Posted by doener 3 days ago
It's correct that a biased die will fall without bias. But when it hits the surface and starts tumbling, it tends to rotate around the center of gravity, which will be closer to the heavy side, and the die wants to end up in the orientation with the "lowest gravitational potential energy." If that term isn't part of your lexicon, then think of a Weebil toy.
A short video about what happened:
The giveaway is the handling of uncertainty. That's too many decimal places for some of these measurements: 10um (0.01mm) is not reliably measurable by a cheapo caliper, and even trying to do it with a good caliper or micrometer, you'll find that everyday objects simply cannot be reliably straightforwardly measured with that level of precision. (You need cleaning procedures, standardized handling, standardized sampling, etc.) And quoting "4.1g (5.1% too heavy)" versus "4.0g (2.6% too heavy)" is just absurd: that last digit really doesn't mean much. So don't treat it like it does.
For example, on my random first d6 at hand, I get 4.47g from my nice scale and somewhere between 14.82 and 14.85 mm on the first face dimension, depending on how I measure, from my Mitutoyo caliper. I have a micrometer in the shop, but you can see that it'd be pointless to go get it. The next two faces are (14.79 to 14.84) and (14.76 to 14.87), so it's consistently like this.
Likewise, χ² to five decimal places isn't terribly useful... especially since you haven't really described the test you're running....
In general there's a lot of "look at me make measurements" here that might be impressive. There is very little "what is the true value of this measurement, and how well can we assert that", and simply not enough "is this the right thing to be measuring, and how much does that factor matter". That last one is critical: the actual weight of a die is, I think, not important at all. It's weight distribution that matters, so who cares about 0.1g of difference. Unless you're making a batch uniformity claim? But really this evidence just says more about your measuring equipment. And it's well known that different color resins, especially black, white, and red, are pretty differently loaded with pigments, so they have different properties. You can't just expect them to be the same, but the author seems surprised that they aren't.
And then we get to "These dice are safe to use" without any real description of the criteria or threshold. I say "this report is not safe to use (for serious purposes)"!
It's cute, it's a fun little minute to read on the internet this morning. But it's silly, and if my students back in the day or coworkers today sent it to me, they'd be getting red ink and remedial lectures in measurement uncertainty.
https://www.gamescience.com/about-1
(Note: the sprue left by his sharp-edged process has since been proven to result in more bias than the tumbling undergone by the round-edged process.)
> The reason casino dice have such sharp edges is to get the to stop rolling faster with fewer tumbling. The more a die tumbles the more likely it will present any issues with it.
If I understand it correctly, the justification is this: if a die is biased (usually a heavier face), this bias will manifest with a higher chance the longer the die rolls. But if it stops abruptly, for whatever reason (bumping against the edge of the table, other dice, or having a shape that prevents longer roll time, like the casino dice) this bias will be less likely to manifest. Did I get this explanation right?