Random Magic Paths - is it truly random?

[alexti]

Ivan Pedroso said:
The Duck_Number is not an easy tool to utilize in order to check if the distribution of random picks is in fact uniform. It is much easier to just count the different number of FIRE, AIR, WATER,… picks and then do a reduced_Chi^2 test to see if we can uphold the notion, that the random picks are uniformly distributed.

It is not as difficult to test for distribution as to test for independence. Consider pseudo-RNG that produces uniformly distributed numbers from 1 to 8. If we implement it as x(i) = 1+(i%8), it will generate very well distributed samples, however, those x(i) are not independent at all. In fact every x(i+1) is completely determined by x(i).

This lack of independence is a typical problem in pseudo-RNG. They often tend to repeat certain sequences more often that others. So if we're looking for a problem in RNG, I'd expect to find something like if you've sequentially rolled 1,2 and 8, there's about 50% probability that the next number will be 3 or 5.

[Bummer_Duck]

Ok I'm done being sick...

I finished my test to 100, the totals were:

F 13
A 7
W 10
E 16
A 11
D 14
N 17
B 12

It took a little while, cause I wrote them down in the order I recruited them.

The only thing that bothers me, is the streakyness of some picks. For example, I got my first air random on dwarf 17, then no more till #57. Or, I get 7 Earth randoms from Dwarf #8 to #21, and another grouping of 5 between #64 and #75. Astral and Water distribution look a little fishy to me also...

Fire, Nature, Death and Blood *look* random, I guess. So maybe it has just been my perception. Plus everyone else seems to think everything is OK, for the most part.

Thanks for the responses!

[Oversway]

The only thing that bothers me, is the streakyness of some picks

But if you had a higher chance to pick a certain path because you hadn't gotten one in awhile, that wouldn't be random.

[BigDaddy]

I'm inclined to believe the system IS random. I think anyone who doesn't think so, should just start a game and run a test with King of the deep or other applicable units. Hire like 200 of them and count them up. You may need 300 for checking all 8 paths. Don't play the game, just give yourself like 9 starting provinces and go to work. My results of 168 sea kings yielded 83 elemental picks and 85 sorcery picks. This yield no significant statistical difference from the null hypothesis.

Restrain yourself from trusting the tests of others if your test comes out more even. I apoligize in advance to anyone who feels insulted, but the probability of getting the 746 elemental paths to 675 sorcery paths is significantly <1%, so I had to either accept that the system wasn't random, or do a controlled test myself (whick i did, and drew my own conclusions). For instance, non controlled in game test may be skewed by using some random paths for blood hunting or less desireable one as troop ferries.

[Bummer_Duck]

Don't play the game, just give yourself like 9 starting provinces and go to work. My results of 168 sea kings yielded 83 elemental picks and 85 sorcery picks.

All this tells us is the overall randomness. However, if the picks follow some sort of pattern, your conclusion will be wrong, even if it looks distributed. This is why I recorded each mage, in the order I recruited them.

I guess what I am saying is if you get 50 death mages in a row, then 50 blood mages in a row, etc, totalling them all up at the end will look like it is a random distribution, even though it was not. That was the main reason for my first post. I felt, and still do, that it is not completely random. I always seem to get "gaps" and 2-4 paths that have the majority of the random picks, at any given point. Testing on a large scale is somewhat irelevent, as you don't recruit 1000 mages (or I don't)

Again, this seems to be my perception...

[BigDaddy]

Perception is difficult with the study of randomness. You have to repeatedly see the same pattern before you can assume the either random number generator or pregenerated random number table is flawed. I'm not sure which this game uses. Anyway, strings of mages are entirely likely. . . Kind of like a couple having 4 girls and no boys. The likelyhood of that is .5^4 or (6.25%).

If you want to test your hypothesis you need to document patterns. . .BBF ... BBF...

I don't think 1000 mages will produce much more significance than say 400, or even 300. Thats just the way significance works. I've misplace my statistics book, or I'd tell you exactly how to find significance, but trust me, you don't need 1000 mage, 300 will do.

[BigDaddy]

Well, Bummer_Duck, you have to do larger scale tests to get any significance out of your test, like I said earlier about the likelyhood of a couple getting 4 girls and no boys, the likelyhood of getting a couple blood mages in a row is not that remote. The likely hood of getting 6 blood mages in a row is, however, quite remote .125^6=.00038%. Significance increase markedly for the first several units sampled, so you need a significant number of mages to make any judgement. If that doesn't suit your fancy, try hiring 20 mages after starting 10 new games and draw your results from there.

Even after 200 units 4 paths are very likely to have a "majority" of the picks, 2-3, however, are not.

[PvK]

On the other hand, if you _don't_ know the formula a pseudo-random number genrator is using, and it has the desired distribution, and there is no easy way to deduce the formula, then the result may be indistinguishable from a true random number.

Arguing that a distribution isn't predictable by any practical means is sufficient and entirely different from philisophical or even mathematically provable arguments that it's hypothetically possible to predict a distribution.

Certainly it is quite possible to make a pseudo-random number genrator that is impossible to predict or be considered broken from a game-player's perspective. If the distribution is right, the sequence of play itself adds a shuffling that is too complex to predict.

Which is not to say that some games don't have random number problems, or more often, algorithm bugs, which are capable of detection during play.

PvK

[BigDaddy]

PvK said:
On the other hand, if you _don't_ know the formula a pseudo-random number genrator is using, and it has the desired distribution, and there is no easy way to deduce the formula, then the result may be indistinguishable from a true random number.

Arguing that a distribution isn't predictable by any practical means is sufficient and entirely different from philisophical or even mathematically provable arguments that it's hypothetically possible to predict a distribution.

Certainly it is quite possible to make a pseudo-random number genrator that is impossible to predict or be considered broken from a game-player's perspective. If the distribution is right, the sequence of play itself adds a shuffling that is too complex to predict.

PvK

Yes, for all practical purposes, the system likely works as ordered. I have long sustained my opinion that it is random enough to be indistinguishable from the real thing. That's also why ANSI regulated it .

VIA's method seems good enough to be considered theoretically random. Sensor's generally perform randomly (anything P<100% is random by definition).

[Arralen]

So, folks, lets stir up the discussion again:

Ongoing game, Jotunheim, 3 turns.

1st turn - building a Vaetti Hag: Blood-1
2nd turn - doing the same ..... result the same ..
3rd turn - same again .. and the same again...

Likelyhood for this happening: 1,56%

As far as my experience goes, if I keep on building Vaetti Hags, I'll get 1 more Blood-1, then it will switch to some other path. If I build commanders in newly conquered provinces, I'll get some other path this turn. If someone else does I-don't-know-what, I'll get another path.

But after some time, the effect will reoccur. But it will get less likely, as more and more things are happening each turn, what seemingly influences the random number generation.

And it's eactly this effect that I have seen way to often to dismiss it as "statistical". If you do big test buying some hundred units, things will equal out o.c. . Obviously, short term randomization is bugged. But the error occures randomly