- The first story is player's story. In what environment is he (or she) playing? What were the events of his day? How did the game get chosen and who are is opponents? How much time does he have to play and what comes afterwards? Is playing this game going to enhance or detract from his life?
- The second story is the game experience story. Who is the better player? How does the game go? Who makes the better plays? Who messes up? Who will win?
- The third story is the thematic story. What story does the game tell? If the players all start out as goat herders whose job is to get the goats to the other side of the hill, what happens with those goats by the time the game ends?
A weakly themed game such as Chess can have some thematic story: the dashing knight swoops in for a rescue, the bishop defends the queen, the pawn sacrifices for the king. Weakly themed abstracts tend to favor more the game experience story, however. In most chess games, what is remembered is the dramatic tactical move, the sweating brow of the defender, or the inevitable resignation of a trounced opponent.
Go is a funny case of something that should be purely abstract game, and yet a thematic story begins to take hold as the pieces form into shapes and positions on the board.
For board games where the thematic story is more pronounced, the game experience story tends to fade a little. One of the things that makes a thematic story interesting is its plot movement. In Settlers of Catan, the land is getting settled, the roads are being built, and the robber moves around the island. Eventually someone reveals an infrastructure greater than everyone else's and the game is over.
The little bits and pieces provided for the game - the wooden markers, the cards, and so on - are supposed to represent pages of story-telling. How well they do this determines whether we feel the game has a "tacked on theme".
Many war games are particularly good at both types of story telling. That is because the thematic stories of war games follow the same basic formula over and over. Yes, there is a difference between some battle that took place in some year on August 24th at 6:00 pm and some other battle that took place on August 25th at 9:00 am ten years later. But really, either of those stories have a lot more in common than they do with a game of Power Grid.
An aside: It may be that "analysis paralysis" is nothing more than the misapplication of promotion of the game experience story over the thematic story. Players who want the game to "move along" are more interested in seeing the thematic story unfold and less in seeing a gamer master himself to make a better move. Is this just a clash of story interests?
Another aside: This article talks about how the pieces of the games are "metaphors" that enhance or detract from the thematic story structure. It is a good read to help you choose the right elements if you want to consider the thematic story.
Both thematic and game experience stories occur in the context of the players' stories. That is why there are various ideas of what it means to "win" at games. Does winning mean "achieving the highest score" or does winning mean "everyone had fun"? The answer to that question is "both", of course. Winning means a satisfactory ending to all stories in the game.