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?
The dice on that page are in fact the same on all sides. For each of those dice, every face on it is the same as every other face, the same shape and attached to the same adjoining faces at the same angles.
They're not regular - the faces are not regular polygons - but that's not a requirement to have an equal chance of landing on each side. The standard d10 is an example of this in itself.
Those dice look to have either the same face or a symmetrically opposite face.
It would be more impressive to see a die with a pattern of a buckyball with the pentagons and hexagons having equal probability of being rolled. I'm sure its theoretically possible, just not practical.
I don't use dice, but those sure are nice dices. The 120d, the 2/3/4d and alphabetical ones are particularly neat. The uneven dices look like they will roll all over the place.
"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.
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?
Ludology showed that for Pop-O-Matic any individual roll was random, but roll n and roll n+1 were not random. The number on the opposite side of the side of roll n, had a much higher than 1/6 chance for roll n+1.
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?
To boil down the 50/50 one: Imagine your torn between those 2 houses, and your realtor—who also does magic as a hobby—offers you a coin to flip. You ask, "wait, is this a trick coin?"
"Yup!" he replies, "Always lands one way."
"How is that going to help me then!?"
"I got no idea if this is an always-heads coin or an always-tails coin. You see, when they're being minted, each coin randomly plops onto the conveyor before it enters the CBU—"
"—The 'CBU'? What's that?"
"—oh, the Coin Biasing Unit. It's the machine that takes a normal coin and does the proprietary thing that biases it. The coin's orientation as it enters the CBU is the way it'll be biased from then on. As I was saying, the coins enter the CBU randomly, and I've never used this particular one before, so I don't know if it's a Heads coin or a Tails coin."
"... Ok then! Heads I offer on 284 Bayes St, Tails I go with 938 Bernoulli Blvd."
Of course, the realtor wants you to buy the house that gives them the higher commission, so, as a hobby magician, your realtor has two coins and flips the one that they know will result in their desired outcome. That whole story about not knowing is just standard misdirection.
Not if you do it "streaming", just flipping until you get either pattern. (Suppose T is very rare. Then you'll always start with HHH..., so you'll always get HT.) You have to "chunk" them, considering exactly two flips at a time and using each flip exactly once, to get biases to cancel out.
That's great! Come to think of it, drinking games can be 'uncontrolled': 'Watch this CNBC show - every time they use a word starting with 'crypto', we drink!'
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.
I wonder what PRNGs there are that are reasonably easy enough to do in your head but can give better randomness than a person trying to be random normally.
Modular arithmetic can work, but you need to be a little bit careful.
If you want a number from 0-10 then modulo 11 works perfectly (as long as you pick a number well outside any 11 times table you have memorised). This is because it's relatively easy to pick a number without immediately knowing what the mod 11 version of it will be.
For 1-10 you could do mod 10, but that's too easy to cheat. Instead you can take you initial guess n, and multiply (n mod 5) + 1 by (n mod 2) + 1. For example 42 -> ((42 mod 5) + 1) x ((42 mod 2) + 1) = 3 x 1 = 3; 43 -> 4 x 2 = 8.
This second scheme works because we're using a factorisation of the length of our intial range of guesses, and then multiplying the answers. We add 1 because 0s make multiplying boring (and we want 1-10 in any case).
There will still be bias, especially if you've used the scheme before. With the mod5 mod2 scheme the biggest bias is that you only get a 1 if the original guess is congruent to 0 mod 10. A way to avoid that bias, which unfortunately introduces another bias, is to do a two modulo steps. Start with a biggish number, and then do your final one. This is harder to do in your head and makes some final guesses more likely, but only a bit.
So for example, do final guess = (n mod 19) mod 10 + 1. 19 is easyish to calculated because you find the closest multiple of 20, workout that mod 19, and add any leftovers to it. 42 mod 19 = 40 mod 19 + 2 = 2 + 2 = 4
Ahh you’re of course correct, might still be useful if you don’t memorise the mapping.
I should have gone with my gut and generated the first 100 with each scheme to look at what the distribution looks like.
Mod 19 scheme feels like it should be decent but it gives 10 half the probability of any other number. I did find a quick fix that may still be simple enough: take the number mod 19, and add the last digit of the original number. Now take the last digit of the sum, and add 1. So new guess = 1 + (n mod 19 + n mod 10) mod 10. Doing a quick simulation there is no obvious bias.
Concisely: Randomness exists if and only if there is ignorance.
As a DM, if I reach my hand in my bag of unfair chessex dice, make a biased choice of which which biased die I unfairly throw... From my perspective, the odds of a 20 are still 5%, because I don't have good enough memory to know what direction any of those biases go.
If one of my players, who have much less to do than a DM, rolls their same d20 every session, they will eventually pick up on its tendencies and know their die is more likely on average to crit.
If a cheating player understands the velocity of their roll, they can toss in such a way that 20 is much much more likely to appear.
The DM I describe can roll the same die as the player I describe but experience different probabilities because of ignorance. A fair player I describe who rolls their die in the same way as the cheating player I describe is experiencing different probabilities because of ignorance.
Situations we think of as random are just good at quickly spreading ignorance. A tiny change in velocity for the cheating player will spoil his plans, and the dice numbers are spread nearly equally so that this small ignorance about velocity quickly becomes large ignorance about the probability distribution of the result. Knowing half the bits of the seed of a PRNG quickly decays into nearly zero info about it's probability distribution. Knowing the seed of a PRNG precisely and the number of cycles imprecisely quickly becomes worthless, by design.
Dice, PRNGs, other things we think of as random are only different from any other piece of knowledge (future election results, whether the 1000th digit of pi is odd...) in that they are decent at quickly turning what knowledge you have into ignorance.
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.
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.
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.
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.
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).
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.
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.
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.
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.
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
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.
