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I purchased some squared-cornered 12mm (NOT casino dice, same size as the "normal" chessex dice) dice from a vendor on e-bay, to compare those dice with the more commonly used rounded-cornered dice from Chessex.

I rolled the squared dice 1008 times, and got the following results:

1s: 17.3%
2s: 16.9%
3s: 18.6%
4s: 17.5%
5s: 13.6%
6s: 16.3%

The mean result was 16.7% (as should be expected) with a standard deviation of 1.75%. As you can see, the 5s were very anomalous, being more than 2 standard deviations from the mean., and the 3s were more than a standard deviation above the mean as well. To compare "bad" rolls of 1-3 to "good" rolls of 4-6, the bad rolls represented 53% verses 47% good rolls, a 6% difference.

The Chessex dice, which are commonly believed to roll low, were rolled 1020 times with the following results:

1s: 15.9%
2s: 17.4%
3s: 17.6%
4s: 16.2%
5s: 17.2%
6s: 15.6%

Mean: 16.7%
Standard deviation: 1.1
Good rolls: 49%
Bad rolls: 51%

These seemed to roll much closer to "average" with none of the results more than 1 standard deviation from the mean.

I was planning on switching to the squared-cornered dice based on a "feeling" that the chessex dice roll lower than average, but yet again they test as rolling pretty close, where the other dice were much worse.

That follows along with the testing I've done. When ever I get up above 200 rolls of a dice, the numbers fall into place very close to expected values.

I especially tested Chessex dice, since I sell many thousands of sets of them a year. While it might be possible to find a bad die, or even put together a set of bad dice, any of those 36 blocks I've tested have come out very, very fair.

Why 1008? Why the 8?

Unusual results. Test more!

H.B.M.C. wrote:Why 1008? Why the 8?

Getting a nice, round number was not as important as just a generally large-enough sample size, and 1008 is a multiple of 6. It's just how the numbers came out since I was rolling a block of 36 dice in groups of 6 dice each.

I miss Gwar!

LunaHound wrote:I miss Gwar!

Not only is that completely random and off-topic, but I for sure do not miss Gwar.

Its not random, his existence takes up atleast 10% of this thread.


And someone actually rolled dice that many times?

LunaHound wrote:Its not random, his existence takes up atleast 10% of this thread.


And someone actually rolled dice that many times?

I miss GWAR too. He was an asset to Dakka. It took be about 5 hours with Scrubs on in the background today. I figured it would be an interesting way to spend a lazy Sunday.

I agree, seemed to give slight order to the YMDC section for a bit at times.

The results are interesting, second set appear to be better.

n0t_u wrote:I agree, seemed to give slight order to the YMDC section for a bit at times.

The results are interesting, second set appear to be better.

The second set was a "control" set using the "normal" 12mm chessex dice, rolled in the same location and the same general fashion (shaken in hand, rolled on flat, smooth table with no banks).

I was, frankly, amazed that dice that are decently manufactured cubes would have the strange results that the square-corner dice did. I will try to do a test using them again in the near future to see if it replicates the results.

I totally miss GWAR! Also, you should try this with GameScience dice, unless that's what you meant by 'square cornered.' Also, casino dice, which are supposed to be even MORE impartial than GameScience.

Either you have got your SD wrong, or the number of 5s wrong, or 13.6% is less than 2 SD from the mean.

Oh, good catch, 2 SD would be 3.5% off mean. It's still pretty close to 2 SD though.

Basically the premise that they 'roll more 1's' is that some how the influenced rolling is directly related to how the PIPs are drilled and the side with 6 holes VS the side with 1 hole somehow makes it land 1 hole side up.

The scientific experiments show it has almost nothing to do with the PIPs but simply the cheap nature of the dice and a flawed dice can pre-disposed to *ANY* side mostly from internal airbubbles which make them unbalanced.

In your experiment it shows that even flawed dice when rolled in batches over a long haul are 'good enough' to be fair and randomized for gaming purposes.

The real test (which would have been tedious) is to roll and record every individual dice's results and then analyze the entire set along with each of the 36 individual sets. The we could see if specific dice were favoring specific sides bot overall the batch averaged out. If you rolled 36 individual dice 1000 times each it would be good to see which dice were unbalanced to which results.

When it boils down, I think the 'myth' of Chessex rolls more 1's has been proven to be false... But cheap dice are unbalanced when singled out. If someone actually finds unbalanced dice for 1's and 6's then segments the dice when rolling, that is when the problem occurs. As long as players don;t segment dice, then there is no benefit to be had from rolling unbalanced dice in a batch (unless there are rolling techniques being used, which usually require balanced or square-edged dice)

I'm interested in how the experimental standard deviations compare to a theoretical value for a fair die.

Does anyone know how to quickly go about doing that calculation?


Automatically Appended Next Post:
After poking around a bit, I did some simple calculations, and estimate that the standard deviation (with 1008 rolls) should be 0.6%.

It seems willydstyle either didn't properly randomize his rolls, or he showed that both test sets are flawed.

Edit: It appears I made a math mistake. See my post a few more down for correction. willydstyle is actually pretty much perfect in the Cheesex distribution!!!

Grakmar wrote:I'm interested in how the experimental standard deviations compare to a theoretical value for a fair die.

Does anyone know how to quickly go about doing that calculation?


Automatically Appended Next Post:
After poking around a bit, I did some simple calculations, and estimate that the standard deviation (with 1008 rolls) should be 0.6%.

It seems willydstyle either didn't properly randomize his rolls, or he showed that both test sets are flawed.

Can you tell me what math you used to estimate the expected standard deviation?

Grakmar wrote:I'm interested in how the experimental standard deviations compare to a theoretical value for a fair die.

Does anyone know how to quickly go about doing that calculation?

Ideally you'd need the results for each die. One way would be to get a set of differently coloured dice and mark the results of each, that way you could track the skew of individual dice.

It can be done simply by running a t-test of the original scores (not the percentages) against the expected. It isn't appropriate to do this for ever result and compare because there's always a small chance you will will get a false positive and running the test a dozen times means that's likely to happen at least once at a 5% threshold. The way around this is to run a multivariate analysis I believe but I don't recall how to do this appropriately.

Anyway, for the sake of argument - take the roll 5 of the squared die, which appears to be the result furthest off the mean. Willydstyle hasn't given us the original results but 13.6% of the 1008 is 137. The expected result is actual 1/6th of 1008 which is 168.

X = [ (O-E)*2 ] / E = 5.72

Which falls just outside the 5% threshold (, it's close so maybe there's a bit of a skew but the dataset isn't large enough to result it. It's significant at 10% but not 5%. Make of that what you will. It's not really the proper way to examine this data anyway.

willydstyle wrote:

Grakmar wrote:I'm interested in how the experimental standard deviations compare to a theoretical value for a fair die.

Does anyone know how to quickly go about doing that calculation?


Automatically Appended Next Post:
After poking around a bit, I did some simple calculations, and estimate that the standard deviation (with 1008 rolls) should be 0.6%.

It seems willydstyle either didn't properly randomize his rolls, or he showed that both test sets are flawed.

Can you tell me what math you used to estimate the expected standard deviation?

Sure. I'm sure it's not the quickest way, but here's what I did:

First, assume a perfect bell curve for results. With 1008 rolls, you should get 168 of a given result. 68.2% of a given set should be within 1 standard deviation. So, we assume that x results off the average will be within the standard deviation.

So, I found what x would be to result in a 84.1% chance of getting over that number of rolls. I cheated a bit and used this site: http://stattrek.com/Tables/Binomial.aspx

The value for x that best matches is between 11 and 12, we'll call it 11.5.

So, 11.5 rolls off the average is your standard deviation. That translates to (by dividing 11.5 by 1008) 1.14%.


I went and double-checked my math, and went back to double-check my earlier work. They disagree. It appears I forgot a factor of 2 in my previous estimate. So, I take back what I said earlier. You've shown that Chessex dice give you an almost perfect distribution!

Well, I've shown that the particular block of chessex dice used in my experiment gives an almost perfect distribution

ph34r wrote:

LunaHound wrote:I miss Gwar!

Not only is that completely random and off-topic, but I for sure do not miss Gwar.

I don't understand why you miss them, they put out a new album last year.

http://www.amazon.com/Bloody-Pit-of-Horror/dp/B00466339O/ref=sr_1_1?ie=UTF8&qid=1318961188&sr=8-1

LunaHound wrote:I miss Gwar!

Not matter how many times you try it, you will get the same results.