Hm, Aslan this is an interesting topic with interesting posts so far! But maybe we should call it "The interdepence between strategy, dice, deployment and cards" or something like that. So if we talk only about strategy and dice, we have to be aware of the fact that we exclude deployment and cards. So we have to know that "luck" is not equal to "dice" --> I can have bad dice in a triple, but our team gets 3 rainbow sets and the others 3 red sets ...
Strategy itself consists of many subgroups: Map knowledge and understanding, stacking, hiding, when to stop attacks, COMMUNICATION (in team games MOST important) .............
Dice are only dice
- a subgroup of "luck"
Now I want to use some reverse logic concerning team games: When a game has ended, I am always analyzing it afterwards briefly. I guess, at about 80% of my won team games we have won because of better strategy, 20% because of luck (mostly when we were even in strategy). So, to be fair, I take it as given that in case of having lost a game it is the same: 80% lost because of better strategy, 20% because the foes were lucky.
Now that luck is not equal to dice, the influence of dice has to be lower than that of luck, maybe 10%-15% - difficult to say.
All in all I would prefer a good deployment, especially in team games, to good dice. Good deployment (often it is enough if the opponents do NOT have a good deployment), good strategy --> There the enemies would need LOTS of good dice to compensate that (in quads nearly impossible as dice tend to be even there in sum.)
I am no expert in single player games so my theories above are only meant for multiplayer games.