Another thing I would point out is that luck dependence and strategy aren't entirely separate aspects of the game. At times, the decision of whether or not (or to what extent) to make your success dependent on luck is itself a strategic question. A very clear example of this is laid out in the
strategy article for Treasure Map:
Because you can’t open with a pair of Treasure Maps, at a minimum, it will take at least three turns to get 2 Maps, another 2 to hit a reshuffle, and at that point you have to rely on luck . . . Your odds of hitting before the third reshuffle without help are a mere 29 percent . . . Now, 29% is pretty bad in a 2-player game. But Treasure Map is one of those cards that subtly gets better with more players: you don’t want to be winning just 29% in a two-player game, but 29% looks pretty darn good when you’re sitting in fourth position in a 4-player game against three people who are all better than you.
Now, Treasure Map is the most blatant example where a player has a choice whether or not to make luck a bigger element of the game, but there are other, subtler ways it can happen. On the first discard with Storeroom (assuming you are playing it terminally), the question of whether or not to discard Silvers depends in part on the probability that they will be replaced by a Gold/Platinum (i.e. how good of a bet it is), but also on all of the surrounding circumstances: Will hitting $8 mean you win the game? Will failing to hit it mean you lose?