I've been thinking recently about the dangers of symmetry in a game. That is, if all players start with equivalent positions, and there is no mechanism for breaking that starting symmetry, you often wind up with a degenerate game.
By a "degenerate game," I mean one that breaks down for one of several reasons. One reason might be that the game is solvable, in the fashion of Tic Tac Toe and that, once solved, the interest in playing it evaporates. Hex is an example of a much more complicated game that nonetheless is solvable (or at least, has been solved for up to 9x9 grids).
Another form of degeneracy is a game in which it becomes virtually impossible for one player to win or lose, except by making an error; optimal play retains the balance eternally.
And another form of degeneracy is a game in which strategy is fairly obvious, and optimal play by both sides simply produces a victory for one side of the other on the basis of any minor asymmetry that may have existed despite its apparent symmetry, such as a first-mover advantage.
Medici is interesting both because of the simplicity of its design and because it demonstrates symmetry-breaking very clearly.
Each round, a pile of commodity tiles is mixed; it contains six tiles per player. A tile contains a depiction of one of five different commodities (cloth, fur, grain, dye, spice), and a numerical value from 0 to 5, the "value" of this tile.
Each player has a "ship" with five compartments, and in a round may purchase only five tiles. The first player draws one tile, and then optionally draws up to two more; the three tiles are auctioned together as a single lot, in a once-around the table, single-bid auction. Winner puts the tile(s) on his ship; if no one bids, they are discarded. The next player then draws tiles, and so on, until the pile is exhausted or all players' ships are full.
At this point, the player whose ship carries the highest value of commodities scores 30 points, the player with the second highest value scores 20, and so on, as per a table in the rules. "Score" is also money, and as is typical in Knizia's auction games, one easy way to lose is to consistently overbid at auctions. After players "ship commodities," two more rounds are played.
Now, if that's all there were to the game, it would be -- not perfectly, but very -- symmetrical. Any given lot of commodities at auction would have, in essence, the same value to all players, with minor variations for how many spaces you have left in your ship. The player with the finest ability to divine the end-value of lots and obtain them without over-paying would be the winner. It would also be a pretty dull game.
Knizia breaks this symmetry by awarding additional points for the leading purchasers of each commodity each round. The "board" of the game is essentially a set of five tracks, one for each commodity; each player has a token on each track. At the end of each round, players advance their token on a commodity's track one space for each of that type of commodity they bought. The player who has, over the duration of the game, purchased the most of a particular commodity earns 10 points, and the second most, 5 points -- these are scored for each of the 5 different commodities. In addition, there's an additional award of 20, 10, or 5, for reaching very high numbers on the tracks.
In other words, players have a strong incentive to specialize in different commodities -- and this means that if, say, I am specializing in spice, a lot containing spice is far more valuable to me than one that does not. The question of what to bid on, and how much, suddenly becomes far more complicated than it would be without the commodity tracks; I have to balance not only the end-of-round value of stuff in my ship, but also where I and others stand on the different commodity tracks and how likely purchasing this particular lot is to boost my earnings from the commodities involved.
The commodity tracks break the symmetry of the game -- which is utterly essential to increasing its strategic complexity.
There's always a temptation, when designing a game, to assume a symmetrical start; symmetry is inherently fair. Everyone starts with the same stuff, so they're on a level playing field. But symmetry is also a trap; it leads to degenerate play. Breaking symmetry quickly is essential to making the game strategically interesting.
Degeneracy
I don't know whether you've ever played Kingmaker, but that can degenerate a bit too. Players are randomly dealt starting "factions" of noblemen squabbling for power in the Wars of the Roses. The objective is to seize one of the leading contestants to the throne of England (from either the house of York or Lancaster), crown them, and slay all of their competitors (including younger brothers and children of the same house). The trouble is, the stakes for combat are quite high: every time you go into a fight you don't know which nobles are coming out alive. If your army is based around one very powerful landed duke with a few minor hangers-on, a single fight could spell disaster.
I've seen "turtling" emerge as a degenerate strategy: you sit in your castle, biding your time while the rest of England has it out and the competitors to the throne get slain one by one. As nobles die, they are shuffled back into the deck. At the end of every player's turn, they draw a card. So after a few hours of play, anyone who hasn't taken any casualties the whole game will have a substantially greater force than anyone who has... perhaps greater than all other players combined. And once the deck runs out, no one is going to get any reinforcements to come after you.
The only way to deal with this strategy is to nip it in the bud: aggressively go after any players who are on the defensive. There are (limited) gains to be made, in terms of ransoming back captured nobles to a player that is over-averse to casualties and capturing castles... but again the risks of going after a well-fortified player tend to outweigh the rewards. So you make alliances. But then again, the only thing more risky than going into battle is going into battle with allies you don't trust (and it's a zero-sum game, so you never do).
The game deals with it by a high degree of randomness, which tends to disrupt short-term plans that require the co-ordination of large numbers of troops. But again, this is more likely to mess up an assault on a fortress than its defence. The randomness is enough to minimise the game's degeneracy, but over the long term not to abolish it. Turtles can still play the averages.
I find the best way to play these games is with a bit of an ethic. Everyone sitting down to play tacitly agrees to CONTEST the throne, or at least their own corner of power. When grand alliances start forming, people take sides (though according to Machiavelli, that's the wisest strategic/diplomatic plan anyway). It doesn't always work, but it generally keeps the game playable.
I don't play tic-tac-toe any more, though.
Kingmaker
Yep, Kingmaker often has an end=game in which everyone sits around with large armies waiting for one of their opponents to get plagued at random, and therefore vulnerable to an attack. The end-game does suck. But it has such color that it's still fun. It could certainly be fruitfully redesigned, of course.
On the other hand, multiplayer boardgames with such long playing times are not hugely popular in the market today.