I have always wondered what makes a die fair, and lately wondered whether a 3D printer can build a fair die —
Die on the left is 3D printed and the die on the right is comparison die from a board game set. The 3D-printed die was designed so that the dots take up equal volume on each face. As you can see, each dot on the 3-face are deeper than each dot on the 6-face. It doesn’t look like the comparison die has this feature, each dot on it look around the same size as any dot on any of its faces.
With the help of a “volunteer”, we went through the tedious task of rolling each die a couple of hundred times to test its fairness. Here are the results in number of times a number between 1 to 6 was rolled (percentage):
3D-Printed Die
1: 49 (20%)
2: 42 (17%)
3: 33 (13%)
4: 43 (17%)
5: 44 (18%)
6: 36 (15%)
Comparison Die
1: 38 (16%)
2: 38 (16%)
3: 48 (20%)
4: 48 (20%)
5: 31 (13%)
6: 36 (15%)
Interestingly enough, with over 200 rolls, neither die seems very fair, but the range for the chance of rolling any number between 1 to 6 is between 13% and 20% for both dice. Standard deviations for the 3D-printed and comparison dice are 2.4% and 2.8%, respectively.
The sample sizes may be too small, but this quick-and-dirty study shows that a 3D-printed die, with engineered dots 🙂 can prove just as fair as a die that wasn’t made through 3D printing. It also means that, with a bit of back-and-forth design, print, and testing, you can make loaded dice very easily. Imagine the possibilities!
SansCanvas blog 