Crafters: Question on frequency of masterpieces

[Draylor]

Since hitting 1000 armourcrafting Ive created 4 100% quality items. Thats around what Id expect given the 1 in 50 chance - no complaints there.

However these werent evenly spread through my skilling. The first two came within 4 attempts of each other, followed a few days later by another two within 3 attempts of each other.

Ive read a few posts on US boards that suggested the chances of multiple masterpieces being created within a few attempts of each other seemed to be very high - but assumed this was just coincidence. Statistically this is bound to happen from time to time. Having had it happen to me twice Im starting to think there may be something in this idea.

Anyone else experienced this?

Sorry if this makes little sense - its late

 

[old.LandShark]

Could it not just be because this game is very bad with randomness? I.e. you tend to get "streaky" luck rather than smooth random luck...
Gah, that didn't make much sense either, did it =)

 

[drunkard]

That made perfect sense LandShark, I've often wondered how DAoC deals with generating all these random numbers.

Computers can't generate random numbers without using something like a ticking device(usually the internal clock) to get some sort of randomness. Does anyone know how daoc deals with this, I've often found I get 'streaky' luck when crafting too.

 

[old.Odysseus]

randomness is random.
you should start suspecting errors in the random generator if you start making MP's excactly every 50 tries.
it gives good meaning in a statistical perspective that MP's are spread as you describe.

 

[old.FIN]

imo its because tailor parts r made by Uber cabby =)

 

[SilverHood]

here's an example of 10 random numbers between 1 and 10

1 1 1 1 1 1 1 1 1 1

how do you know they're random?

thats the thing with random numbers... you can never tell

 

[old.Odysseus]

Only way to draw some conclusions on the random number generator would be to draw a very large number of numbers, plot them with frequencies and see if they make a uniform distribution, which is the one i assume they used.

 

[SilverHood]

well, since you can plot random numbers on a graph, you can see patterns.

When there's a pattern, it can't be random

 

[old.Odysseus]

With a very large sample size of random numbers, the frequencies will diverge towards the distribution from which the samples were created.

 

[Danya]

Random numbers are quite hard to get in computers, likely daoc uses pseudo-random numbers which might not have a uniform distribution.

 

[SilverHood]

the thing is, if it has a uniform distribution, is it random?

random = equal chance for a number to apear

non uniform wouldn't be random then would it?

 

[old.Odysseus]

It can make good sense having normally distributed random numbers, used a lot in AI and evolutionary computing.

 

[old.LandShark]

Originally posted by Danyan
Random numbers are quite hard to get in computers, likely daoc uses pseudo-random numbers which might not have a uniform distribution.

I'm fairly sure i saw in an old, old grab-bag, the statement that this was the case...
The Grab-bag question was pretty much the same as draylor asked, IIRC

 

[old.Odysseus]

Random number generation is in itself a science, but using the computer clock is widely used.
Some use a looooong sequence of fixed digits, then use a seed as a pointer where in the sequence to start. Using time or computer clock as seed makes it appear random although its 100% deterministic.

 

[old.Fangrim]

Personally, I have made about 10 MP items in the last 2 weeks. Some "real" items (like armor pieces), some "trinkets".

TWICE I have made 2 MPs in a row. Once was two AF 102 Studded pieces, the other was one AF 102 Studded piece, the other a trinket.

Coincidence, statistics, luck, or bugged random generator? I dunno...

About the random generator: Try making a /macro ROLL /roll 4 and tell me how many times you roll a "4" or a "24" on that. I haven't been able to yet... I think the Random number generator is a bit un-random...

 

[old.Fangrim]

Only way to draw some conclusions on the random number generator would be to draw a very large number of numbers, plot them with frequencies and see if they make a uniform distribution, which is the one i assume they used.

This would statisically be an even spread, as long as you only draw one number, but with the "Roll 4 Dice", you should get a bell-shaped curve, where the majority of the results should be in the middle of the 4-24 range.

well, since you can plot random numbers on a graph, you can see patterns. When there's a pattern, it can't be random

Depends on your definition of a pattern - if I roll a 6-sided die 10000 times, I should get approximately the same amount of 1, 2, 3, 4, 5, and 6's. If I plot that into a graph that shows me the number of 1, 2, 3, 4, 5, & 6s that should ideally form a somewhat stright line. That's a "pattern" I guess, but the numbers are still random. Try reading your math books again

 

[Jiggs]

shit happens

 

[Draylor]

Odysseus - I know, I agree.

Like I said - thought nothing of this until it happened to me. It just made me curious to find out what other people had experienced.

As long as the occasional (non-hinge) MP pops out Ill be happy.

 

[old.Odysseus]

This would statisically be an even spread, as long as you only draw one number, but with the "Roll 4 Dice", you should get a bell-shaped curve, where the majority of the results should be in the middle of the 4-24 range.

As far as I recall, this would yield a normal distribution, hence as u say a bell-shaped curve.
This is because the average die will roll 3.5. Hence the curve will be centered around 4*3.5=14 with fall-off towards the extremes.
This is ofc similar to rolling 2 dice - you will see a sum of 6-7-8 far more often than 2 or 12 simply because more combination of the dice sum to this result.

 

[Moody]

The system may be random, but certainly not very consistent. When I fail constantly, with material loss and everything for more than a certain time I consider 'normal' I just relog and the points start flowing in when I come back. Now that's sick

 

[pcentella]

As far as I recall, this would yield a normal distribution, hence as u say a bell-shaped curve.

Not exactly (first of all, sorry for my english if there are typos or completely wrong words). If you rolled a very large number of dice (the more, the better), the distribution would be very similar to a normal one (it converges to a normal distrib.), but is in fact a sumatory of discrete uniform distributions.

Well, the thing is that, in fact, it is quite hard to get 4 ones or 4 sixes when rolling 4 dice. The chances of getting each is one amongst 1296 (or getting any of those is one amongst 648). That doesnt mean you will get 4 ones when you've rolled 4 dice 1296 times. You could, in fact, get 1296 times that, but i think if you do that, you'd better had bought a lottery ticket .

This reminds me of Diablo II, when the change to get a so-called unique item is dependant on some things (which monster you will, equipment you have,...) but also random. There were many strange beliefs about doing things in a certain way (playing when there were few players, or at certain hours, or calling the game you created in a certain way) to improve chance of getting uniques, but that was because of "streaks of luck".

Hmm, hope this makes some sense (or not ).

 

[old.Odysseus]

distribution would be very similar to a normal one (it converges to a normal distrib.), but is in fact a sumatory of discrete uniform distributions.

Yes that is ofc right, a normal distribution is a continous one, whereas a uniform is a discrete and as you correctly point out there will be convergence when rolling a (infinite) large number of times.

 

[Cowled]

Anyway, about MP..

I've noticed i fail alot, loose materials & make other quality than 99-100, just before i'll hit qua 100 - and afterwards.

 

[pcentella]

It's me again!
I found a dice-rolling-simulator for you to play around, and watch the bell-shaped graph and all that.
http://www.geocities.com/thesciencefiles/rollthe/dicepop.html
Each time you hit "roll the dice", the results are added to the graph. To reset it, reload the page.
Let's roll!

 

[old.Ramas]

well, since you can plot random numbers on a graph, you can see patterns.

When there's a pattern, it can't be random

here's an example of 10 random numbers between 1 and 10

1 1 1 1 1 1 1 1 1 1

how do you know they're random?

Not really true.

A variable is random if you cannot predict it with the information available.

Whether it is 'fair' or has 'a uniform distribution' is another matter entirely.

The list of 1s above are not random, because we can see what they are. However, if we cannot show what the next number will before it is revealed (and from the information given in this example we cannot), then *the next number* is still random.

Patterns aren't important unless we know enough about the pattern to predict the next outcome.

Randomness is a concept applied entirely from a certain point of view. Numbers/variables/outcomes themselves are not inherently random, and can only become random from the point of view of an observer who has insufficient information to predict them.

But back on topic...

Yes DAoC 'dice rolls' do seem to be very streaky. The same sort of thing happens with spell resists - they tend to come in a string of 3 or 4.

 

[Draylor]

Originally posted by pcentella
I found a dice-rolling-simulator for you to play around, and watch the bell-shaped graph and all that.

Sure - but this proves nothing about the randomness of the random number generator DAoC uses.

 

[old.Odysseus]

A possibilty would be to do, say, 1000 /roll 's with chatlog on.
Then parse the results and plot frequency versus sum.

If u can be arsed, do 10000 or 100000.

When ure done doing that, seek out a therapist cuz u really need one

 

[pcentella]

To test the randomness of the DAoC dice generator, what one should do is roll 100 dice (i think 100 was the highest number at a time) a big number of times, do an histogram with the data accumulated (a graph similar to the one obtained in the dice simulator link i posted before), and look at it to see if its shape is a bell like a normal distribution. I found this info by Sanya on a grab bag after patch 1.51:

the cards and dice aspects took fifteen minutes of extrapolating the code he used for /random.

So i strongly believe "/dice 1" is the same as "/random 6", and "dice n" does "dice 1" n times and adds the results, so the quickest way to check if /dice and /random are ok would be to do that.

 

[old.Ramas]

To test the randomness of the DAoC dice generator

Your method....

1) Does not test the 'randomness' of anything - it tests the central limit theorem, which would still come out to be true in many cases where the outcomes are not random from your point of view.

2) Nor does it test the 'fairness' of dice (which I assume you take to mean 'having an equal probability of all possible outcomes, and that the outcome of any individual roll is independant of (not affected by) all previous rolls'). As any symmterical distribution of individual dice values would come out with the same distribution of means over a large number of trials with 100 dice each. (this is because a mean die roll outcome is the same if, for example, you increase the probability of a 6, and you also increase the probability of a 1 by the same amount).

The only real way to show that dice rolls give a uniform probability of outcomes 1-6 is to roll *one* die a large number of times and to plot frequencies. If the frequencies after a large number of rolls are about equal, then this is evidence that the dice command does produce outcomes that fit a uniform distribution.

Another slightly dull but worthy test would be to roll sets of dice equivalent to the length of the anecdotes above of 'streaky' behaviour (say 10 dice at a time). Taking a large number of samples of the total of 10 dice rolls, and calculating the standard deviation might give evidence that the random function in use is somewhat streaky.

It is possible to calculate what the standard deviation should be for samples of a given size, assuming that the distribution of dice rolls is uniform, and each individual dice roll is independant (not affected by) all previous rolls.

A comparison between the 2 deviations would tell us...

Uniform SD << Samples SD

Could be explained by streaky behaviour

Anything else

No evidence either way.

There are better tests of course, but they would be longer, harder, or don't-spring-to-mind-right-now.

 

[pcentella]

this is because a mean die roll outcome is the same if, for example, you increase the probability of a 6, and you also increase the probability of a 1 by the same amount

Uh that's true, my method is quite flawed actually

Anyway maybe it's worth a try. If everything seems ok, you don't have much information about the "okness" of /dice anyway, but if the results are weird, then quite probably /dice is not ok.

The good method would be using "/dice 1" a LOT of times, but that is quite slow and boring . As far as I know, you can only /macro one command, so you can't do a macro that does that; and anyway you can't "/macro dice /dice 1", put it on quickbar and put a heavy thing on number 1 so it is pressed non-stop, because it breaks the EULA (doh ), so you have to actually be there rolling one dice at a time.

Hmm, maybe if high-lvl crafters or people waiting for a group wanted to help us by doing that while waiting, logged the results and sent them to someone, that could be done without someone wasting hours roling dice.

Hehehe sounds fun:

"Attention all realms, we must set aside our differences and work together to know the truth! The truth about /dice shall be discovered!"