Non-transitive Dice with Cards

Non-transitive dice are a fascinating phenomenon. However, I don't really want to buy more dice*, especially dice that look, at a glance, like all my other dice. So I've been trying to think up a way to have non-transitive dice without actually needing new dice.

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.