a*n, where a = p0 + epsilon.
Then P(m+,n) = sum[k=m..n]{P(k,n)}
= p0^(a*n) * sum[k=a*n..n]{C(k,n)*p0^(k-a*n)*(1-p0)^(n-k)}.

And that's where I'm getting stuck. p0^(a*n) quickly goes to 0 when n grows,
but the sum part has number of elements proportional to n,
with the dominant n! on the top, so it will grow very quickly.
Does this P(m+,n) converge to anything? And if it does, to what value?
</pre><hr />

I have tried to run a test program to see what is happening.
I didn't have few billion years to wait until the probability to get within the epsilon = 0.00000001 will become distinguishable from 0, so I took 0.002 as epsilon. Unfortunately, at around n=3000 my program is running out of precision of double. At that moment P(m+,n) is around 40%. Until then it was slowly going down, but the rate of descend was decrementing. So, the experiment didn't suggest any conclusion

That looks wrong. You could do this if your frequencies were independent random processes. However, in our case they are dependent from each other, because the total of all frequencies is always 1. And of course, sum of three largest frequencies is always &gt;= 3/8, but that isn't a problem.

I'm still unsure if your theorem is right or not, but your proof needs fixing.

Re: Random Magic Paths - is it truly random?
 

To everybody who submits statistics from the real games. Please make sure that you were not conducting any particular strategy with those random mages (meaning that you sure that some of them couldn't have been killed in the battles or by assasins, remote spells etc). Also if you were buying those mages until you got some particular pick, your statistics is also invalid (because it's guaranteed that it doesn't contain more than once instance of that pick)

Re: Random Magic Paths - is it truly random?
 

Hmm, strangest thread I've seen in a while. I have a feeling it tells us something. Perhaps not about the topic of the thread. Interesting reading anyway http://forum.shrapnelgames.com/images/smilies/happy.gif

Re: Random Magic Paths - is it truly random?
 

Yeah. It tells us that we're all a bunch of nerds. :-)
Not that that's a bad thing. I'm a nerd, my wife's a nerd, and hopefully my son will grow up to be nerd.