Catan very much requires "playing to luck", and I wonder how that fits into the rest of the analogy. Sure, there's an optimal strategy, but because of the resource discard rules on rolled 7s (the most common roll, of course), you very often have to make the purchase that you can. It's either that or not make a purchase at all and lose out to the discard.

"Playing to luck" is different than "playing to the board" in my book because it requires making probabilistic decisions that have no place in, say, Chess.