Intransitive Dice

If A is better than B, and B is better than C, it logically follows that A is better than C. This is known as transitivity.

However, there are instances where this doesn't hold true. These dice exemplify this phenomenon, but non-transitive cases also arise in elections (hence, the system where the two most-voted candidates proceed to a runoff is mathematically flawed; an eliminated candidate might have directly won against the runoff victor).

These dice do not have the standard one-to-six pip distribution, but rather alternative arrangements.

A: 6 - 3 - 3 - 3 - 3 - 3 

B: 5 - 5 - 5 - 2 - 2 - 2

C: 4 - 4 - 4 - 4 - 4 - 1

The probability of die A winning a duel against die B is higher than that of die B. A duel between die B and C is more likely to favor B. However, when die C faces die A, die C now has a greater chance of winning.

Printing two of each die allows for matchups such as AA versus BB, and so on. Now BB surpasses AA, AA surpasses CC, and CC surpasses BB, where "surpasses" signifies a higher probability of a superior sum of pips. That is, the order reverses! Fascinating!

The pips on these dice are intentionally sized differently to ensure uniform material removal from all sides. Print the dice on a smooth surface to prevent textural inconsistencies between faces.

If you utilize my print profile and possess an AMS, you should load the color for the box into slot one, and the colors for dice A, B, and C into slots two through four respectively. An alternative, single-color print bed is also available for those without an AMS.

In an earlier version, I incorporated multicolored recessed text, which proved aesthetically unappealing. The current iteration features flush text on the multicolored box, while the monochrome version retains recessed lettering.

I eagerly anticipate your photographs and color schemes!