I still think this could form the basis for an interesting dueling system, perhaps coupled with rules for War.

Recovered: Non-Transitive Dice Using Cards

Non-transitive dice are a fascinating phenomenon. However, I don’t really want to buy more dice,¹ 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 non-transitive dice. Opposite sides match. (Wikimedia Commons, Public Domain)

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 post was first shared on September 17, 2012.

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1. This is a lie.↩︎

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