|Example of non-transitive dice (opposite sides are same) (Image Source: Wikimedia Commons).|
By far the simplest thing I've found, is to make each "die" from a stack of playing cards. This has several advantages:
- If all piles are the same size, then they will appear identical when face-down. This means that each pile can be chosen with incomplete knowledge or assigned at random.
- As cards are played, they may be discarded by some rule. Thus, while the stacks may initially be non-transitive, their relation can change over the course of a game.
- Playing cards are readily available, and can be used to emulate any set of dice that doesn't need numbers higher than 13.
I don't personally have a use for them yet, but if you come up with one I'd love to know.
* = This is a lie.