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I wanted to get peoples opinions on dice and their impact on the game. I decided to take a look at some of the dice I commonly use to see if there was any inherent differences between them. I want to provide 2 examples that really jumped out; my best and worst.

In the following two data sets I decided to do some batch testing. I took 10 dice for each group and rolled them 30 times for a total of 300 rolls with the results shown below.







The first thing that jumped out is that the GW dice have a serious bias towards the number 3 at a detriment to just about everything else. The GW dice also demonstrated a standard deviation of more than 3 times that of the chessex dice.

The thinking with the batch (10) rolling was that if there are random manufacturing biases, during polishing for example, that they should balance each other out with batch rolling however, with the GW dice that appears to not be the case. I'm working on individual rolling stats now for comparison, but I wanted to get peoples thoughts on this. It seems like depending on what you use, you could be introducing huge biases to the game.

Side note: I'm not a professional statistician, so if I did something dumb, let me know.

Engineer so not a statistician but know enough to be dangerous. The standard deviation on the GW set looks way off (and maybe slightly off on the chessex). I also wonder if 300 rolls is enough is there still a heavy randomess element or are you really starting to see manufacturing biases ? There's probably some formula you could use or maybe just repeat the experiment with the same set of dice and see if you get the same results.

76 is a very high number. The probability of rolling at least 76 3s when rolling 300 fair dice is 0.005%.
In other words, 300 rolls is a sufficiently large number of rolls to conclude that the GW dice are far from fair.

The repeated experiment would be the key to seeing a pattern. Ensuring sufficient randomization before the “throw” would also be important. If you always use the same pattern of placing the dice in a cup, shake twice and roll from the same height, you may unexpectedly be creating a bias.

From there, determining if all dice are flawed, or just one or two. While extreme, one die that always shows a 3 would skew your results tremendously.

First thing that springs to mind is, check another cube. Secondly, who makes GW's dice and who makes anyone else's dice.

I've included the raw roll data for the GW dice below. As far as the bias towards the 3 side, it isn't just a single dice or two skewing the stats. If you look in the 3 column, you see multiple instances of multiple 3's being rolled.

If you take the average count for each column, you get the following:

1=1.40
2=1.70
3=2.53
4=1.57
5=1.31
6=1.53





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I'll definitely try repeating the experiment. I'll let you know what I find.


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I'm not sure who makes the GW solid red dice. They are those red (also come in white) dice that have come with everything over the years.


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Here are the other dice sets that I ran,

30 rolls seems like a very small data set to me. Something more like 300 rolls would likely even out those outliers.

That’s the real point of dice anyway, to provide a more or less average set of random numbers over time.

Well its 30 rolls with 10 dice roll each for a total of 300 unique rolls. This initial round was for batch testing. The idea was that randomly introduce manufacturing defects should balance each other out when using 10 dice unless there is a non-random bias (injection point/flash bias for example).

Some dice have air bubbles or other imperfections in them. This is more obvious with translucent dice than opaque dice.

This might interest you:
https://makezine.com/2015/06/16/check-balance-gaming-dice/

Cleatus

This might interest you:
https://makezine.com/2015/06/16/check-balance-gaming-dice/

I'm going to have to try both the salt water float test and cutting one of these die in half. Thanks for the link.

I figured out why your stddev looks weird, you calculated the stddev of the totals not of the individual dice rolls.

Also you might find this interesting.
http://ccnmtl.columbia.edu/projects/qmss/the_chisquare_test/about_the_chisquare_test.html

Jerram

Also you might find this interesting.
http://ccnmtl.columbia.edu/projects/qmss/the_chisquare_test/about_the_chisquare_test.html

I did find that interesting thanks. If I understood that correctly, would I be accurate in saying that the if all of the dice were fair, then Chessex orange/clear had an 87.61% chance of rolling those values whereas the GW solid red had only a 0.27% chance?

I think so, I tried calculating the chessex value and just grabbed any old table that probably had lower fidelity than the one you used and got <90%.

I literally cannot believe that you haven't seen this article on dakka yet...

https://www.dakkadakka.com/wiki/en/That's_How_I_Roll_-_A_Scientific_Analysis_of_Dice

This article is the reason i spent ~£60 on 'Vegas Dice' and started a YouTube gaming channel with the same name..

SirDonlad
I literally cannot believe that you haven't seen this article on dakka yet...

https://www.dakkadakka.com/wiki/en/That's_How_I_Roll_-_A_Scientific_Analysis_of_Dice

This article is the reason i spent ~£60 on 'Vegas Dice' and started a YouTube gaming channel with the same name..

I actually didn't see that, thanks for posting it. Quite a bit comes back if you search this forum for "dice" and related terms. The article was very interesting. I ordered some of the vegas dice mentioned, I'm curious to try them out.

Casino dice are designed to be thrown vigorously the length of a craps table; if you're dropping them into a dice tray or a space on the table between a ruin and a squad of Marines, they won't roll enough to randomise properly. Plus, you really should replace them frequently; that's why casinos sell dice as souvenirs, those are the ones they're about to bin.

 SirDonlad wrote:
I literally cannot believe that you haven't seen this article on dakka yet...

https://www.dakkadakka.com/wiki/en/That's_How_I_Roll_-_A_Scientific_Analysis_of_Dice

This article is the reason i spent ~£60 on 'Vegas Dice' and started a YouTube gaming channel with the same name..

Why on earth did you do that?

Hold on.

Which GW Dice? I use the ones in the old plastic cubes shaped like a die.

Are you testing with newer ones? Have you tried a different set?

 SirDonlad wrote:
I literally cannot believe that you haven't seen this article on dakka yet...

https://www.dakkadakka.com/wiki/en/That's_How_I_Roll_-_A_Scientific_Analysis_of_Dice

This article is the reason i spent ~£60 on 'Vegas Dice' and started a YouTube gaming channel with the same name..

Before I read that write up a long time ago, I bought the Chessex 12mm rounded corner dice, they were nice as wound markers and small enough that when I had to roll a ton of them it was easy.

But I did notice the 1 was showing up more than it should have, even had opponents comment on it, even let them use the dice with similar 1s showing up more. At first I attributed it to the fact people tend to notice the negative more than the positive.

Then I did my research and sure enough, it seemed to be an actual trend.

I ended up getting 16mm more of a square corner dice ( https://diceemporium.com/product/16mm-square-corner-dice-sets/ ), these are not casino level, but good and they have been a lot more reliable at being evenly random.

The GW Solid Red dice are just horrible.

I was playing a game the other day and out of 50 dice roles over a single game turn (charges, shooting (to hit and wound), as well as Assaults (to hit and wound) I rolled 40 1's and 2's

It was completely flabbergasting. My opponent couldn't believe the sheer amount of "fail" rolled during a single turn.

 SirDonlad wrote:
I literally cannot believe that you haven't seen this article on dakka yet...

https://www.dakkadakka.com/wiki/en/That's_How_I_Roll_-_A_Scientific_Analysis_of_Dice

This article pops up every now and then. Most people think it is nonsense: nobody has been able to duplicate the results.

I have done 600 throw test (60x10 dice) with my blue opaque Citadel dice. Distribution was very close to standard deviation and got more close to it as the test progressed. In fact '1' was the least common result.

People generally underestimate how long it takes for variance to even out. In poker they go "yey 10000 hands and i'm winner". Even 100000 hands isn't really enough to be sure you are winner and it wasn't just variance smiling for you...

Bookwrack wrote:
Why on earth did you do that?

I wanted to be sure that whatever the result of a roll was, that it was the fairest roll you cold have - now if i roll a huge number of ones or whatever, i know it is a genuine result and i can deal with it a hell of a lot better.
I knew i would need 20 minimum per side and i don't want to use the same colour dice as my opponent so the outlay was worth it to me - plus they are nice and visible on video provided the glare of the lights don't catch off the surface.

These sorts of discussions pop up in Role Playing Game forums too. It is a very deep rabbit hole. People wondering about the 20 sided dice, and other polyhedrals .

I'll summarize. Yes, there is some bias in the dice. The dice with the least bias are GameScience dice-- once they are properly trimmed-- when it comes to polyhedrals. The amount of bias is not significant unless there are large sums of money involved. Chessex and Koplow dice are just fine since the difference between them and Gamescience is negligible, unless, y'know, big money. There are some truly crappy dice. Wiz Dice for example. Transparent dice are preferable, because one can see if there are air pockets in them, and avoid those dice.

You can start here, http://deltasdnd.blogspot.com/2009/02/testing-balanced-die.html The author is a College lecturer in mathematics and computer science so qualified. There are, if you search, other interesting blogs where the authors build dice rolling machines and hook them up to cameras to automate rolling and recording.

A final thought: Casinos swap out the dice frequently because rolling the dice rounds the corners and this introduces bias.

tneva82 wrote:
People generally underestimate how long it takes for variance to even out. In poker they go "yey 10000 hands and i'm winner". Even 100000 hands isn't really enough to be sure you are winner and it wasn't just variance smiling for you...

That's a terrible example. A standard deck of cards has billions of trillions of combinations possible, a d6 has far, far less (at its core its 52 vs 6). "Evening out" in a deck of cards is nigh impossible, on a d6 its very easy because there are far less possible combinations, and you can calculate when a specific dice reaches near parity in terms of results

Not if you’re looking for statistical signifance.

The point he’s making is clear, is it not? That none of us here are likely to roll enough D6 in a lifetime to be of statistical significance.

 Rygnan wrote:

tneva82 wrote:
People generally underestimate how long it takes for variance to even out. In poker they go "yey 10000 hands and i'm winner". Even 100000 hands isn't really enough to be sure you are winner and it wasn't just variance smiling for you...

That's a terrible example. A standard deck of cards has billions of trillions of combinations possible, a d6 has far, far less (at its core its 52 vs 6). "Evening out" in a deck of cards is nigh impossible, on a d6 its very easy because there are far less possible combinations, and you can calculate when a specific dice reaches near parity in terms of results

I agree with Rygnan on this. A deck of cards has far, far more combinations than a simple D6. In the card example you have 52 unique cards to be drawn randomly and the probability changes as cards are removed. A D6 is always 1 of 6 sides and that doesn't change with multiple rolls.

Below are my results from yesterday. What your looking at is a total of 600 rolls (10 dice x 60 rolls). All dice are clearly not created equal. For the GW red dice, if everything was true random, the chance of rolling that combination is less than 1%.

I'm not saying you need 100k's of dice rolls...But 600 is pretty small amount. Expecting it to be exactly 100 of each is pretty silly.

And less than 1% events happen periodically anyway. You are acting like less than 1%=impossible.

tneva82 wrote:
I'm not saying you need 100k's of dice rolls...But 600 is pretty small amount. Expecting it to be exactly 100 of each is pretty silly.

And less than 1% events happen periodically anyway. You are acting like less than 1%=impossible.

I'm not expecting it to be exactly 100, but you do get that that is the basis for the math involved right? In a perfect world where everything is perfectly random that is what you would expect. 100 is used purely as a base for comparison.

What I've seen so far is that if you run multiple separate batches you find similar occurrences. I've run the GW red twice (10x30 for a total of 300), for example with Chi-Square results of 3.42% and 0.27%. These dice consistently produce results that are far away from statistical random. In addition they always favor the 3 side. 1% is possible, but what are the odds that batch rolls roll under 4% twice? These dice have a bias.

Take the Chessex Orange/ transparent results for example, in a similar study as above they generated Chi-Square results of 87.61% and 79.15%. They are considerably closer to random than the GW red and that's the comparison I'm trying to make.


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Below is a combination of the batch rolls previously posted including casino dice. The casino dice were rolled as 5 dice x 120 rolls instead of the 10 dice x 60 like the other dice (only half my casino dice order arrived)

I agree that the more data the better and I plan to periodically add to these when bored.

Say what you like but I've done this sort of testing many times with many different dice. When the Mrs asks it's to "find the dice with the best results" (she's a mathematician and it really winds her up) but in actual fact rollign dice is therapeutic.

I've plenty of friends who are statisicans / mathematicians and though they've never seriously sad me down to explain how many times I should roll the dice the "over a pint" comment is 1,000 is a "good number".

My experience has shown me:

1) Smaller GW dice give results biased towards 1-3.
2) Chessex & casino dice have given me results broadly inline with expected results.
3) No set of dice I've ever rolled have given me the expected number (or above) for 6 after 1k rolls.

And not based on testing ;-)

4) Anyone who uses smaller GW dice in a game will get the impression the dice are rubbish and will blame them for losing.
5) Anyone I tell I want to use my "lucky" dice will insist on using those same dice the rest of the game.
6) My opponent will rage and curse my dice/luck when I make more than 3 6++ saves in a roll (that's not rolling 3d6 at once, but 3 separate saves).

In all seriousness... I personally don't use GW dice anymore ;-) and I'm having my own custom set made up .