I was trying to think of a way to put a strategy into a game with dice. Yet nothing in my mind. I'm well aware of the issue. It's just that I can't think of a way to do it. But if I find a way, I will try to release it in the next version.
I was thinking about this while playing your game, but what if the dice would decide how far the snake goes in a direction? so the player can steer the snake, but not control how far it goes. It might add that little layer of strategy you were looking for and would prevent the typical snake experts from winning the game by covering the whole board lol. Just a thought tho.