Roll the Dice!

Dice are one of the most well known components in gaming, whether they are used in board games, role playing games or chance games. Originally used for generating random values and moving game pieces on the board, they are now employed for a much more diverse range of actions.

In Teotihuacan: city of Gods, for instance, dice are never thrown, but used to indicate the power of a worker. Some actions allow to upgrade those workers, giving more potential rewards.

Sagrada is another board game that makes use of dice in a variety of ways: dice are thrown, but then used as stained glass components to create a beautiful window. Players have to think strategically on where to place each dice according to its value and colour in pursuit of maximising their total score.

In other games, like a feast for Odin, dice are not used to move pawns, but to check if an action succeeded, like raiding, pillaging or hunting whale.

A traditional die is a cube, with each of its six faces marked with a different number from one to six. The sum of opposite faces is 7. (1 and 6, 2 and 5, 3 and 4). When rolling a dice, each value should be equally likely.

The most common tactile dice use raised dots (not braille) to allow the player to read the surface with their fingertip. The more prominent the dots are, the easier to read for most people. But this has its drawbacks: by adding a variable amount of material on the different sides of the dice, there is an increased risk of unbalancing the center of gravity of the cube, which will alter the ”each value equally likely” rule.

I had some fun throwing 3 types of tactile dice to check if there was a significant difference in frequency. Bear in mind that this is a ”100 throws by hand”, so nowhere near a scientific study.

The first dice I tested was a plastic dice with raised dots from the braille superstore (http://www.braillebookstore.com/Plastic-Dice.1).
Dice characteristics:

The second one was a wooden dice from the same shop (http://www.braillebookstore.com/Wooden-Dice.1). The dice is made out of carved wood with metal pins for the raised dots.
Dice characteristics:

The last one was 3D printed on my creality 3S1 pro using the model created by Zulloc (https://www.thingiverse.com/thing:1522413). I used PLA and an infill of 20%. I added supports everywhere.
Dice characteristics:

Here are the compared results after 100 throws of each dice

As I expected, there is no perfect distribution between values. I was really surprised to see how 6 got a higher probability than average on the two plastic dice, while i would have expected gravity to ”drag” that face down.

I then decided to investigate the different axes by comparing the grouped results of numbers on opposite faces, i.e., 1 and 6; 2 and 5; 3 and 4.

This was all a fun bit of math, but nowhere near enough throws to give final results.

After having thrown the printed dice, it is obvious that I should try to print a downsized version. I also want to reprint the same size increasing the infill, as currently the dice felt really light in my hand, especially compared wit the smaller other ones I tested.