GameScience Dice

By Shamus Posted Wednesday Dec 3, 2008

Filed under: Tabletop Games 88 comments

Here is a video (broken into two parts) from GameScience, where one Colonel Louis Zocchi makes the case that standard gaming dice are not very accurate (that is, not very random) and that his dice (this is part of a sales pitch, mind you) will perform better during play.


Link (YouTube)


Link (YouTube)

I love this guy. He’s the prototypical old-school wargamer: An opinionated, irascible old codger. He’s the kind of guy that inspired characters like Chuck from Chainmail Bikini and Gimli from DMotR.

  1. He asserts that the cheap dice are sometimes egg-shaped and thus do not roll true. He makes a pretty good case for why this would be so, but he never gives us any numbers. Just how far off are those dice?
  2. He claims that GMs are killing off characters prematurely with their egg-shaped dice, “because their dice can’t make saving throws.” Setting aside the fact that most players make their own saving rolls with their own dice, this still doesn’t make sense to me. On a standard d20, 20 is opposite 1, 19 is opposite 2, 18 is opposite 3, and so on. You can make a die give more / less criticals by making it egg-shaped, but I don’t see how you can make it roll higher or lower on average. If you increase the number of 19’s, you also increase the number of 2’s by the same proportion. That’s by design.
  3. The most pressing question – which I notice he never acknowledges, much less answers – is why in the name of Gary Gygax’s beard did they use “China Girl” for the intro music? (This song would be for more appropriate, and is in fact what I hear every time someone at the table tells me they’re rolling for something.)

I must say the crisp-edged dice he’s selling do indeed look fabulous. He makes a big deal about how his stuff is so much more expensive, but the prices on the website are actually quite reasonable and comparable to what you’d pay for the fancy dice at a typical gaming store.

I don’t know quite if I’m buying what he’s selling in terms of dice behavior, but I do see myself buying what he’s selling, if you see what I’m saying.

 


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88 thoughts on “GameScience Dice

  1. Calle says:

    The dice you buy at the typical gaming store probably are Zocchi dice, thus the similarity in price. Those guys have been around pretty much forever. I remember ads for GameScience back in 1984 when I first started buying roleplaying games in English.

  2. Telas says:

    Sadly, this year’s Gen Con was Louis Zocchi’s last year to attend. :( (At least that’s what he told me.)

    If a die is “true”, then any two opposite numbers should add up to n+1, where n = the number of sides on the die. Check it on a standard d6; opposite numbers always equal 7. Many dice are “spindown” dice – the 20 is next to the 19, which is next to the 18, etc; this allows you to use the die as a counter by rolling it over one edge at a time. One of my problems with the otherwise-cool Q Workshop dice is that they are spindown dice.

    And yeah, it’s disappointing that Zocchi’s brand of absolutist attention to detail is something that is disappearing from today’s “lowest common denominator” economy.

  3. MadTinkerer says:

    Regardless of whatever reason he gives, here are MY reasons why I like GameScience dice:

    1) Like makers of fine swords or wine they’ve been around since the cretaceous period and are just plain experienced at making a good product.

    2) The dice themselves make a very satisfying “clack-clack” when rolled.

    3) The dice themselves continue to make a satisfying “clack-clack” when rolled because they last practically forever even if you try to wear out a particular set.

    4) Unless you plan on not using your dice for gaming (maybe you want to make a diorama or something with cheap dice), GS dice will save you money in the long run because of point 3.

    5) Like Baskin-Robbins, they come in a bazillion flavors.

    6) They’ve successfully stayed in the business of making esoteric hobby supplies for two and a half decades, as opposed to Wizkids, WEG, Ral Partha, FASA, Guardians of Order, and even TSR. So they’re doing something right.

  4. Jeremiah says:

    Now I’m going to be paranoid about all my dice from now on. Dammit.

  5. Eric says:

    All I know is his dice look pretty sweet. He may not have actual numbers to back his claim, but the every thing he says sounds plausible.

  6. Illiterate says:

    I’ll have to watch the rest of that video after work, but this seems very serious. The molding marks on his dice is an interesting point. I’ll have to look over my 2-twenties for that.

  7. Rhykker says:

    Thanks for posting this, Shamus.

    When I started introducing D&D to some college friends between classes, I didn’t have my dice with me, so what we used instead was the RANDOM function on our calculators. It felt totally geeky (even more geeky than just outright playing D&D), and definitely failed to capture the excitement of dice rolling, but everyone had a calculator, and no one had dice. Now and again, we would have a session at someone’s house, at which time I would bring my dice. My players began to hate their calculators, and love my dice – because, apparently, their calculators hated them and gave them poor rolls. But while they were using my dice, I continued to use my calculator, because an issue of randomness began to creep into my mind…

    I had always felt that I would get very mediocre rolls with my d20. 20s were rare, 1s were rare. But I felt as though I had mediocre “luck,” in general, so I didn’t think much of it until I switched to my calculator, and discovered I was getting more 20s and more 1s. Without any real programming knowledge, I figured a RANDOM function is completely indiscriminate – it’s a calculation that cannot favor any outcome. But dice… I didn’t know the exact mechanisms of how dice were made, but I knew that tiny imperfections could cause uneven weight distributions, favoring certain rolls over others. The numbers carved into the faces, for instance, each removed an unequal amount of weight from its given face. The “1” has the least amount of weight removed, so shouldn’t it be the heaviest “face,” and thus making the opposite face, the 20, which was also the lightest face, the most probable roll?

    We eventually switched to playing online, using a dice program that also makes use of a RANDOM function. According to my players, the software hates them even more. My players eventually informed me that the RANDOM function is not, in fact, random ““ it is a pseudorandom number generator that is only an approximation of truly random numbers. The sequence of numbers it generates is not truly random in that it is completely determined by a relatively small set of initial values. Apparently, on old calculators with RANDOM functions, you could eventually match the sequences, and have both calculators spit out the same results (one of my players managed to achieve this with classmates in high school).

    I nonetheless still feel as though (present-day) pseudorandom number generators are “better” than imperfect dice. With today's technology, the sequences are so long that no casual-gaming human would be able to recognize any kind of pattern in his dice results.

    After watching these two videos, I decided to measure my d20. The one that seemed to roll mediocre numbers. The height of the die, from 1 to 20? 1.775 cm. From 10 to 11? 1.675.

    I'm not crazy after all.

    1. Colonel Louis Zocchi says:

      Please enter d20 Dice Randomness Test on your computer. It will show you the findings of the Awesome dice company, which rolled a Gamescience and a Chessex D-20, 10,000 times. If the dice did exactly what was anticipated, the would roll each face 500 times. They said that if the die faces turned up 33 times over or under 500, they would be counted as 500. The Only chessex face to come close was its 5, which came up 488 times. Gamescience dice had 8 faces come up within 10 of the 500 mark, and 13 faces came up within 33 of the 500 mark. This test proved that the protruding clip mark on it #7, caused the 14 face to come up dramatically short of other faces. Consequently, Zocchi is now trying to assure that buyers will cut off any protrusion to improve randomization. A second independent test will be found if you enter “HOW TRUE ARE YOUR d20’s.” The second test evaluates dice made by Crystal Cast, Chessex, Koplow and Gamescience. Colonel Louis Zocchi

  8. Rob says:

    He leaves out is another contributing factor to your dice not being perfect.

    Your dice bag.

    Your dice grind against each other constantly while in the bag is this is a bad thing in creation it’s a bad thing overall. One of my GMs has joked (maybe?) that when his GameScience dice show up he’ll be carrying them in foam to keep them from touching.

  9. Gregory Weir says:

    Much of my respect for his attention to detail is wiped away by his tendency to refer to a single die as a “dice.” The irregularities he’s talking about can’t affect the probabilities very much. You’d think he’d be equally nitpicky about his terminology.

  10. Nathan says:

    “Fresh oats cost more than used oats…..” Classic line.

    I wonder if anyone out there makes gaming dice that are machined rather than molded. He seems to think believe that machining would make better dice (good enough for Vegas, right?), but he doesn’t use that process himself. Too expensive, I suppose.

    On a related note, does anyone make dice out of metal? I wouldn’t use them for gaming, but that might make a nice gift.

  11. Jeysie says:

    I have to say that, despite whether they’re more accurate or not, I’d buy the GameScience dice anyway just because they’re spiffier and sturdier-looking.

    (If I had a need for dice… one of the couple downsides of playing D&D online. The number generator just doesn’t have the same panache (although we’ve still managed to tack on a few superstitions).)

  12. Stein says:

    About the dice killing of the players prematurely. I can see that happening due to the rounding of edges. If the edges are rounded just so, the dice would always roll over the saving number, and consistently land on a high/low result.
    How often this would happen is another question. I tend to agree with MadTinkerer about the clack-clack sound, though.

  13. MintSkittle says:

    Metal dice can be found at dicepool.com

  14. McNutcase says:

    Nathan: “Dwarven metal”. Plug that into Google, and rejoice.

    Moving on to Zocchi, I would take him more seriously if it weren’t for two things: first, the Zocchihedron; the Mk. 1 was found to be unfair, and I still don’t trust the Mk. 2. Second, he sells ten-sided d10s. I don’t like the current d10 shape; my instincts tell me it can’t be fair, since the faces don’t have any rotational symmetry. I would far prefer a truly old-school d20, of the “0-9 twice” numbering. Astoundingly, these are still made and sold…

    Oh, and he sells d4s. The regular d4 doesn’t roll so much as “thud”, and his safety tips don’t really help. A d12 numbered 1-4 thrice would be far better, not least because it would be another use for the glorious dodecahedron…

  15. Bryan says:

    When I first started gaming in the ’80s, I bought some TSR polyhedral dice. They were what we now call “clay dice.” The plastic TSR used to make them was so soft that the dice edges chipped and cracked badly. They rolled OK… for about 2 months.

    I looked at the dice a couple of years ago and noticed that the edges are so bad that there are rough areas and large gouges in the edges. No wonder they rolled so poorly…

    I have much better dice now, but I may invest in some GameScience dice just to compare them.

  16. Penn says:

    Watching those videos (a couple weeks ago, I think) made me decide to get some Gamescience dice next time I see some. I don’t agree with everything he says, but his points about most dice not being nearly as random as his appear to be accurate. I remember them from back in the day, but I don’t believe that they came in gem style back then.
    You can get metal dice from several manufacturers, I believe. Including precious metals.

    –Penn

  17. Roxysteve says:

    Don’t sweat the dice clacking together, Rob. I’ve had my Gamescience dice since 1979 and they have no visible wear on them.

    Zocchi dice had to be hand painted, and each twenty had to have two colours because Azathoth-forbid they put a second number on any face like they did on the d12. That meant you always had an argument over whether “white was high” on your dice after you rolled and claimed a twenty.

    But I do love my Gamescience polydice far and above the more easy to read Chessex polished-edge ones I use most of the time. I don’t use the d20s for everyday play though. I go with the easier-to-read, unambiguous Chessex version (the hideous Orange one excepted) :o)

    BTW, Zocchi has more going for him in the gaming world than just dice (although, as the grand daddy of polydice you might cut him some slack for making your D&D life easier – I had to make a 220 mile round trip to get my first set of poly dice). Somewhere I have a really neat Star Fleet Battles game he produced (NOT the Task Force/ADB game of the same name) which was best played on the floor of an empty university common room. The phaser fire arcs were 5 feet long!

    Didja know he holds a patent on the D100, and that it is called a Zocchihedron because he was the first person to bring it to market? Not that I’ve ever been tempted to use such a thing, but the effort alone is worth applause.

    As for “spin” numbering schemes, they are no more or less likely to roll a sequence of numbers than the other types (I’ve got two distinct versions of the “21” scheme in my collection) provided the dice are “fair”. Which is where we all came in. Zocchi is saying his dice are fair and a.n.othergize dice aren’t. The numbering scheme is immaterial to that argument. It does bear on Shamus’ high/low pairing version of it though.

    Regards,

    Steve.

  18. Kevin says:

    I did a little study of drilling dice (cutting out holes to try and change the way they roll) for a statistics class in school. It took a lot of drilling to make an difference over a couple hundred rolls. I suspect ‘good’ dice to have, at most, a 1% edge in randomness, over thousands of trials. It is good enough to make money cheating at dice games, but unlikely to make much of a difference in play.

  19. Maddy says:

    True, dice grinding together in a bag won’t be perfect any more (if indeed the dice are able to wear each other down), but they should, theoretically, wear out fairly evenly on all sides.

    If the sides get rounded evenly, then your odds of rolling a 20 shouldn’t change, even if it takes the die longer to stop rolling.

  20. Roxysteve says:

    [McNutcase] The decahedral D10s do possess rotational symmetry, but I get what you mean.

    I agree with you that if you want the rolling action (which isn’t important to the process of getting a random number from the dice as long as they are tumbled when thrown) 20- and 12- sided shpes work best (even as d6’s if you think about it). The problem is that in the heat of battle, it is easier to select from “trad” polydice than go hunting for the d12 that is really a D6 or the d20 that is really a D4, and that people like to see all the different shapes in front of them. I’m not trading in my 500+ D6s (all right, I confess. I played second ed Wonkhammer 401k).

    Not only that, you don’t have a handy roughly-spherical substitute for the trusty D8, which shares many of the unattractive ballistic qualities of the splatty D4 (I once gamed with an AD&D fan who insisted that you didn’t need those “horrible D4s” and used D8s when they were called for. Horses for courses.

    Regards,

    Steve.

    1. Colonel Louis Zocchi says:

      Gamescience Sells a D-8, which is numbered 1-4 two times. It has clipped off its vertices, so that it can be quickly identified and not mistaken for a standard D-8. Because an 8 tumbles more than a d-4, it provides the user greater randomization. Colonel Louis Zocchi

  21. Sesoron says:

    Hm. I feel like I could take him more seriously if, as a purported expert in the field, he used the standard singular “die” instead of the colloquial plurale tantum “dice”. Probably the same reason I wouldn’t trust the nuclear weapons to someone who insists on saying “nucular”. That doesn’t say anything about the product, though. I just wish I had my dice on hand so I could do an actual study.

  22. McNutcase says:

    Roxysteve: the dice as a whole, yes, but the faces aren’t rotationally symmetric.

    Having said that, my dice bag contains several d10s, because you need them, and I believe my wife’s Consumermas gift to me is going to be an unholy number of d6s for Arkham Horror…

    But then again, dice are a religious topic among roleplayers. It’s like starting vi vs. emacs in a computer lab…

  23. balrog62 says:

    I got a pair of GS 20-sided d10’s way back in 1979 and I still use them today as my d% dice. It throws the “kids” off who are used to the current sets of dice with 00-90 printed on d10’s. They do last forever. One of mine even was run over by a car and has no damage. I love GS dice and now buy them whenever I see them and then pass them out as gifts to the people I teach rpg’s to.

    Oh, and I haven’t used a bag for my dice in years. I have them sorted in a fishing tackle box. It looks ridiculously geeky to pull out the box and have all the dice sorted by sides, but it’s really useful when you need a certain on (or several) in hurry. And somewhere, I think it was GS, I picked up some d8’s labeled 1-4 twice. They’re pretty nice for true rolling.

  24. Zimboptoo says:

    Besides the bit where he refers to a single die as “dice” as mentioned above, I have a problem with his implication that an imperfect die will necessarily have a negative impact upon the outcome of a roll. Statistically, an imperfect die is as likely to roll unfairly high as it is to roll unfairly low. It doesn’t mean that you’re rolling is truly random, but bad dice aren’t going to artificially kill your players any more than they are going to artificially save them.

    If he ran a study wherein he bought 100 or so decent dice from another company and used some 100 dice from his company and rolled all of them several thousand times and the other company’s dice consistently rolled in a non-random fashion relative to his, then maybe I’d listen to what he has to say. This is all just talk, and there is far too much superstition and misunderstanding in the Everyman’s perception of statistics for talk to be of much use here.

    Also, they’re 1.5-3 times as expensive as the singles and sets you can get in most game stores, and they don’t sell d10 or d6 sets, so I wouldn’t have much to do with them.

    They are very pretty though.

    1. Colonel Louis Zocchi says:

      Please enter “d20 Dice Randomness test on your computer to read the results published by Awesome dice, of the 10,000 rolles it made with Gamescience and Chessex D-20’s. A second independent test “How True are your d20’s” will show how Crystal Cast, Chessex, Koplow and Gamescience dice compare.
      Colonel Louis Zocchi

  25. Catsclaw says:

    To everyone annoyed at Zocchi’s use of “dice” for the singular: it’s perfectly acceptable English. It may not be common in your neck of the woods, but it’s common enough to be in any number of dictionaries. And at least the proprietor of Grognardia feels it’s actually the correct term in the way Zocchi’s using it.

  26. John Lopez says:

    Crooked six sided dice are the reason why casino dice are hard edged and machined to such tolerances.

    http://www.geocities.com/dicephysics/0107.htm shows the following result: “Dice that have the distance between the 1 and 6 face shortened by 3% have 1’s and 6’s come up 6% more often than one-sixth of the time.”

    When you consider that the “house advantage” on craps when betting the more “fair” bets ( http://www.ildado.com/craps_house_edge.html ) is less than 2%, shaved dice can reverse the advantage completely.

    Combine the polyhedral die’s smaller surfaces, lesser angles (a six sided die has to have a lot of energy to change faces, a 20 sided requires *far* less) with the variances in wear and tumbling, a 6% eccentricity seems highly plausible, if not even a bit low.

    http://www.maa.org/editorial/mathgames/mathgames_05_16_05.html discusses fairness and links to other interesting articles.

  27. Dev Null says:

    3) The dice themselves continue to make a satisfying “clack-clack” when rolled because they last practically forever even if you try to wear out a particular set.

    You wear your dice out? Seriously? I’ve been a gaming geek for a long time now, but I can’t say I’ve ever heard that one before. I’ve got dice that have been in my family for generations (sixes, mind) and I’ve never noticed any sign of wear on them.

    However, when it comes to making a good sound, I’m with you all the way. I made some sixes for playing Farkle out of square brass bar stock. They’re wicked heavy, have a very satisfying heft, and make an absolute racket when you roll them in anger. And when it comes to killing your players with the dice, well, I’ve never needed to as such, but out of a decent sling these things would definitely put holes in teeth.

  28. Drew says:

    As far as the unfairly high/unfairly low issue, look at it this way. If the dice are numbered in a “spindown” fashion, so the highs are one one end, and the lows are on the other end, and the dice are indeed egg-shaped, then you’re going to tend to roll numbers in the mid-range. Now, if you’re going to need, say 17+ to make your saving throw, your odds are going to be lower of getting it. Sure, the odds of a 20 are as good as the odds of a 1, but in the context of “I need a 17 or better”, you don’t care if 20 is balanced vs 1, you care if you actually have a 20% chance, as you should, of rolling one of those 4 numbers, instead of (say) an 18% chance. I think that’s what he’s getting at with the saving throw issue.

    And as far as the D4 goes, if you don’t like a pyramid, and you don’t like using a D8 or 12 or 20 or whatever instead, you can always get one of those rolling-pin style D4s, like this guy:

    http://dicepool.com/index.php?_a=viewProd&productId=1223

  29. McNutcase says:

    Dev Null: I have an older d20 that shows severe signs of wear. I keep it around out of historical interest – it’s so dinged that I don’t trust it to roll even remotely close to fair. It’s actually had at least one vertex smooshed out. Soft plastic dice do wear out. Newer hard plastic dice don’t, at least not anything like as fast, but I still can’t stop myself wanting to buy more dice…

  30. B. Wayne says:

    Catsclaw: no, it isn’t. The first polyhedral randomizers were originally bones taken from the toe-joints of livestock (hence the slangs “bone” and “knucklebones”), but around the 18th century they started being made from lead or pewter, possibly by soldiers sitting around with nothing to do.

    In order to make them, they were, in fact, die-cast, meaning liquid metal was placed into a die to be shaped into a cube, and then having its faces marked. By metonymy, as a product of a die it was called a die, and the plural “dies” was used to describe games played with them (since they used two or more). Over time “dies” came to be spelled “dise”, and once the ‘s’ shifted to an unvoiced sound it became spelled “dice”, and homonymous with a word for chopping things into small bits.

    Fun fact, though, it’s been known from the time of ancient greeks that the only possible regular polyhedra are the four-sided, the six-sided, the eight-sided, the twelve-sided, and the twenty-sided, although it was not until recently that all those geometric shapes were used as randomizers.

    Other fun fact, conforming to the X+1 rule doesn’t in any way preclude a die from being spindown. If you want to minimize prejudice, in addition to X+1, you also have to make sure that for every die face, the total value of the face plus that of all adjacent faces is a constant across the die, and I’m not sure if that’s possible on a regular polyhedron.

    Also, I like ten-sided dice because they are well balanced for spinning.

  31. MechaCrash says:

    Ah, computerized RNGs, how they hate me. I play D&D online with some friends and routinely get boned by the dice.

    In the first session of one game I’m in, I rolled a natural one three times in a row.

  32. Shamus says:

    On computer RNGs:

    For years I’ve used the Mersenne Twister. I treat it as a magical black box, and if it has some egregious failings then I don’t want to know. :)

  33. Factoid says:

    That last sentence in the post was a delightful turn of phrase. Well done.

  34. Oleyo says:

    If the midrange numbers are not enough to get a save on an “egg” shaped die, then even though the extreme-range numbers are just as likely to give a one as a twenty, at least you have a fair shot at the twenty (and one) with a balanced die.

    Thats how I heard it. He does mention that you will be more likly to get the one AND the twenty. Makes sense.

    Also, I cant even imagine how much harder it would be to machine a dodecahedron over a cube :) Would be cool though.

    I want some “sharp” edged dice myself :)

  35. Rhykker says:

    Sharp-edged dice: injuring gamers since 1974.

  36. Doug Sundseth says:

    1) “Uncle Lou” is one of the genuinely nice folks in the industry (and a pretty good Dixieland trombone player, IIRC).

    2) That said, of the three big dice companies in the adventure gaming industry (Chessex, Koplow, and Gamescience), Gamescience is the company I’m least likely to search out for dice. Their dice just aren’t as pretty as premium Koplow and Chessex dice.

    As to fairness, I regularly do statistical analyses* of dice variance and have yet to see a die from any major company that is significantly non-random.

    3) Most common random-number generators implemented on computers use the LSDs of your time as seed numbers. While not random using the strictest available definition, they are more nearly random than pretty well any manual randomizer.
    * Hey, it’s something to do when you’re waiting for your turn to come up. 8-)

  37. Eric Meyer says:

    You know what were great dice? The ones that came in Victory Games products in the 1980s. Big, sharp, and uncolored– they came with a crayon that you rubbed hard into the number grooves in order to fill them in. As the crayon came out over time, you just rubbed more in.

  38. Brian says:

    …why did you do that, Shamus? Every single set of that guy’s beautiful dice are now gone, thanks to traffic from your hilarious blog.

    What am I supposed to buy myself for Christmas now?

  39. Adeon says:

    @B. Wayne:
    On the gripping hand the English language is constantly evolving and it does seem as if we are getting towards the point where dice and die can be used interchangeably. Personally that suits me fine, I can never remember which way around they are anyway.

  40. Al Shiney says:

    Nice post mentioning Dwarven Metal. For Christmas a few years ago, I bought a set of steel and brass dice for two of my close gaming friends. They steel set was especially appropriate, because the friend I gave them to is a construction foreman. I don’t know if they roll true like GS dice, but they sure are “awfully purrty” to look at. :-)

  41. Telas says:

    Adeon @ 38:

    Did you just use a sci-fi phrase to describe the evolution of language?

    +10% XP for coolness.

  42. Taellosse says:

    Seconding Brian’s post @ 37. All the ones with the numbers painted on are out of stock!

    Not that I can afford to be buying new sets of dice right now. Nor do I actually use physical dice anymore, since I always use an electronic roller when I game now…but still!

  43. Claire says:

    He claims that GMs are killing off characters prematurely with their egg-shaped dice, “because their dice can't make saving throws.” … You can make a die give more / less criticals by making it egg-shaped, but I don't see how you can make it roll higher or lower on average. If you increase the number of 19's, you also increase the number of 2's by the same proportion. That's by design.

    You’re assuming that the target-numbers are evenly distributed… but they aren’t. To make an extreme case, imagine you have a die, arranged so that the numbers on opposite faces always sum to 21 (like most/all d20s), but due to (severely) shortened 10-11, 9-12, 8-13, 7-14, and 6-15 axes, it will produce a number between 6 and 15 (inclusive) 60% of the time, rather than the expected 50% of the time. Assuming equal probability distribution within these limits (6% per face with mid-range numbers, 4% per face with extreme numbers), you’re going to fail saves more than you ought, and worse, you’ll fail saves more when it counts most .

    So, let’s take this die to combat, and say we’re taking our swings with an attack bonus of +8 vs. AC 24. So, we hit on a result of 20, 19, 18, 17, or 16. Instead of hitting the expected 25% of the time, we’re only going to hit 20% of the time!

    Of course, that’s an exaggerated result, and probably no die is that bad. Gambling over 1000’s of rolls, the die differences can make a real difference in real money… gaming over tens of sessions, any perceived blips in probability distribution are more appropriately attributed to confirmation bias than misshapen dice.

  44. Kacky Snorgle says:

    “Other fun fact, conforming to the X+1 rule doesn't in any way preclude a die from being spindown.”

    Yes it does. A spindown d20 has to have 10 next to 11, while a d20 conforming to the X+1 rule has to have 10 opposite 11….

  45. qrter says:

    Personally that suits me fine, I can never remember which way around they are anyway.

    Surely it can’t be that hard to remember, if you look at the words phonetically – adding an s-sound makes it plural.

    If you can remember the difference between ‘shoe’ and ‘shoes’, you should also be able to manage ‘die’ and ‘dice’. ;)

  46. T-Boy says:

    Goddamn. Maybe I might want to get a hardware random number generator and force everyone to use that instead.

    I mean, if I can’t rely on the Heisenburg Uncertainty Principle, what can I rely on? D:

  47. Sauron says:

    @T-Boy:
    “I mean, if I can't rely on the Heisenburg Uncertainty Principle, what can I rely on?”

    I’m really not sure….

  48. Claire says:

    Heisenburg is crap, the universe is deterministic. The proof is in quantum entanglement.

    *sees a burgeoning throng of rabble-rousing physicists charging from the distance*

    You’ll never take me alive! John S. Bell was rat fink!

  49. Greg says:

    Aww, Claire wrote the post I was going to while I was watching the video.

    Wot she said!

  50. Lintman says:

    Reading through the comments, I was planning to make a post about the Mersenne Twister (my favorite pseudo-RNG), but Shamus beat me to it.

    A good while back I was working on improvements to a community random map generator for a TBS game called Dominions II, and the maps weren’t looking as varied as I would have expected. The program was using the basic, stock, rand() that MS C++ provides. I replaced it with the Mersenne Twister, and the maps suddenly became dramatically more varied. I was hoping for improvement, but hadn’t expected anything that big. The effort really paid off.

  51. Shawn says:

    Uncle Lou provided me with my first set of polyhedral dice back in ’77, if I recall correctly. As has been mentioned, dice weren’t his only gig back then – he marketed Trek minis and rules, other figures, brushes, paints – everything you needed to become an OG (Original Gamer).

    He used to challenge people to speed painting competitions at cons and extol the beauty and practicality of his Nipple Pink paint, which he called the best bargain in the hobby paint world because, “even if you painted a thousand 25mm nipples, you’d still have paint left in your pot.”

    If you never got to see Uncle Lou working a crowd of gamers at a con, you’ve really missed out.

  52. MadTinkerer says:

    Balrog62: “I got a pair of GS 20-sided d10's way back in 1979 and I still use them today as my d% dice.”

    I have a few of those as well, and they never cease to amuse new players.

    Dev Null: “You wear your dice out? Seriously?”

    Well almost none of the dice I’ve bought as dice (as opposed to dice that have come with something else) have worn beyond use. The exception being some very cheap (one dollar for a few dozen) plastic d6s that showed significant wear after a while. Pretty much anything I’ve bought from a game convention or a comic book store is good though. :)

    By “try to wear out” I meant “just use those dice ALL the time”. I still have a standard set of blue polyhedrals from two decades ago, the first set I ever bought (and I initially used them exclusively for several years because I didn’t have any other dice), which have no sign of wear at all.

  53. Face says:

    I was fortunate enough to be at Origins and Gencon this year. Origins was supossed to be Lou’s last con, so I made sure to buy a full set of dice….even though I don’t need the d14 or d24.

    When the Gencon folks heard that he was “retiring” they offerred him a free booth, which is why he was there this year. I got this from several sources including the man himself. I suspect he’ll be at future cons as long as he’s invited and given a booth.

    Like most of us, I too have a ton of dice. Now I have several sets of GameScience dice and I do like them more than any other. Some of my buddies have GS dice they’ve used for years and the par for the course is that they are simply made of better stuff. I was shown some of his older dice and they look like my brand-new dice.

    Aside from my HackMaster Honor Dice, I’m sticking with GameScience dice…well I do have some wooden 6 siders from TSR that are my “lucky” PC creation dice.

  54. Justin says:

    Did anyone else think they were about to be RickRolled on the “This song” link?

  55. Arquinsiel says:

    Rhykker, I’m guessing you’ve never played much Blood Bowl via Fumbbl, or you would be familiar with the concept of “re-rolled double-skulls.” In real numbers it’s like rolling a three for one of a D&D character’s stats, yet it happens all the time. In fact, veteran player’s often won’t waste a re-roll token on a double-skull, it’s that common.

    I agree with the concept of a deterministic universe mentioned above. My university professors, for the most part, do not. I have used this to convince them that using stupidly huge numbers of dice to generate prime numbers for cryptological purposes is a good idea and thesis worthy.

    It is in no way an excuse to buy myself 1024 d6. Not at all.

  56. Insanodag says:

    Regarding die vs dice, I would like to point out that my household communication protocols demand colloquial usage at all times and my GF smacks me for being pedantic and pompous every time I dare to use the word ‘die’ for the singular of dice. This makes any explanation of rulesets lengthy and painful, since I am the one normally explaining the rules. However, looking at some of the posts on that topic, I am starting to think that I should be grateful for the effectiveness of her aversion therapy.

  57. JB says:

    About computers and random numbers:
    As been said before in the discussion, ordinary random functions in computers do not produce random numbers. They produce a series of deterministic numbers that appear to be random.

    There are several meassures for how good these algorithms are, for example how evenly distributed the results are and measures for what order the numbers comes in.

    Consider rolling: 1-2-3-4-5-6 vs rolling 1-3-4-2-6-5. Both are evenly distributed, but the second is more random than the first.

    There’s a lot more to this, but my knowledge about these things stops here.

    The ordinary rand() function used by many is not a good function. It has patterns in the lower significant bits that repeats themselves regularly. So this function should be avoided. Use drand48(), a mersenne twister or something else instead, if you want pseudorandom numbers.

    All pseudorandom algorithms are seeded. That is, you give it a number, and different numbers will give different series of number. But starting with the same seed, will always give you the same numbers. Often the seed is based on the internal timer in the computer, to give you a new seed every time.

    A computer can give you true random numbers. Based on activity on the computer, such as keyboard presses, harddrive activity and other things, an entropy pool is generated. And from this random numbers are generated. On linux reading from /dev/random will give you such numbers. Useful when you need random numbers for generating high security encryption keys.

  58. TashunkaSapa says:

    I do agree that Zocchi makes a quality product, but personally I don’t like the man at all. I spent a considerable amount of money at his booth at GenCon/Origins ’88, and when I wandered back into his booth later in the afternoon to peruse more merchandise, he accused me of shoplifting some of the items I’d already purchased previously. I didn’t like being treated like a thief when I was, in fact, one of his better customers.
    Twenty years later, I remember the way I was treated, and his competitors benefit from his indiscretion.

  59. Sesoron says:

    Insanodag (56): Now, I think we’re justified in promoting a morphologically distinct singular form. If nothing else, it makes meaning clearer when appending a definite article to the word. Since it has that function, it’s not a useless appendix of archaic language.

  60. Maddy says:

    Funny what Doug Sundseth says about the GS dice not being as attractive – I bought a pair back in 91 or so and I remember it saying on the bag that they were deliberately molded in ugly colors to discourage theft.

    And they were MUCH uglier then…

  61. McNutcase says:

    The true solution to the die vs dice argument is very simple: count how many sides the item you’re about to refer to has, and then call it a “d[number]”. If it has six sides, it’s neither a die nor a dice, it’s a d6.

  62. Rick C says:

    @50:

    I modified the Roguelike Omega to use the Mersenne twister, and I thought the gameplay became pretty different as well. (Actually, it seemed to me that combat became noticeably easier.)

  63. Heph says:

    No offense, but after having read the page about the total die, I can’t bring myself to buy anything from there. It’s their, original, idea to ignore/reroll non-applicable numbers?
    Yes, that way a d24 can generate any and all of the lower d’s…but, honestly, claiming you came up with it is pretty..;err…no.

  64. Sheer_FALACY says:

    @JB:

    1, 2, 3, 4, 5, 6 and 1, 3, 4, 2, 6, 5 are both equally “random”. If people see a random number generator generate 1, 2, 3, 4, 5, 6, they’re inclined to throw it out… which would make the random number generator less random.

    Just because something has a pattern doesn’t mean it isn’t random. In a truly uniform random system every possible result has the same probability to show up.

  65. When it comes to PRNGs, I prefer Arcfour (RC4) due to its elegant simplicity as well as its strength (as long as you discard the first few bytes of the stream). The first gigabyte or so is indistinguishable from a true RNG, which would provide enough dice rolls for more than a lifetime. The algorithm, as well as some test vectors, can easily be memorized and implemented with a small amount of code.

    For true RNGs, the Linux kernel provides a high-quality, hardware random number generator at /dev/random, however its output is very slow, probably too slow for even a tabletop game to use live. If you use Debian (Ubuntu probably has it too), there is a randomsound package that, once installed, runs a deamon that will feed soundcard noise into /dev/random, increasing its generation up to something like a hundred megabytes per hour while keeping the same high quality numbers.

    Random.org has some good literature on the subject as well as providing a true random number generation service.

  66. naa says:

    You can make a die give more / less criticals by making it egg-shaped, but I don't see how you can make it roll higher or lower on average. If you increase the number of 19's, you also increase the number of 2's by the same proportion. That's by design.
    He is not speaking about average but about exceptionnal moments where you have to make a 20. I don’t care about the 9 other pairs, I dont want them to come out, I want the 20/1 pair, and there, yes, I will have a 50/50 chance.

  67. JB says:

    Sheer_FALACY,

    in that sense 6,6,6,6,6,6 is also equally random as the other sequences. But it would fail a test for randomness when requiring an algorithm that provides uniform distribution.

    I was not talking about one sequence being more likely than another, all sequences are equally likely (given uniform distribution). I was talking about tests for randomness. And such tests would be run on much much longer sequences of numbers than six numbers as provided in the example, and then the law of big numbers would kick in.

    My point was to demonstrate with a simple example that there is more to randomness than only providing uniform distribution. There are several tests that can be performed, and different pseudorandom algorithms may behave well in some tests, and worse in other.

  68. Claire says:

    JB,

    6, 6, 6, 6, 6, 6 is not a random distribution. “randomness” is a measure of whether and how well we may induct the results of future die rolls from a history of recorded trials. Whether 1, 2, 3, 4, 5, 6 counts as random in this context depends on how much we know about the process of generating the numbers. If the numbers are being recorded from a d6 roll, we would call that random. If the numbers are being recorded from the display of a simple count-up chip, then we’d say it’s NOT random, and we would fairly draw the conclusion that the next number would be 7.

    There IS more to randomness than “uniform distribution”. In fact, any decent experimenter would raise an eyebrow at truly uniform distribution and look for alternative explanations… like fudging of observed data.

    However, knowing what we know about the physical processes involved in a die roll, there’s no mechanism by which we could reliably roll a continuous sequence of integers. We might load the dice to return 1’s and 6’s more frequently, we might even re-mark the faces so that it returns ONLY 6’s. However, there’s nothing you can do to a die (short of turning the die to display the desired face after rolling, or having one of the bastard-children of Laplace’s demon do it for you) to probilify sequential results.

  69. vdgmprgrmr says:

    This was noted above, but…

    Dayum! All of the dice I would even have thought about buying\requesting for the Winter Solstice is out of stock!

    This leads me to question, is it because of Shamus’ awesomeness, or is this simply a coincidence?

    I vote: Shamus’ awesomeness.

  70. JB says:

    Claire,

    you need to read my first post and Sheer_FALACYs comment to see why I say that “in that sense” 6,6,6,6,6,6 is just as random.

    Any sequence of numbers have equal probability in a uniform stochastic process. 6,6,6,6,6,6 is just as likely as 1,2,3,4,5,6 and 1,3,4,2,6,5.

    However, the probability of getting six equal numbers in a row, or six consecutive numbers in a row is less than getting six numbers that show no such order.

    The reason for this is that there are far more combinations not showing this kind of order, than there are combination having this kind of order.

    No sequence of numbers is in itself random. And no pseudo rnadom number generator generates numbers that are random. It is all very deterministic. If you know the algorithm and its current state, you can with 100% certainty predict all the following numbers, forever and ever.

    But, when you have a sequence of numbers, and you don’t know where it comes from, the numbers can be analysed to see if they appear to come from a true stochastic process.

    I tried to illustrate this with only six numbers in a row. But when doing an analysis of the result of a pseudo random algorithm, a much longer sequence would of course be used.

  71. Avilan the Grey says:

    I remember having this discussion with a clerk when I turned in my LOTTO ticket once; I had picked the numbers 1-7, and she argued that the chance of that number coming up would be so small it was no point in picking them. She refused to believe that that sequence had just as big a chance of coming up as say 2,6,7,11,22,23,29…

    (The fact that it statistically is a higher chance that you get struck by lightning than to get all seven numbers coming up on your ticket is another matter entierely…)

  72. Scotticus says:

    Zocchi used to have a store in Gulfport, MS, which was about an hour from my house. I have such fond memories of going there with my gaming buds when I was in high school. I have actually had the “pleasure” of hearing this dice sales pitch, along with pitches for other Zocchi products on many occasions.

    And I use the term store loosely here, as it was actually more of a medium sized warehouse. I think the “stock” on display was the same used by his distributorship; when in order came in the employees would walk the same rows that patrons did to select their merchandise. Visiting it was like going to a gaming holy site with rows upon rows upon rows of gaming books on shelves. One whole wall of the place was just original print Judges Guild products, and half the store had out-of-print, rare gaming books, minis, and other assorted stuff.

    His store in Gulfport closed down sometime over 6 years ago and I miss it still. I think my wife may be tired of hearing me say that every time we drive through, by, or near Gulfport.

    Ahh, Zocchi’s. There will never be another place quite like it.

    (As an aside, he also had a “branch” store in Biloxi, MS which his ex-wife received in their divorce. It managed to stay hope until recently when it just “vanished” and the location was overtaken by a neighboring gaming store. If anyone knows what happened to her or her store, please do share.)

  73. Scotticus says:

    Oh, and thank you, Shamus, for linking to these videos. I honestly thought he had died. It made me extremely happy to know he was still alive. And to run get my wife to drop was she was doing to watch these videos so she would know what I’ve been talking about all these years. Though I still think she doesn’t know, she did appreciate the points he was making.

  74. Doug Sundseth says:

    Avilan the Grey: “I remember having this discussion with a clerk when I turned in my LOTTO ticket once; I had picked the numbers 1-7….”

    Your analysis is, of course, correct. That said, your choice was still sub-optimal. Payout expectation value depends both on the probability that the numbers you chose will come up (the same for any legal set of numbers) and the number of other people who choose the same numbers (since the grand prize payout is divided between all winners). Simple sequences like the one you chose are noticeably more likely to be chosen than more “random-looking” sequences.

    Sequences with all numbers at or below 31 are also more common than sequences with other numbers included, because of the common use of birth dates to pick numbers. Autopick works pretty well to pick a unique (or at least less-common) set of numbers for these games, but whatever method you choose, those of us who don’t buy tickets thank you for your generous contribution to (whatever). 8-)

  75. FNORD says:

    I can’t speak to the precise physics of the situation, but there’s at least as much spin as science in the discussion. Most of the defects are likely to be random and small, and probably more likely to help the players than hurt them. They seem to reduce randomness, and reduce the standard deviation of results, which helps players (who usually win). Fair dice or not, a player who needs a 20 on a regular basis is toast. But fewer critical failures is something many players would embrace.

    Most default RNG functions are bad for repeated use, as anyone who has ever done Monte Carlo simulation can tell you. Mersenne Twister is pretty darn good, though.

  76. Louis Zocchi — I had no idea he was still around.

    Gee, the world keep shrinking in some ways.

  77. Miako says:

    rhykker,
    well, the good RNGs are better than dice. Most are crap, though. ADOM uses a good RNG. That’s why it’s technically (and stupidly) illegal to download in America (if NSA can’t crack it, and they can’t, then you shouldn’t own it. or so they say)

  78. Miako says:

    jb,
    not all rng are deterministic. this is especially so when you’re talking about self modifying rngs. They can get cranky. (there was one that would kill the player before the end of the game. the closer you got to the end, the wackier the death would be. but you always died.)

  79. Laura Witten says:

    Wow, the number of comments is astounding here, and I didn’t read them all (yet). I would like to clarify a few things about Lou and GameScience.

    I filmed and posted the video in reference. This was Lou’s last year exhibiting GameScience as his own company. GameStation is completing the buy-out of Zocchi’s great company and will be bringing him along to Origins, GAMA Trade Show and GenCon for as long as he is able, as a Guest of Honor or otherwise.

    d10’s: Lou does make 10-sided d10’s and Tens d10’s (also called Deckaiders). In addition, we also sell his d20’s number 0-9 twice, and d20+, with 0-9 once, and 0+-9+ once. The 20+ are available with the other precision dice at gamestation.net.

    Veracity: When you look at the photo Lou has closely, you can tell the size difference in the dice because of the graph paper they were in front of. His use of the word “dice” instead of “die” should’t deter you from the truth. After all, he sells dice…many, not one. Habits die hard ;)

    -Laura, co-owner of GameStation.net and soon to be GameScience

  80. Chris says:

    “On a standard d20, 20 is opposite 1, 19 is opposite 2, 18 is opposite 3, and so on. You can make a die give more / less criticals by making it egg-shaped, but I don't see how you can make it roll higher or lower on average. If you increase the number of 19's, you also increase the number of 2's by the same proportion. That's by design.”
    ===
    It’s not strictly that the dice is “egg-shaped” but also that the surfaces of a d20 vary depending on the wear. Certain faces will have a larger surface than another, meaning that it’s more likely that the die will stop on that face.

    In addition, some edges are going to be sharper than others. So some surfaces are more likely to stop than others, while others are going to be more likely to roll over.

    So it’s a combination of factors that really matter. Along a single axis, we have two surfaces. But those two surfaces vary. So the die can be biased toward that axis and then have an additional bias to one of those two surfaces.

    So a die can be flat along the 20-1 axis, but the “1” face can have a smaller surface and rounded edges compared to the twenty. Conversely, the “20” face could have a large well-defined surface with crisp edges. Therefore, a “1” is highest probability while a “20” is second more likely.

    And this doesn’t account for the die being flat along multiple axises. Therefore, it possible for multiple low numbers to be favored by a die.

    I have a purple gem d20 that rolls like crap but a glittery d20 that rolls highish. And these are d20’s I got out of the cheap dice bin.

  81. Dave says:

    I just got a $27-dollar set of these “precision” GameScience dice from my FLGS back in the US (I live overseas), and I have to say that I have NEVER been more disappointed by a dice purchase in my 30 years as a gamer. Every die has a glob of leftover molding plastic on it. The box helpfully says this can be sanded away, but how the hell can they claim to be “precision” and charge top dollar when the customer is required to (very imprecisely) modify the dice by hand? On top of that, the area around the mold-blemish is often warped or dented, and some of the hard edges of the dice (particularly the 4-sider, with its acutely angled edges) are chipped. Several of the faces also have imperfections. There is no way to repair these flaws.

    I really cannot see how the company can claim that these dice are in any way “precision” dice. They are the most irregular dice–as well as the most expensive dice–that I have ever purchased on purpose (by which I mean, not dice that came in a game box). I’m astonished that GameScience knowingly sells them with production flaws, and then absurdly claims that they are more accurate than other dice. There sure are pretty pictures on the website, but if I had been in the store and had a chance to look at them before buying, I would not have bought them.

  82. Steve @ g2ch says:

    Dave, I do agree the appearance could be better with Gamescience dice (though the cost would be even more expensive). But as someone who has dealt with Lou Zocchi and now the Wittens (the new owners of Gamescience), I feel that someone needs to speak up here and point out that Gamescience has every right to call their dice precision and there is outside evidence to back this up. Even with the mold marks they seem to trump the other dice out there hands down. I won’t repeat what I have already typed elsewhere, but see this link to read about the creation of the D5 and the extra testing on other Gamescience dice. Hopefully I got that link posted right.

    I also recently dealt with a person who decided he was going to test the batch of Gamescience dice he ordered from us and he has shared his results with me. I plan on publishing those on our site at some point soon (when I get the chance – it’s been busy lately). To quote him, he said his results “undeniably show just how much more random the GameScience dice are compared to the tumbled stuff.”

    So I have Lou Zocchi who I trust telling me Gamescience has passed the test and another person who is a math / computer science major telling me the same independently. I have to believe there is something to that.

    Please understand I’m not trying to be argumentative at all. I just feel a need to point out some positive points in favor of a company I like and people I think of as good, honest people.

    Give those dice a shot before you write them off. You just may find you like them after you use them a bit, blemishes and all.

  83. Vegedus says:

    When I went to the USA, and by extension, the biggest RPG shop I’ve been in, I managed to snatch a set of dice of this type. Not sure if they were actually GS, but they are translucent, sharp and have those little flaws he talks about. Some of the edges are also made flat, so you can’t actually piece the flesh with the d4 (though it’s still a fine caltrop). I’ve squandered no opportunity to show them off to the everyone I game with and absolutely love them to death. Just re-reading this article made me bring them out so I could play around with them. I would definitely have bought more if they had them, and I wouldn’t even had been on the lookout for them if not for this article.

  84. Sydney says:

    I think TashunkaSapa’s comment is the clearest and crispest anti-DRM argument on this whole blog.

  85. Alan says:

    “Just how far off are those dice?” I can’t tell you about the dice Zocchi stacked, but my wife and I reproduced his stacking experiment across 79d20 and we measured every damn face pairing.

    Now we’re trying to roll every single one of them 350 times to try and find out what the actual impact is, because we are obviously insane.

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