In the course of discussing Tzaar a couple of weeks ago I parenthetically mentioned that there are games which have no random element but which I do not necessarily consider "pure strategy games" because of the fact that they are designed for more than two players. Ordinarily I am not a big fan of this type of game, but not because it fails to be purely strategic, but rather because of two problems that almost always seem to crop up. The first problem is that the games tend to be a bit slow because competitive players will want to examine every possible option. This happens in two-player perfect-information games as well, of course, but since there is only one opponent there is usually not too much down time overall. Multiply the thinking time by three opponents, however, and a person can find himself with rather a lot of time to kill. The thinking required can also be more involved than that in a two-player game, since players have to take into account the goals of more than one opponent and then consider the potential reaction to the potential reaction to their move.
Contrast this to a game that has randomness or hidden goals; in this case players will often settle on a move fairly quickly, even in a complex game, because after a certain point the law of diminishing returns will kick in. If I don't have all the information, I can only make a guess about the best move, and calculating every possible chain of cause and effect might be a waste of time. Really it's more of a psychological issue than a logical one, however; in the case where a situation has uncertainty, we feel that fate is a part of the process and ultimately we submit to her, whereas in the case that all the information is available to us, to make a suboptimal move is our failure, even if discovering the optimal move will take an extraordinary amount of time and effort, even if the time required to discover the optimal move is contrary to the point of the activity, which is not to win but to have an enjoyable social experience.
The second problem with this type of game is that very competitive people can easily get bent out of shape if they feel that one of their opponents made a poor move which upset the balance of power. This can happen in any game, to be sure, but it is less of an issue when there is information hidden from opponents. How can you say I made a bad move unless you know exactly what I have to work with? Regardless, this sort of thing has soured more than one gaming experience for me, and in the end I would rather just avoid particular games than to have to listen to whining.
It happened that this past weekend I played two games that more or less fit the description of "perfect-information games for more than two," namely Recess and Shear Panic. The former has no hidden or random element whatsoever, but Shear Panic does have some dice that come into play in a minor way. I ended up enjoying Recess the more out of the two, despite the fact that it is the game that ought to be more prone to the two issues just mentioned. Why is that?
The reason, I think, has to do with the different kinds of turns that the players have in the different games. In Recess the turns are simple in terms of how each move contributes to your overall progress. You are moving pawns to either achieve a short-term goal (jumping one of your opponents' schoochildren and beating the milk money out of them, tattling on another child, et cetera) or to make quantifiable progress towards a long-term goal (bringing one of your boys and one of your girls together for a smooch). Shear Panic is different in that you are confronted with many different kinds of move, and each can be applied to the situation in different ways. There is an arrangement of sheep, and players have a menu of manipulations that they can apply to the entire flock, which includes both their own pieces and those of the other players. That in itself is more complicated, and what is worse is that players do not always have the guiding light of a short-term goal to direct them. The future is often quite nebulous, and this is when a player will start looking at the other players' tools and goals to see how they might monkey with the state of things. "Is it worthwhile to move my piece to the front of the line if the next guy can change which side of the herd is the front?" The decision-making process in Recess is also easier because there is less ability for other players to disturb your pieces than in Shear Panic, so you're not starting every turn from scratch.
The king of this type of game, as far as I am concerned, is Through the Desert. Here there is no random or hidden element of any kind, players are simply placing two pieces onto the board, and once placed they can never be moved. The pieces form chains which stretch out in various directions to acquire territory and thus points. What makes this more appealing to me? Again, it is because players' moves are simple and incremental and because the state of the board does not change wildly. Players do have to worry about what their opponents are up to, but the game takes away the complication of how they are going to interfere, so the players are left with an experience which you could say is purely about intention and prioritizing. Contrast this to Shear Panic, in which it is the players' intentions which have been simplified and it is instead the various means to the single end which hold all the complexity. I would assert that the simple-ends-complicated-means model can be very enjoyable in solitaire activities such as puzzles or computer games, but when one has the luxury of human opponents with all their personality and psychology and unpredictability, the games which focus on the goals work better than those which focus on process.