Random Magic Paths - is it truly random?

[alexti]

The_Tauren13 said:

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.

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.

The_Tauren13 said:
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.

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%)

The_Tauren13 said:
Perhaps that was not meant as a flame against my intelligence, but it sure sounded like it.

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

[Ygorl]

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.

[FarAway Pretender]

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!

[Bummer_Duck]

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?

[alexti]

Bummer_Duck said:
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?

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.

[Chazar]

Bummer_Duck said:It could very well be a perception thing.

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...

[The_Tauren13]

alexti said:
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.

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.

alexti said:
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.

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.

alexti said:
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

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 . If you give me your email I could send you my turn files and you can check my mage counting...

alexti said:
Of course, that doesn't prove that there's no problems with RNG, but this test, it passes very well.

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

alexti said:
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

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 . 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.

[Bummer_Duck]

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?

[Graeme Dice]

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.

And hardly outside of the realm of possibility either.

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 .

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.

[Yvelina]

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