8 ms·

How True Are Your d20s? (2013)

apocolyps6 5y ago
This all seems a little misguided. All standard dice have opposite sides adding up to the same number and are otherwise evenly distributed, so a bias would have to be quite noticeable to skew the results on average. Dice that tend to roll high/low because of imperfections basically don't exist.
TedDoesntTalk 5y ago
Chi-squared test. When I was in 7th grade, I wrote a science paper on the chi-squared test and applied it to a bunch of D&D dice. I think it is a much better way to assess dice accuracy than stacking dice in this manner.
- slaymaker1907 5y ago
  The issue with statistical testing is that you need to have the patience to roll die many times for useful results, at least for d20s (which are the dice where bias is both most likely and often most impactful).
  - NavinF 5y ago
    That’s a job for machines: https://hackaday.com/2019/06/20/automated-dice-tester-uses-machine-vision-to-ensure-a-fair-game/ https://hackaday.com/2019/06/20/automated-dice-tester-uses-m...
- shagie 5y ago
  Having a chart with the numbers is there... COMPANY MAX 1-20 2-19 3-18 4-17 5-16 6-15 7-14 8-13 9-12 10-11 Chessex 0.014 0.014 0.010 0.006 0.006 0.006 0.006 0.010 0.009 0.008 0.007 The problem is that chart is kind of boring and it doesn't say anything about the manufacturing process. It says that the dice aren't fair for some reason. The image with the dice stacked shows clearly that the manufacturing process and quality control are flawed. From that it isn't a "the dice isn't fair" but rather "the way that the dice are made will make it so that every dice is more likely to not be fair" It is one thing to test the fairness of one dice or ten dice. For a D20 you'd need at least 100 rolls per dice to determine if that dice is fair. But it could just be a bad dice and other ones are fair. Now the question is "how many dice do you need to roll to demonstrate that the dice maker can't make fair dice? On the other hand, if we can take 20 random dice from a maker and stack them one way and measure it and then stack it another way and measure it and show that the dice themselves aren't clearly regular polyhedra, that visual demonstration is much more striking than a table of numbers.
  - TedDoesntTalk 5y ago
    Stacking only reveals physical malformations. It won't reveal weight imbalances, will it? e.g. one part of the die weighs more than the other for some reason.
    - shagie 5y ago
      Stacking reveals physical inconsistencies in the manufacturing process. Weight imbalances would be a characteristic of one dice (and possibly not another). With sufficient rolls of one dice, you could say "yes, this dice is fair" (or not). But one dice isn't a representative indication of "if you buy a dice from X, how much attention do they pay to making dice consistently?" The claim of GameScience is that all their dice are consistently made and equally fair. If you buy a dice from Chessex, it may be fairish, it may not - it depends on how it cooled.
charlieb 5y ago
Wouldn't a better experiment be to roll one 10K times and see if the sides have equal probability? Who cares if the dimensions are a little off if the effect on the roll is minimal, or conversely are even the best toleranced dice still biased?
- bikamonki 5y ago
  https://hackaday.com/2019/06/20/automated-dice-tester-uses-machine-vision-to-ensure-a-fair-game/ https://hackaday.com/2019/06/20/automated-dice-tester-uses-m...
  - mwcremer 5y ago
    And if you read that report, you see: "Gamescience dice are more consistent than the X-Wing dice", with some analysis regarding the flashing from the mold suggesting that sanding it smooth will increase the consistency.
    - YeGoblynQueenne 5y ago
      That's true for d8 used in X-Wing. The report linked from the hackaday article links to a report from awesomedice.com that tested d20s: https://www.awesomedice.com/blogs/news/d20-dice-randomness-test-chessex-vs-gamescience https://www.awesomedice.com/blogs/news/d20-dice-randomness-t... They _manually_ tested Chessex and Gamescience dice by rolling them thousands of time. They found both brands' dice to be off. Gamescience dice had a big dip on the number 14 face, which is the face that has the bit of flash where the die is cut off the sprue by hand. I suspect it's just easier to make a fair d8 than a fair d20. That probably goes for other die sizes also. I was looking for a d14, d16 and d18 and while I found the first two from Gamescience, I could find a d18 only from one brand, other than Gamescience, so I'm guessing that Gamescience decided they simply couldn't make a fair d18 work. I mean, why skip d18 when you have d14, d16 and d20?
- jedimastert 5y ago
  Fun fact: Die don't have to be the same all sides to be provably fair. Check out the "skew die" https://www.mathartfun.com/DiceLabDice.html https://www.mathartfun.com/DiceLabDice.html And a video https://www.youtube.com/watch?v=uAnCL3vhVIs https://www.youtube.com/watch?v=uAnCL3vhVIs
pmarreck 5y ago
His speech on dice quality is apparently hidden on youtube now :/
wolverine876 5y ago
Random number generation is a tool not just for crypto, but for human psychology. There are applications for random, psuedo-random, unpredictable, and 'uncontrolled' number generation. (These are my terminology and concepts. Did I leave out some other property? Has someone actually studied this question?) Imagine it's dinner time and you want to randomly choose a restaurant, so you roll a die. Let's say you know the die isn't truly random; I guess you probably don't care. Let's say you know it's not really even psuedo-random (by whatever standard that's defined); do you care? Let's say it's just unpredictable - significantly biased, but you don't know the bias - do you care? Let's say I told you what the bias is before you roll, but you are yielding control of the outcome to the dice (which I'm calling 'uncontrolled'). Does that differ from yielding control to another free will, another person? What matters to you here? Imagine that instead you are deciding whether to buy a house. You can't decide, it's 50-50, let's roll for it! How do the above questions apply? Dinner is a low-stakes, no-lose situation. The house is a high-stakes, no lose (assuming it legitiately is 50-50) situation. Imagine a low-stakes, win/lose situation, like a low-stakes game of craps. As long as it's unpredictable, is that fine? What about uncontrolled? Imagine about a high-stakes game of craps: Honestly, I might still be satisfied with unpredictable (ignoring the risk that someone might cheat and figure out the pattern), or even uncontrolled, if everyone knew the bias. I might be satisfied with merely uncontrolled for all of those situations, though at a certain level of bias, why roll a die?
- uncletaco 5y ago
  One thing I like about the psychology of random is you can tell what numbers are true random vs what numbers are human generated if you know what to look for. For instance humans will avoid closeness (1 next to 2) and runs (1 next to 1 again). They will also usually avoid starting with the lowest and highest number in the range (asking for random numbers between 0 and 10 will almost never result in the first number being 0 or 10). If they are aware of this and try to compensate they’ll start creating patterns that give them away.
  - Morizero 5y ago
    Here's a topical example that The Economist showed a few months back https://www.economist.com/graphic-detail/2021/10/11/russian-elections-once-again-had-a-suspiciously-neat-result https://www.economist.com/graphic-detail/2021/10/11/russian-...
slaymaker1907 5y ago
We really need a giant machine that can automatically roll dice and record the results to a file. That way we can then take that data and run a bunch of statistical analyses on them to try and figure out if they are fair enough.
- deleted 5y ago
  [deleted]
- turboponyy 5y ago
  Not sure if this is sarcastic, but if memory serves correct, I have seen a machine that shakes a die (or dice?) repeatedly and uses a camera to recognise which side it landed on. Of course, then you have to worry whether you've configured the shaking to be sufficiently fair, so as to not introduce a systematic error
  - nerdponx 5y ago
    It was posted elsewhere in this thread: https://hackaday.com/2019/06/20/automated-dice-tester-uses-machine-vision-to-ensure-a-fair-game/ https://hackaday.com/2019/06/20/automated-dice-tester-uses-m...
hackcasual 5y ago
I've got a set of Game Science dice, and while they measure very consistently, the very sharp edges, even with flashing removed do seem to cause them bias. If you leave the flashing on, then it gets even worse.
stolenmerch 5y ago
I just prefer the sharp edges of GameScience dice, regardless of their trueness. The Zocchi Ruby Gem dice are the closest to the pleasure of rolling casino dice, but I'd still prefer they be about 20% larger and heavier with ink that doesn't lift off from too much handling. I'll take a slight bias in the rolls if it means a superior aesthetic experience.
mLuby 5y ago
Don't forget to scout, train, and exorcise your dice! Part 1: Scouting your die's personality (4min) https://youtu.be/87F-Ind9BaQ https://youtu.be/87F-Ind9BaQ Part 2: Training your dice (4min) https://youtu.be/gNGa-ydu7z4 https://youtu.be/gNGa-ydu7z4 Part 3: Polterdice (4min) https://youtu.be/XXy2awzR-mM https://youtu.be/XXy2awzR-mM
failrate 5y ago
And here I've been actively wondering if I should simulate die "personality" for a video game prototype that is based around giant handfuls of d20s
DannyBee 5y ago
Just to be pedantic - the WR100 is +-0.001 officially. They say it's "accurate to a thousandth of an inch", but that's not quite right. It would have to be +-0.0005 to be actually accurate to a thousandth of an inch. It's accurate to 2 thousandths. So for example, the differences seen between a number of manufactures in the "width standard deviation table" are totally in the error bars (IE CC translucent vs koplow, gamescience vs cc opaque) I also strongly doubt the wixey's used are really accurate to 2 thousandths, either. I have a few of them, and i measured some master gage blocks with the wixeys (WR-100's) and some mitutoyos . One wixey wr-100 was +-.003, another +-0.004 (IE out of spec). The mitutoyo's were +-.0002 (in spec) Don't get me wrong, Wixey is a good product at a very good price, but if you are trying to measure at the 0.00X level with some repeatability, probably not the right choice.

This all seems a little misguided. All standard dice have opposite sides adding up to the same number and are otherwise evenly distributed, so a bias would have to be quite noticeable to skew the results on average. Dice that tend to roll high/low because of imperfections basically don't exist.

TedDoesntTalk 5y ago

Chi-squared test. When I was in 7th grade, I wrote a science paper on the chi-squared test and applied it to a bunch of D&D dice. I think it is a much better way to assess dice accuracy than stacking dice in this manner.

slaymaker1907 5y ago
The issue with statistical testing is that you need to have the patience to roll die many times for useful results, at least for d20s (which are the dice where bias is both most likely and often most impactful).
- NavinF 5y ago
  That’s a job for machines: https://hackaday.com/2019/06/20/automated-dice-tester-uses-machine-vision-to-ensure-a-fair-game/ https://hackaday.com/2019/06/20/automated-dice-tester-uses-m...
shagie 5y ago
Having a chart with the numbers is there... COMPANY MAX 1-20 2-19 3-18 4-17 5-16 6-15 7-14 8-13 9-12 10-11 Chessex 0.014 0.014 0.010 0.006 0.006 0.006 0.006 0.010 0.009 0.008 0.007 The problem is that chart is kind of boring and it doesn't say anything about the manufacturing process. It says that the dice aren't fair for some reason. The image with the dice stacked shows clearly that the manufacturing process and quality control are flawed. From that it isn't a "the dice isn't fair" but rather "the way that the dice are made will make it so that every dice is more likely to not be fair" It is one thing to test the fairness of one dice or ten dice. For a D20 you'd need at least 100 rolls per dice to determine if that dice is fair. But it could just be a bad dice and other ones are fair. Now the question is "how many dice do you need to roll to demonstrate that the dice maker can't make fair dice? On the other hand, if we can take 20 random dice from a maker and stack them one way and measure it and then stack it another way and measure it and show that the dice themselves aren't clearly regular polyhedra, that visual demonstration is much more striking than a table of numbers.
- TedDoesntTalk 5y ago
  Stacking only reveals physical malformations. It won't reveal weight imbalances, will it? e.g. one part of the die weighs more than the other for some reason.
  - shagie 5y ago
    Stacking reveals physical inconsistencies in the manufacturing process. Weight imbalances would be a characteristic of one dice (and possibly not another). With sufficient rolls of one dice, you could say "yes, this dice is fair" (or not). But one dice isn't a representative indication of "if you buy a dice from X, how much attention do they pay to making dice consistently?" The claim of GameScience is that all their dice are consistently made and equally fair. If you buy a dice from Chessex, it may be fairish, it may not - it depends on how it cooled.

charlieb 5y ago

Wouldn't a better experiment be to roll one 10K times and see if the sides have equal probability? Who cares if the dimensions are a little off if the effect on the roll is minimal, or conversely are even the best toleranced dice still biased?

bikamonki 5y ago
https://hackaday.com/2019/06/20/automated-dice-tester-uses-machine-vision-to-ensure-a-fair-game/ https://hackaday.com/2019/06/20/automated-dice-tester-uses-m...
- mwcremer 5y ago
  And if you read that report, you see: "Gamescience dice are more consistent than the X-Wing dice", with some analysis regarding the flashing from the mold suggesting that sanding it smooth will increase the consistency.
  - YeGoblynQueenne 5y ago
    That's true for d8 used in X-Wing. The report linked from the hackaday article links to a report from awesomedice.com that tested d20s: https://www.awesomedice.com/blogs/news/d20-dice-randomness-test-chessex-vs-gamescience https://www.awesomedice.com/blogs/news/d20-dice-randomness-t... They _manually_ tested Chessex and Gamescience dice by rolling them thousands of time. They found both brands' dice to be off. Gamescience dice had a big dip on the number 14 face, which is the face that has the bit of flash where the die is cut off the sprue by hand. I suspect it's just easier to make a fair d8 than a fair d20. That probably goes for other die sizes also. I was looking for a d14, d16 and d18 and while I found the first two from Gamescience, I could find a d18 only from one brand, other than Gamescience, so I'm guessing that Gamescience decided they simply couldn't make a fair d18 work. I mean, why skip d18 when you have d14, d16 and d20?
jedimastert 5y ago
Fun fact: Die don't have to be the same all sides to be provably fair. Check out the "skew die" https://www.mathartfun.com/DiceLabDice.html https://www.mathartfun.com/DiceLabDice.html And a video https://www.youtube.com/watch?v=uAnCL3vhVIs https://www.youtube.com/watch?v=uAnCL3vhVIs

pmarreck 5y ago

His speech on dice quality is apparently hidden on youtube now :/

wolverine876 5y ago

Random number generation is a tool not just for crypto, but for human psychology. There are applications for random, psuedo-random, unpredictable, and 'uncontrolled' number generation. (These are my terminology and concepts. Did I leave out some other property? Has someone actually studied this question?) Imagine it's dinner time and you want to randomly choose a restaurant, so you roll a die. Let's say you know the die isn't truly random; I guess you probably don't care. Let's say you know it's not really even psuedo-random (by whatever standard that's defined); do you care? Let's say it's just unpredictable - significantly biased, but you don't know the bias - do you care? Let's say I told you what the bias is before you roll, but you are yielding control of the outcome to the dice (which I'm calling 'uncontrolled'). Does that differ from yielding control to another free will, another person? What matters to you here? Imagine that instead you are deciding whether to buy a house. You can't decide, it's 50-50, let's roll for it! How do the above questions apply? Dinner is a low-stakes, no-lose situation. The house is a high-stakes, no lose (assuming it legitiately is 50-50) situation. Imagine a low-stakes, win/lose situation, like a low-stakes game of craps. As long as it's unpredictable, is that fine? What about uncontrolled? Imagine about a high-stakes game of craps: Honestly, I might still be satisfied with unpredictable (ignoring the risk that someone might cheat and figure out the pattern), or even uncontrolled, if everyone knew the bias. I might be satisfied with merely uncontrolled for all of those situations, though at a certain level of bias, why roll a die?

uncletaco 5y ago
One thing I like about the psychology of random is you can tell what numbers are true random vs what numbers are human generated if you know what to look for. For instance humans will avoid closeness (1 next to 2) and runs (1 next to 1 again). They will also usually avoid starting with the lowest and highest number in the range (asking for random numbers between 0 and 10 will almost never result in the first number being 0 or 10). If they are aware of this and try to compensate they’ll start creating patterns that give them away.
- Morizero 5y ago
  Here's a topical example that The Economist showed a few months back https://www.economist.com/graphic-detail/2021/10/11/russian-elections-once-again-had-a-suspiciously-neat-result https://www.economist.com/graphic-detail/2021/10/11/russian-...

slaymaker1907 5y ago

We really need a giant machine that can automatically roll dice and record the results to a file. That way we can then take that data and run a bunch of statistical analyses on them to try and figure out if they are fair enough.

deleted 5y ago
[deleted]
turboponyy 5y ago
Not sure if this is sarcastic, but if memory serves correct, I have seen a machine that shakes a die (or dice?) repeatedly and uses a camera to recognise which side it landed on. Of course, then you have to worry whether you've configured the shaking to be sufficiently fair, so as to not introduce a systematic error
- nerdponx 5y ago
  It was posted elsewhere in this thread: https://hackaday.com/2019/06/20/automated-dice-tester-uses-machine-vision-to-ensure-a-fair-game/ https://hackaday.com/2019/06/20/automated-dice-tester-uses-m...

hackcasual 5y ago

I've got a set of Game Science dice, and while they measure very consistently, the very sharp edges, even with flashing removed do seem to cause them bias. If you leave the flashing on, then it gets even worse.

stolenmerch 5y ago

I just prefer the sharp edges of GameScience dice, regardless of their trueness. The Zocchi Ruby Gem dice are the closest to the pleasure of rolling casino dice, but I'd still prefer they be about 20% larger and heavier with ink that doesn't lift off from too much handling. I'll take a slight bias in the rolls if it means a superior aesthetic experience.

mLuby 5y ago

Don't forget to scout, train, and exorcise your dice! Part 1: Scouting your die's personality (4min) https://youtu.be/87F-Ind9BaQ https://youtu.be/87F-Ind9BaQ Part 2: Training your dice (4min) https://youtu.be/gNGa-ydu7z4 https://youtu.be/gNGa-ydu7z4 Part 3: Polterdice (4min) https://youtu.be/XXy2awzR-mM https://youtu.be/XXy2awzR-mM

failrate 5y ago

And here I've been actively wondering if I should simulate die "personality" for a video game prototype that is based around giant handfuls of d20s

DannyBee 5y ago

Just to be pedantic - the WR100 is +-0.001 officially. They say it's "accurate to a thousandth of an inch", but that's not quite right. It would have to be +-0.0005 to be actually accurate to a thousandth of an inch. It's accurate to 2 thousandths. So for example, the differences seen between a number of manufactures in the "width standard deviation table" are totally in the error bars (IE CC translucent vs koplow, gamescience vs cc opaque) I also strongly doubt the wixey's used are really accurate to 2 thousandths, either. I have a few of them, and i measured some master gage blocks with the wixeys (WR-100's) and some mitutoyos . One wixey wr-100 was +-.003, another +-0.004 (IE out of spec). The mitutoyo's were +-.0002 (in spec) Don't get me wrong, Wixey is a good product at a very good price, but if you are trying to measure at the 0.00X level with some repeatability, probably not the right choice.