Maximum attainable points for a single player in a two player game of Carcassonne
Note: This answer below is using 1st Edition scoring rules (Cities only scored once). Although parts of the analysis are valuable to calculating the highest score possible (36 Scoring opportunities, try to score with Meeples that have a high point value per the 36 turns, the highest score of 278 is not correct. I will have to do further analysis to determine if 7 farms can be created scoring the most cities multiple times, will result in a maximal score. (Edit: The maximum theoretical score is 338, as posted in my other 3rd Edition rules analysis)

Hackworth's analysis about optimal play exists is correct, although he is right about the difficulty in evaluating all possible moves, I believe that tengfred is closer in estimation of what we need to determine the maximum score possible. We only need to evaluate ending maps, not all possible moves from the beginning to the end. Once we have found the maximum scoring map, we only need to backtrack to find a legal set of moves that will lead to that end map. That is as tengfred points out, a much smaller problem.

The Rules show 72 tiles, and scoring as follows:


  Road (1 point per tile), Cities (2 points per tile, 2 Points per pennant), Cloister (1 point for each tile, cloister tile and surrounding tiles), Farm (3 points per completed city)


A similar question was asked on The Opinionated Gamer.


  My challenge to you is to see how many points you can score using only the 72 tiles in the base set – following all of the rules as printed in the box — EXCEPT that you can only use one meeple!


Wie Hwa (animation) solved that problem with 277 points.


He didn't always score on odd turns, so his solution isn't the correct answer to this question. But, someone with more desire than me might want to take his end map and modify the order of the turns so that player 1 is always the one to score.

This gets you a grand total of 278 points (the board actually will have an unmatched city tile that cannot score I think, and still place a farmer). It is amazing that Wei Hwa almost achieved this using only a single meeple in single player. Feel free to figure out if his end map is an optimal solution for 2-player. 

The maximum number of scoring opportunities is 36 if you go first since you can only place meeples on your turn. The optimal solution will include:


one farmer, 45 points
15 completed cities, 116 points (10 pennants = 20 pts, 48 city edges = 96)
6 cloisters, 54 points.
The remaining points divided between the most points that can be scored on roads with the remaining 14 moves (1x Quad road = 4 pts,7x Tri Road = 21 points, 32 straight/elbow non terminals, 5x Dead End)