"There are at least two kinds of games. One could be called finite, the other infinite. A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play." —James P. Carse
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Tabletop games of the finite variety

In this realm I generally like beautiful maps, a problem space that allows multiple approaches, i.e. replayability, tight economies, technology trees, and often but not always, a theme tied to a mythologized past or to a distant future. Unique player powers and victory conditions are nice. I try to approach other domains with a sense of continual play, but my mood and success are variable.