Try playing existing adversarial games with them. Instead of a single dice, each player gets a set of them and picks one of them before rolling, without showing it.

Risk gets much more fun that way, for example - because suddenly, even the individual battles are about imagining you can read the other players intentions.

Non transitive dice are really fun.

If you want a jumping off point, I wrote some simulations with this set of dice in python. The source [0] is on github.

https://github.com/deltasquared/grime/blob/master/grime.py