When I can't find an opponent, I play solitaire Carcassonne, a version of my own invention. Remove everything but the basic set -- ditch the river, inns & cathedrals, dragon & princess, laurel & hardy, etc. Forget the meeples; you won't need 'em. Start with the starting piece and play tiles one at time. Your goal is to get a complete city, surrounded by a ring-road around the city, surrounded by an unbroken chain of completed cities around the ring-road, surrounded by another ring-road around the chain of cities. Oh yes, it can be done; I did it the first time I tried, although I have never repeated the accomplishment. Sometimes I'm just a tile or two short.
Scoring makes it more interesting. Count your innermost city as usual. If it is surrounded by a ring-road, add in any other complete features (monasteries and cities only), double the total, and add a point for every tile in the ring-road. If the road is surrounded, add in any other features, double the running total, and score the ring-cities as normal. If the ring-cities are surrounded, repeat the process. I've scored over 200 points.
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