There seems to be a paradox surrounding my definition of clarity. In a game of perfect information like Chess, the "strategy tree" is entirely open and non-mysterious. At any stage of the game, you technically have all the information you need in order to calculate the perfect move. Of course, realistically, the strategy tree is so mind-bogglingly huge that there's no way to determine with certainty what the best move actually is. The "paradox" is that this must be viewed as an instance of opacity, and opacity is supposed to be a bad thing.
Although the "paradox" is easiest to see in the context of games of perfect information, the same fundamental issue applies to games that contain elements of chance or hidden-information. In Backgammon, or even Carcassonne, there's an objectivly "best" move on each turn, just as certainly as there is in Chess. It's the move that has the best expected value. You have all of the information you need in order to calculate this, but in practice that calcualtion is too difficult to carry out. Once again, this counts as an instance of opacity.
So is a game supposed to be clear, or opaque? My answer is: both. A game is supposed to have the good kind of clarity and the good kind of opacity. The fact that a game's "strategy tree" is too deep and rich to be fully explored counts as the good kind of opacity.
The bad kind of opacity is the kind that keeps players from focusing on the most interesting aspects of the game. I don't want players to spend much time doing math, counting pieces, or trying to remember how many red tiles have been discarded. I want them to focus on agonizing choices.
In essence, I want it to be very easy for a player to grasp the current game situation and to see what the different options are, but I want it to be agonizingly difficult for a player to decide which of those options will be best in the long run.