Brilliant idea, I think we should play with four dice.
1=Queen move
2=King move
3=Bishop move
4=Knight move
5=Rook move
6=Pawn move
I would roll 1, 1, 3, and 6 and go for 4 move mate :)
Theorhetically, isn't there a 1/9th (4/36) chance to roll a mate in one on the first move with 4 dice?
Playing chess with dice is a great leveller. It was originally a dice game (6 different pieces) similar to backgammon with a blend of skill and luck. My favourite is with 3 dice. Throwing three of the same can be devastating.