Monday, September 05, 2005

Carcassonne: The Math


No, this is not some bizarre new variant. It is a discussion of one aspect of the tactics of play: the value of a tile. So often I see new players making odd choices. They fail to understand the simple math behind the tile placement. For the sake of clarity, I will be ignoring other aspects of strategy. This discussion is for the basic game only. Many of the expansions significantly affect the evaluation of scoring.

The Basics

There are 72 tiles in the basic set. That means each player in a 2-player game will be placing 35 or 36 tiles over the course of the game. In my experience, final scores tend to be in the 100-150 point range. That's an average of 2.8 to 4.3 points per tile played. Do you need to score this much every time you play a tile? No, but there are considerations to maximize profit.

Roads

Roads would seem to be the least favorable play since each tile is only worth 1 point. Even so, new players love to take otherwise useless* road tiles and add them to one of their roads. This practice is often inferior.

In general, roads should be a secondary consideration. However, since roads appear on many tiles and must be connected as tiles are played, there often exists many 2/3/4+ unoccupied but connected road segments. If your meeple situation warrants AND the road(s) are reasonably situated, it is usually better to take advantage of an already created road than to extend one (1 point vs. 3+ points).

You can also get some sneaky points with roads. Consider the following case. You have a meeple at A on the south side of a 4-way intersection.

......... +-------+
+-------+ |...x...|
|...x...| |xBxxxxx|
|xxxxxxx| |...x...|
|...A...| +-------+
+-------+-------+
|...x...|...x...|
|...xxxx|xxxx...|
|.......|.......|
+-------+-------+

Adding the 4th tile and placing a meeple at B completes the road under A for 4 points and scores an additional 2 points for the new road.

Cloisters

These are perhaps the most misunderstood features for new players. Since they are worth 9 points, there is a huge incentive to play and complete them. However, each tile is still only worth 1 point for that cloister. Adding a tile to a cloister is the same as adding a tile to a road. Unless you need the meeple back, or there is some other reason, do not simply add a 1-point tile to a cloister.

The real value of a cloister is in its initial placement. 4 to 6 points is not uncommon. Also, placing a cloister against an opponent's feature means that your opponent will need to help you if they want to complete their own road/city. Also, 2 cloisters side by side allows for 4 of the tiles to be shared. This is still only 2 points per tile, but better than 1.

Always consider the value of a cloister as "in the bank". As yourself what you add specifically by playing the tile. Do not think of it as getting 9 points only when you complete it.

Cities

Cities are the most complicated of scoring issues. They can be worth 1, 2, or 4 points per tile depending on the size of the city and any shield icons present. Also, cities give points to farmers.

Unless you are trying to score farmer points, avoid making 2-point cities. Also, rather than starting a city for yourself each time, favor extending an existing unoccupied city cap with a non-cap piece.

If you have 2 or more incomplete cities, favor placing new city tiles onto the largest of them. This way you will more likely finish the larger cities, leaving the potentially incomplete smaller ones for the end game scoring.

If you have the option of extending a city or starting a new one by extending an unoccupied city tile, opt for the latter if you can spare the meeple. This is worth 4 points instead of 2.

Fields

Fields are very straight forward, but because their total value is accumulated until the end, they create an ever increasing tension as the game draws to an end. In addition, players incorrectly feel the need to attack opponents who have large fields.

Here's an example. Player A has a farmer (A) in a field with 5 cities (C):

....A....
.........
C-C-C-C-C

This is worth 15 points (new farmer scoring). Player B wants to attack this field. To do so, he must play a tile/farmer, then later play another tile that connects the field. This means he must play 2 tiles AND take the risk that he'll even be ABLE to connect. Why not do this:

....A....
.........
C-C-C-C-C
.........
....B....

It's a single tile, it's no risk, and it still grabs all 15 points.

A related example. This time not all the cities are on the same border of the field:

..C...C..
.........
....A....
.........
C---C---C

Player A still has 15 points. Again Player B could attack this field with the same 2 tiles and risk. Player B could also play the same way as in the previous example:

..C...C..
.........
....A....
.........
C---C---C
.........
....B....

Player B gets 9 points to A's 15. This is particularly good near the end game.

Cities + Fields

If you already have a field that you think you can keep control of, then the creation of cities changes quite a bit. Forming a 2 point city nets you 5 points overall. That's 2.5 points per tile. Using the "double cap" tiles to complete an existing city AND start a new one at the same time can earn you 10 points for 3 tiles.

In Summary

Always ask yourself how many real points you are adding to your score, counting just the tile being played. This will help you evaluate your options when you add in all the other factors that occur in the game. If you find yourself simply adding to a feature you already control, you may want to think again.


* I would assert that almost no tile is useless. If you can't directly help yourself, you can either indirectly prepare for some future opportunity, or attack an opponent by trying to negate/steal/block a feature.

11 Comments:

At 4:24 AM, Blogger Yehuda said...

I wrote something similar about two years ago: http://www.boardgamegeek.com/geekforum.php3?action=viewthread&threadid=5627

 
At 11:09 PM, Blogger Steve Janecek said...

Carcasonne sucks.. does it really deserve this much attention?

I mean really :P

 
At 1:32 AM, Blogger ekted said...

If you have the attitude that it's all the luck of the draw, then the game will give you nothing. I find some incredible depth in the game, especially with the expansions or in The City.

 
At 12:25 PM, Blogger Naturelich said...

Hi Ekted. I enjoyed reading this blog entry. Thanks for pointing these things out.

Despite the math, I sometimes like playing a tile that looks esthetically nice and adds symmetry to the board. No matter if this is most beneficial to another player. Anyone else feel these strange urges sometime? ;)

 
At 7:49 PM, Blogger dave said...

Good tips for beginners here. Maybe meeple management isn't as critical with the new farm scoring rules, but I find it to be a dimension your article overlooks. A couple of examples:

"placing a cloister against an opponent's feature means that your opponent will need to help you if they want to complete their own road/city."

This also gives your opponent more opportunities to place tiles that will make it difficult or impossible for you to get your meeple back.

"If you have the option of extending a city or starting a new one by extending an unoccupied city tile, opt for the latter if you can spare the meeple. This is worth 4 points instead of 2."

On the other hand, the more cities you have open, the harder it will be to compete in the late-game vying for farm control; also note, it will be harder to close them all off before game-end, losing the double scoring (in which case your move is 2 points either way, but what you call the better move costs a meeple investment as well). Also important in making the decision to claim a city is whether an opponent has free meeples, as you will be stealing an opportunity from him.

- d, who prefers the original farm scoring.

 
At 8:20 PM, Blogger ekted said...

Yes, I was only trying to discuss the point values of plays, leaving out all other aspects. This of course is only one factor when making tactical decisions.

 
At 4:10 PM, Anonymous Anonymous said...

Nice article, I was wondering if you'd be interested in allowing us the honour of having a copy of it on Carcassonne Central? I'm sure Carc fans everywhere would love it read it! Of course feel free in any case to sign up as a member and submit a link to your site. You can contact me (Gantry) from the Contact Us page on the main menu. cheers! :)

 
At 5:09 PM, Blogger ekted said...

Thanks! Feel free to re-port it there or to link to it here.

 
At 9:25 PM, Blogger nysphere said...

I have published over 500 math help video clips so far. Please visit Math Video Help

 
At 6:08 PM, Anonymous Anonymous said...

I bought this WONDERFUL game of carcassonne over at Empire Board Games where they have the Best Board Games

 
At 3:12 AM, Blogger rduht said...

This comment has been removed by a blog administrator.

 

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