Let one six-sided die carry the faces {1, 2, 2, 3, 3, 4}; let a second carry the faces {1, 3, 4, 5, 6, 8}.

When rolled together, this pair of dice have the same probability distribution as a normal pair of dice.

This is the only arrangement of digits to do so that doesn't include negative numbers. They're called Sicherman dice after their discoverer.