I have a thing for dice. Yes I have even bought them by the pound. So I have lots of dice. The problem I have with my own 40k games, is that I often get horrible dice results. I just cannot even get games in where I can get my dice to approach average results. Hence.... The Quest for the Holy Grail... Average Dice!

Here is a link to Part 2 of this article

It should be said that the standard dice people buy for this game are horrible. I will let you read the study below on why, but they are bad. I am not a practiced roller (equivalent of cheating). The dice we gamers normally have are small hard things with rounded edges and pips in them. Scientifically these are bad.

The new munitorum dice by Games Workshop are excellent dice. The quality is actually very high. The edges are not rounded, they are light (great for our tabletop rolls), and the graphics on the dice are nice. Haters will be haters, but these are excellent dice. In fact I have had one game with them, and I can say that as someone who looks closely at how well I am "really" rolling and not "perceived" rolling, these dice did indeed hit average. Are these the Holy Grail? Only time will tell, but I for one will be putting them to the test.

This study was first written on Warseer several years ago, and the study was probably published elsewhere, but Warseer is were I first read it. here is the original link....

Before any gamer begins this Holy Quest, he or she should definitely start with the following study. Enjoy......

A huge thanks to Yade for doing this for the community.
I am an engineer and I teach at ASU. In the beginning of every semester there is a lot of book work that my students need to do such as circuit board design and circuit mapping. During this time I have 4 students and a giant mechanical engineering lab at my disposal. So I decided to use my students to improve my 40K game.

In the Spring semester of 2006 I decided to debunk the dice myth "I always roll more ones". So I took a box of the red and white GW dice, a cube of 36 chessex dice, 36 square corner dice with pips (pips are indentations on the side of dice to indicate the value of the face), and 36 Vegas style square dice with no pips.

I then constructed a series of plastic barriers that would be used to keep each die independent of the others. In the lab we have a table that is 4 inches thick solid slate built on hydraulic legs to keep balance and resist independent movement. On this table we put all of the dice in the rolling container and labeled each case, giving each individual die its own chamber and number. My 4 students then shook and rolled the dice 1000 times, recording each individual result. Each die was individually rolled 1000 times, so 4 sets of 36 dice (144 dice) rolled 1000 times equals 144,000 rolls. Each die was tracked on its own and kept separate from the rest.

Afterwards we calculated the results and the Chessex and GW dice averaged 29% ones. Mind you that this is an average and our high was 33 and our low was 23. We removed any statistical anomalies and came up with 29%.

Game room logic, a poor source of anything, would dictate that the side with the one is heavier and would therefore be on the bottom more. Unfortunately this is just not true, take popcorn or batholiths as an example. The 6 is too light to stop the momentum of the die, the rounded corners cannot prevent the die from turning due to the weight. In the end 1s are by far the most common result. On a 6 sided die any given number should appear 16.6% of the time, the Vegas dice were dead on and the square dice with pips were pretty close, only displaying a 19% ratio for ones.

I contacted the casino Caesar's Palace in Las Vegas and accessed their research, after much duress because they wanted to make sure I was not some gambling shark, and they had results that corroborated mine.

Following up
I then proceeded to buy more GW dice and we filled in the corners of the very same dice that we used, carefully melting the new plastic on to the old dice and filing in the corners to the right size and leveling them to .001 for accuracy. The dice then rolled more accurately but still 19% rolled ones. Over 1000 rolls from 36 dice (36,000 rolls), this variance from the expected values is just not acceptable and cannot be considered truly random.

Finally we dissected all of our dice and looked for air pockets or constitutional inconsistencies. We found a few and compared those to the results of the rolls of that individual die and there was no consistent affect generated by the dice with plastic seeds but there was one with dice that had air bubbles. We dissected the dice using a hydrogen cooled diamond saw which prevents the blade from heating up and scarring the soft plastic. Which you can imagine would melt and tear at the presence of any heat or undiverted pressure.

I sent a copy of the study to Chessex and their official response was to inform me that the amount of plastic saved from rounding the corners and hollowing out the pips of 2 dice actually gave them enough left over plastic to make a 3rd die. Economics wins.

We thought about using metal dice and because they are so heavy the weight differential is going to be significant compared to plastic dice. The ratio is so much smaller that we speculated that metal dice would be a lot more likely to be average and accurate though we did not test this assumption directly.

Lower numbers rolling more frequently is not entirely logical as the heavier part of the die ends at the top. I submitted my results to a friend in the physics department. On the original outset he also agreed that the results were counterintuitive. But he proceeded to test my theory because the results were overwhelmingly in support of the opposite expectation.

There are 2 major forces that affect the dice as they roll — gravity and centrifugal force. Gravity is a constant force and the centrifugal force is generated by the weight of the dice as they are tossed. The two forces work together but one clearly takes precedence over the other. The weight differential of the pips directly affects the centrifugal force more so than gravity. In the end, without going into research, he said that this is probably the route that I should take to determine why the dice do not roll evenly.

Interestingly, the data from Caesar's Palace proved that the dice were more likely to flip once than anything else. If you held the dice in your fingers and had the 1s face up you were more likely to roll 6s because they are on the opposite side. They were using Vegas style dice when they conducted this study. There is definitely a correlation to the way that the dice are thrown. Consequently if you go to Vegas now and you do anything at the craps table the way you roll the dice is heavily monitored. If you palm the dice at any time they are removed. You have to hold the dice in the tips of your fingers and when you toss them they have to hit the table and a wall in order to be considered a valid toss!

Conclusion - Casino Dice!
My own criticism of my study is that the nature of it was observational. It is possible, though highly unlikely, to toss a coin 144,000 times and always get heads. Does that disprove the existence of tails? Not at all.

My conclusions are highly probable and very accurate, in my opinion, based upon our results. Which in the interest of science were truly unmanipulated and random.

So I advise players to use square-cornered dice with no pips and only buy clear ones, like in Vegas, so you can see if there was a problem with the making of the dice. This is not going to prevent you from having a bad dice day but it will better ensure that you have some level of consistency.

One thing to consider is that all games workshop games (and most boardgames in general) are designed with these dice and so should reflect this in the gameplay accordingly. If you see somebody using games workshop dice for leadership tests and vegas style dice for everything else, then you can be sure that they are trying to get an unfair advantage though! Try to ensure you are using the same dice as your opponent.

here is a link to part 2 of this article on dice


  1. The problem is that the corners of the casino dice will chip with use. It's one of the reasons that casinos dispose of used ones. I ordered a bunch of squarish dice from gamestation.net (at a great price I might add) and have had VASTLY improved luck with them. :)

    1. yup, as far as I know, they change them in every 60 minutes.

    2. Thanks for the tip! I'm thinking about those 14 mm square transparent dice. Chaos colors and sacred numbers gets me 30 of them.

    3. @Son of Dorn: Would you mind providing a link to the dice you got from gamestation.net? Are they precision edge or just square? I'm really interested in ordering some as I often have horrid luck with dice :D.

    4. @ Milford: Not at all. Here's a link.


      I picked up about 2 dozen of these for my Imperial Fists. While they do only achieve about 19% 1's, I feel they're the best balance between price and statistical average rolls. They have all sorts of colors, sizes, and numberings; I'd highly recommend them. :)

    5. Thanks for the tip. Some of those look much better aesthetically than any chessex I've ever seen.

      Im thinking about getting 30 in chaos colors. 6 purple 7 green 8 red 9 blue.

    6. Glad I could be of help. :) I've talked to Chessex and they're incapable of pipped square dice :( and the set of numbered ones I got from them roll like crap. I'd stick to similar ones in the link. :)

  2. Indeed the question is where to get these dice for a good price. I checked a few sites, found the dice to be expensive ex shipping to Europe. One would need quite a lot of dice, around 27 to be able to roll most things in one go.

    1. Check Gamestation.net If shipping through their site is too high, check them out on Amazon as they run a store through there as well. I'm very pleased with the price I got there.

    2. @Son of Dorn

      Thanks for the tip! Will check out Amazon right no....

    3. You're welcome. Hope you find what ya need :)

  3. Another question:

    Most casino dice come with small drillings which I assume are to mark that they are no longer for casino use. Won't that mess with your statistics as well?

    1. He's talking about brand new ones. Though you can spend up to $10 a piece on them.

  4. That is very interesting.
    I will try to get hold of real casino dice and give it a try.

    Thank you for digging up this article.

  5. when i was starting out with 40k i actually bought some alledgely official casio dice but ended up changing to gamesworkshop dice due to the smaller size the big casio dice had tendencys to knock over my minitures or be difficult to roll when i need to roll 100+ for the ork shooting or assault phases. overall i liked this report very anylitical but really when i tranfered to gamesworkshop dice i really have found no really difference in some cases better rolls and others worse but it is all chance only chance

  6. :D. Lol
    There is nö auch Thing as avarage dice!!!!

    You cant play like that and win
    You have to suspect Worst dice possible

  7. Is there a site you suggest that sell casino dice Natfka

  8. Dice are Not the determining Faktor for los or win
    Analyse youre Game Not youre dice !

  9. Knight of Infinite ResignationJuly 31, 2012 at 2:10 AM

    If you roll your casino or square edged dice in a box they don't knock your miniatures over and roll even closer to average.

  10. Use the dice of your preference, I imbue my dice with holy prayers to the god emperor of mankind. They seem to roll better than average, but I know it's because I am an optimist.

  11. I have two sets of dice I roll. For psychic tests I roll my purple set which always seems to roll low, and my green dice that average higher rolls. I had nothing but crap rolls until I played through a large number of games, doing much the same as this study. I just picked up the minitorum dice Saturday and used them the same day. They rolled a majority of 4+. I'm going to see if they hold out in my nedt few games.

  12. "If you see somebody using games workshop dice for leadership tests and vegas style dice for everything else, then you can be sure that they are trying to get an unfair advantage though!"

    This really needs to be bolded and underlined.

    Whether or not you're actually trying to cheat, you can be sure that if I'm going to THINK you're a filthy cheater if you have two special leadership test dice and judge you accordingly. Also, people very much notice this. You might think you're clever and are getting away with it... you're not.

    So just don't do it.

  13. The one thing this ignores is that if 99% of us use GW or Chessex dice with rounded corners, anyone who is using cornered dice is actually pulling an unfair advantage in a way.

  14. The problem with Casino dice is they was designed to be thrown down a craps table and have enough space to roll. In a wargame situation, you do not have enough space for the ability to throw like that to give them a fair chance to turn evenly. In essence you skew your dice rolls. I have played against people using Casino Dice and have amazing luck. The proof is simple, pick them up a certain way, toss them, they are likely to land that same way or with little roll. Plus to boot they are deadly to the models on the board.

    Personally, if you want "balanced" or "un-biased" dice buy the professional backgammon dice. Two will cost between $10-$20 for a good pair (notice I said pair) that are cast to very specific standards and balanced as close as dice will ever be.

  15. I'm odd but here's what I do with every set I get - roll them all a couple hundred times each and tally the results. Any which deviate outside of 13-19% I don't use. I'm crazy like that :P.

    And yes, this is with rounded dice which are unfortunately almost necessary if you want to roll 20-40 dice at once due to ease of rolling and size generally. Not saying this is correct just speed of play, etc.

  16. I'm 'dice paranoid'. I have separate dice for all my armies, and some of them I use different leadership dice. I also freak out/get squeamish if anyone touches my dice. I truly believe in the mojo!

  17. You guys didnt think my dice craziness was done did you? Part Two coming shortly..........

  18. There are a few statistical problems with this, but the biggest being that he used the same pool of dice for the whole thing. He could treat the dice as nested within the cube, but would be better off having multiple cubes of dice and considering them as a whole. By using a single cube, his results are really only applicable to that cube and not that type of dice in general. In this experiment, the impact of a few poorly weighted dice is overestimated.

    alternatively, I would recommend using an approach similar to the one Kirby suggested above (sort out the misbehaving dice) and do that for multiple cubes of dice. Then, compare the proportion of dice that were removed between the different dice types.

  19. I always steared toward square edged dice but for convenience I now use GW style dice but I think it's time to go back to my old faithfuls

  20. Interesting read regarding testing of GW red munitorum dice:


  21. My dice always roll 6's when needed, or 1's when needed.....

  22. I just rolled my own GW dice to see if I could duplicate this study (of course on a smaller scale). I made the following throws:

    1. 18 dice at a time 10 times.
    2. 6 dice at a time 20 times.
    3. 1 dice at a time 100 times.

    In all three experiments I did not observe any significant variation from the null expectation (that the dice would throw with equal probability of each outcome).

    Given I observed 18 ones after 100 rolls it is very very unlikely that the "true" probability of rolling a one is 29% as the article suggests. It is much more likely that my probability of throwing a 1 is 1/6 as expected.

  23. I bought some munitorum dice today from GW, I couldn't wait for them to arrive in the post. But when I checked them later I noticed they had chipped on the edges. Anyone else get this problem?

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