Look at the next 250 rolls.  The values certainly flattened out some though it didn’t invalidate the first set by a long shot.  If anything it underscored how small a sample even 500 really is.  I think we’re looking at doing 1,000 minimum at this point.  The possibility of three values being too low and the three mirrored values coming up too high is still looking very possible though.

Before I publish that though we’ll have an interlude of some of our Khallam goodness again.

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So, here are the first 250 rolls.  I had previously discussed doing a chi-square test for randomness but the more I thought about it I’m not sure it would help.  First of all the typical things you look for in chi-square don’t apply here, there aren’t multiple variables, etc… In other words I think it might be over kill and frankly the sample size isn’t likely to be large enough to really matter.  As much as I want a good answer to this question I’m not sitting here and rolling a die/dice 25,000 times times ten dice.  250,000 times?  Yeah, I’m a geek who is obsessed with dice.  But there’s obsessed and obsessive compulsive.

Besides, I don’t think its necessary.  I’m just looking for frequency.  My methodology was to roll the die/dice down a dice tray of my own making.  The felt isn’t perfect so if the die ever ended up a little off center I didn’t count the roll.  This happened three or four times in 250 rolls.  I recorded the rolls, put them in Excel and did some basic calculations.  You can see a copy and paste of that above.  You can see that there is some very significant statistical variance.  I need to check the dice and see if where the values vary significantly they represent opposing faces where a rounding or weight issue would be significant.

A rounding / cleaning problem seems like a significant risk while weight is unlikely.  I’m told that if I want to test weight, get a bucket of water, drop the die in and over the course of a hundred rolls it will show a clear preference to settle weighted side down, far more than you would rolling it.  I reserve the right to do this.  And, I intend to test other dice from this same bag.  More about the test method in a later post.

The Mean is 5.6 and the theoretical perfect mean would actually be 5.5, the dead center of the two “middle” values of 5 and 6.  So, that looks fine but it’s misleading.  Since a screwed up die/dice won’t be weighted towards low or high values but certain faces or sides (and values do not necessarily correspond to physical location.  In fact the top “half” of the die is even values and bottom “half” odd values with no apparent order to me otherwise though someone may correct me on that.  I haven’t compared it with other d10s in my collection but I’m not sure there is a standard scheme for the ordering of numbers on a die/dice faces.  Anyway this lack of relevancy of things like mean also screw up a number of statistical tests.

However, frequency is definitely important.  Let’s look at the most common scores. We expect each value in a perfect random sample to show up 10% of the time (10 values) or 25 times out of 250 rolls.

If we look at the highest value, 10, it is 6% above it’s expected value or 60% higher.  That is … well, beyond significant.  It’s like saying John Holmes was significantly endowed.  1s are pretty high up there too, 40% up there.  By the time we get at the 4th highest, 6s, they are right on the expected norm.  4s and 8s are the least frequent values and also well below the expected frequency.  So, let’s look at the facing.

The 0 or 10 is on the opposite half and one full face separates it from the 1 so its unlikely the same imbalance or unevenness of the die/dice would cause both of them to be exceptional.   However, the 4 and 8, least common value are on mirrored sides of the 0.  Could something ‘wonky’ with this facing cause most rolls that lean towards these three value to infact come up 10 regularly?  That would be an problem with the 5, 9, 1 part of the die.

Hopefully, more rolls of the White Wolf dice will bear it out.  I’m going to roll this die/dice 250 more times for a total of 500 to get a better sample and we will see where we end up.  Depending upon results I may got for another 250 or even 500.  And then I will compare those results to at least 1 more die from the same batch.

I thought about titling this post “I’m a geek.”  This isn’t a secret at this point even if I don’t have any impressive nerd arguments to brag about.  The thing is I’m several kinds of geeks as is fairly common and a tiny bit of a math and statistics geek so this post at Delta’s D&D Hotspot about calculating values for randomness wasn’t news to me.  The follow up post largely supports the evidence of the gentleman at Game Sciences’ assertion about sharp edged dice. (Nor is it lost on me that I am obsessively testing my dice, that thing the poster above is afraid they will do.)  It doesn’t make sense to me that sharp edged dice would be more random than soft edged ones.  In fact it would seem to me that sharp edges would primarily just kill the energy of the roll sooner.  My own experience does in fact indicate that soft edges make the dice roll further and perhaps that makes any flaws in the dice more apparent by exaggerating their opportunity for influencing the roll.

Now, I am a bit of a statistics geek but this is going into an uncomfortable area where statistics meets physics and beyond reading some Stephen Hawking I am no Robert Oppenheimer.  In fact let me refer back to that Shameful Topless Robot Post above and let you read about the arguments between physics and engineering majors that eventually involved a vaccuum tunnel and randomoness tests until it took 4 montsh to get the game actually going. No, for the record, I won’t be going that far.  Nor am I qualified to.  But my experience in statistics largely involves databases and populations – tracking randomness in traits that are already occurant in the environment (collection or population) and I don’t have to wonder how it got there until I find a pattern.

The dice are different because these aren’t naturally occurring incidents – I’m experimenting.  So, the question comes up about the state of the experiment.  I had originally detailed out an excruciating exact plan of holding the die/dice (there is a valid linguistic argument about the singular being die or dice, more on that another time) a certain way, rolling it, positioning, etc…  Then, I began to get concerned that I was becoming too precise and might skew the results by the sample not being allowed enough naturally occurring randomness.  The answer I think is to control the force, use a dice rolling tray (White Wolf’s dice do have worn edges), grab the die/dice as it lands, take it back to roughly the same starting place and throw it with roughly the same force in roughly the same direction.  In other words, keep the environment for the roll consistent but not precise allowing the dice to act as they should ‘in the wild’ and do a large enough sample that it will create a representative sample.

Rolling with the right force but not controlling it may take a tiny bit of practice but I think will work.  Ideally I should do the test for a full set but I think I’ll start with a single one.  50 is the minimum sample for something like this (5 * 10) for a chi squared test.

500 I think will do it.

My mind is very much on dice and randomization lately.  I’ll be cross posting between here and another new blog I’m working on here soon but for now I want to point your eyes to these videos on Youtube.  There are some issues still not addressed.  Primarily to what degree is randomness effected and how can we test randomness of dice?

Still, watch these.  More will follow.