The recreational dice scene has lots of these "not really useful in real world but we still cracked the math" kind of solutions. https://www.youtube.com/watch?v=5q32heFz1bs (Go First Dice - Numberphile)

I think these sorts of irregular shapes are very sensitive to how they are rolled. Like, the distribution when they are dropped on a surface from directly above may be very different than being rolled laterally.