Dominion is definitely NOT a game of luck. I'd wager it's at least 90% strategy. But at the higher levels I'm sure the luck comes out as players get better at finding the best strategies available to them. In Bridge tournaments, pairs have to play the same hand and see who does better at it. Obviously in Dominion tournaments you'd have everyone play the same kingdom sets, but how do you compensate for bad shuffles? If there's a Mountebank/Witch/Treasury or any other awesome opening cost-5 card and no good opening cost-4 cards, any player who starts 5-2 is going to have a substantially better odds of winning already. Likewise if you have a lot of villages and terminal actions, but virtually never get them together, you're also at a substantial disadvantage.
How do Dominion tournaments compensate for this? Is it possible to play Dominion in a form where it's 98+% strategy and <2% luck, or is luck of the draw just an essential part of the game? How often does luck determine the winner of a game of Dominion?