“Fair Spherical Dice”

The concept behind this dice is quite simple; the outside of the dice is spherical (or as much as we can get with an FDM 3D printer), and the inside is cut out with a regular octahedron. The octahedron has 6 vertices which line up with the “faces” of the outer spherical dice. By placing a small weight inside (I used a 7mm ball bearing), when this dice is rolled, the ball bearing will always fall into one of the inner vertices and the opposite outer face will face upwards.

I did a small sample of rolls with this dice (n=50) and got a pretty even distribution of results. I may end up doing a larger experiment just to see how “fair” this dice actually is.

There are two print profiles:

1. Multi-Colour Dice - This profile is for AMS users and has coloured spots a split parts of the model, so any two colours can be used. This is the version I used for my fairness testing as it has the most even outer surface (prints at 0.12 high quality with brims to ensure good bed adhesion)
2. Single Colour Dice - This profile is for all users and instead of have coloured spots, has small indents to represent the dots on each side of the dice. This version is likely far less fair and will be biased by the outer surface. I am considering editing this version slightly to only have minor indents, but this is still a work in progress

Why a round dice:

• It's cool, it's different, and not many people have used a dice like this before!
• It's an interesting look at physics/geometry and ways it can be used in physical builds
• It's still pretty “fair” compared to a regular dice!

The build is very simple, add a small amount of super glue onto the pins and glue them into the cylindrical slots on one half of the dice. Add the ball bearing or alterative weight object into the centre cut out. Apply some more glue to the other end of the pins and also a bit of glue on to the surface which will be joined. Push the other half of the dice on, being careful to line the numbers up correctly and using the pins for alignment. Allow the glue to dry and enjoy your cool new dice!

If anyone has any other suggestions, variations or tips then just drop me a message in the comments and I will get back to you!