I'm not sure, but my gut feeling is that every roll above 3 and maybe even equal to 3 is an immediate checkmate or at the very least a crushing advantage. Like, rolling a 4 on the first move wins the game, rolling a 3 wins the queen, ... that much tempo is devastating.
However, it does remind me of a rather funny chess variant. In that variant, each player has three D6 and each face value corresponds to a piece - 1 for a pawn, 2 for a knight, and so on. Each turn, you roll your 3 dice and you can make one move with either of the pieces you rolled.
This ends up being pretty instructive, because you really have to activate all pieces because you might not roll your most active pieces on a turn.