Thursday, April 13, 2006

Anatomy of a Game: Carcassonne, Part Two: Balance & Tiles

In my first article in this series, I talked about the design of the game Carcassonne, breaking it down by parts and seeing how they all work together. However, Carcassonne is a lot more than than just the basic game. Nine supplements of various sizes have slowly expanded that base game, moving it in various directions (and not always the ones suggested by the original game).

Over the next few articles in this series I'm going to examine those supplements, to show how they've evolved the SdJ winning Carcassonne's gameplay. But first, a brief overview of all the supplements to date.

Each supplement adds new tiles to the game, but also provides some big new ideas:

The River. Adds a new starting setup to the game: a 12-tile river. (Now available as part of the base game.)

Inns & Cathedrals. Adds inns, which made roads worth double or nothing, and cathedrals, which made cities worth triple or nothing. Adds a "big meeple" who is worth double the value of the other meeples in token conflict. (Originally published as "The Expansion".)

Traders & Builders. Adds cities with goods; a player closing a city now collects goods, worth VPs at the end for majority control. Adds pigs, which increase the value of one field. Adds builders, which allow faster building of one city or road.

King & Scout. Gives VPs to players who close the biggest road and city.

The Count of Carcassonne. Adds a new starting setup to the game: a 12-tile city. Adds a Count who can allow players to move meeples to regions just as they close & score.

The Cathars. Adds Cathars besieging cities, who decrease the value of the city to knights, but increase its value to farmers. (An exclusive micro-expansion; I mention it here for completeness, and I'll include it in my various charts, but don't think it has much relevence to the evolution of the game.)

The Princess & The Dragon. Adds a dragon which removes meeples. Adds a fairy which protects from the same & gives points when a location it's at is scored. Adds magic gate tiles which let you place on any open, unoccupied region. Adds princess tiles which remove a meeple from a city.

The River II. Yet another alternative setup for the game: a 12-tile river, this time with a branch. Fixes some of the field size problems of the original river, and also has a link to each of the major supplements to this point.

The Tower. Introduces towers which can be used to capture nearby followers, or which can be "capped" by one of your meeples to protect your own.

In my articles on Carcassonne's expansions I'm going to draw a distinction between two sets of supplements. First is "Classic Carcassonne", which is the original game plus the first two major supplements, Inns & Cathedrals and Traders & Builders. If you bought the gold-box Carcassonne that was sold in stores a couple of years ago, this was it. I also tend to include the mini-expansion, King & Scout, in this category. Second are the "later expansions", which center on the two large supplements, The Princess & The Dragon and The Tower as well as the mini-supplement, The Count of Carcassonne, and the micro-supplement The Cathars. There's a number of huge changes in design between King & Scout and The Count of Carcassonne, as we'll see.

This week I'm going to concentrate on the "good" evolution of Carcassonne: how the classic expansions helped to balance the game and the tile mix (though we'll also get our first hints at how the later expansions begin to turn from early ideals).

Balancing the Game

One of the real problems with the original release of Carcassonne was tile balance.

In general the four different types of terrain could be pretty easily ranked. Roads were the weakest, because they scored just 1 point/tile. Cities came next at 2 points/tile, then cloisters, which were typically worth 4-5 points at placement and could be finished while working on other terrains. Fields, meanwhile, were the best, not because of their straight-up valuation, but because they could become so large that a single field could easily be worth 30-40 points at endgame.

Balance among arbitrary randomizers (e.g., cards or tiles) isn't always desired. However, the less balanced they are, the higher the luck factor. Carcassonne suffered from two issues because of the lack of balance of the early terrains: (1) the arbitrary nature of the game was, as noted, increased, because a player could do considerably better or worse depending on which terrain types he drew; and (2) the strategy of the game degenerated down to a single most successful path, the control of fields.

Classic Carcassonne: Classic Carcassonne, managed to notably improve this gameplay by improving this balance:

The value of roads and cities were improved respectively by the inns and the cathedrals of Inns & Cathedrals. The improvement to roads was the biggest because it upped the maximum value by 2x. Cathedrals, meanwhile, improved maximum value of cities only by 1.5x. Inns and cathedrals could each be used as spoilers, to devalue a road or city late in the game, but this is usually only of value in a city, because roads tend to be much easier to close and harder to block. Because of the blocking possibility the marginal increase of value to cities is even less than the 1.5x implies.

When the next supplement, Traders & Builders, came along roads and cities were further improved thanks to the builder. He allowed you to double build on the appropriate terrain type. I find that his best use is for road construction. Even after the classic supplements, roads are still a little less in value than any of the rest of the terrains. The builders lets you control your luck (for more on which, see my articles, Luck and Luck II). If you're unlucky enough to get a lower-value road tile, here's a way to make it more valuable: you get another turn.

The effect of the supplements on cloisters is a little more subtle. The main issue with cloisters tends to be that it's possible to get your meeples stuck there after your initial 4-6 point windfall for placement. In the original set, where you have 72 tiles and 7 meeples per player, this isn't a big deal. If you get a meeple stuck every ten tiles (or every 2-5 turns, depending on the number of players), that's fine. However with the tiles from the three classic supplements you're up 47 tiles, and just one meeple, so your 7:72 ratio is suddenly 8:117. You now have to hold on to your meeples 40% longer before losing them, and thus the valuation of the cloisters drops.

The fields are actually slightly increased in value through the inclusion of the pig in the Traders & Builders supplement, who makes one field better. It's very similar to the inns & cathedrals from the previous supplements, but not quite as good and not quite as plentiful. The field valuation did also decrease in these early supplements, but it was due to tile distribution, not any specific rule. I'll talk about tiles shortly.

On the whole, looking at the new rules in the classic Carcassonne supplements, roads are notably improved in value, cities are somewhat improved, cloisters are devalued, and fields are slightly improved. Generally, points went up, but everything also moved toward a better balance.

(I haven't discussed big meeples and goods. These and many other expansions had nothing to do with the idea of balance; I'll talk about them more when I discuss issues of competition, cooperation, and complexity, in my next articles.)

Later Expansions: The later Carcassonne supplements seem pretty single-minded in bashing any higher-value terrain types. The Cathars decreases city values and The Princess & The Dragon makes cities chancier by giving Princesses an opportunity to remove meeples from them. In addition both The Princess & The Dragon and The Tower discourage long-term meeple placement on the board, by introducing dragons and towers to take them away. This hurts all meeple placement, but it's farmers that it particularly discourages, because they're the only one who stay on the board the whole game.

It's possible that the later Carcassonne supplements actually continue to move valuation in the right direction. Dragons & towers introduce a player feedback loop, which gives players the explicit opportunity attack any high-scoring terrains which remain too valuable. Meanwhile, the princesses attack only cities, and the value of cloisters continues to decrease thanks to the increased tile count. 7:72 becomes 8:165 with all the supplements in, over double the original ratio. Meanwhile, roads are scarcely touched, since they'll be some of the last terrains hit by dragons and towers.

My feeling is that it's been overdone, but that's partially because I don't like how the competition to cooperation ratio has changed, which again will be discussed more in my next article.

Below is a chart showing all the valuation changes in the later Carcassonnes. For reasons of space I haven't listed the fact that dragons and towers can hit every meeple type; I've just listed their effects on fields, because it's considerably greater than other results, thanks to the long-term commitment. Nonetheless, cloisters and cities can be dangerous thanks to these new predators too.

If you want to play a Carcassonne game with any particular terrain type valued more highly or lowly than normal, this chart should help out. It could make for some interesting variation.

Tile Distribution

The tile distribution of the original Carcassonne game was a bit subpar. Its biggest problems were threefold: (1) fields got too big; (2) it was too easy to block a space by making it impossible to fill; and (3) it was too easy to get into an opponent's large terrain by a diagonal placement of a meeple near the terrain.

Thanks to Caracsssonne's expansions, this distribution has changed a lot.

Classic Carcassonne: The following diagrams show the tile distributions for the original Carcassonne and each of the first two major supplements. In each case you can click on the thumbnail if you'd like to see a larger copy of the picture:

Main GameI&CT&B

(Thanks to Roy Levien [Aldaron] over at BGG who gave me the OK to use his helpful distribution pics in this article.)

Decreasing Field Size. Even just glancing at the tiles it's easy to see that the newer distributions were intended to combat the large field problem. In the original 72 tile set there is just one full-tile city, which is exactly the sort of thing that starts to spread fields out. In the 18 tile set from I&C we have 2 full-tile cities, plus one tile with an entirely internal field. In the 24 tiles from T&B we find another 2 tiles containing only one internal field, plus another 2 tiles with an internal field as well as an external field.

In addition these supplements feature the first tiles which purposefully elongated cities to cut off fields. There's one city "cap" in I&C (#7 in the I&C diagram) which cuts down to the opposite side of the tile and there's three city "corners" in T&B, each of which draw out a corner to cut the field in two (#5, #10, and #16 in the T&B diagram, with oddly enough one per good type, one of many symmetries in tile distribution).

Perhaps a better way of looking at this is mathematical, by counting the number of distinct fields on a tile, ignoring all of those full city tiles. Distinct fields within a tile could be connected up based on how other tiles are laid above them, but clearly the higher the field/tile ratio, the more likelihood that fields will be cut up. The original Carcassonne has a field/tile ratio of 1.75. Inns & Cathedrals has a much higher 2.26 ratio and Traders & Builders edges up even more, with a 2.36. Playing all three sets together pulls the original Carcassonne's average up to 1.94 fields/tile.

(For what it's worth, the 5 new tiles in King & Scout had a field/tile ratio of 2.25, right in line with the new average, plus one more full-city-and-internal-field tile.)

Looking at those numbers there's little doubt that decreasing field sizes was a real goal as additional expansions were released.

Decreasing Blocking. One of the frustrations with the original Carcassonne is getting blocked in such a way that no tile exists that can close your terrain. Fortunately the first few supplements introduced a couple of tiles to fit common situations that the original game didn't. I&C includes two city-road-city-road tiles (#5 & #10 in the above chart for I&C), one city-city-road-field (#8), one city-city-field-road (#11), and one road-field-city-file tile (#9); each of these was a guaranteed block before. T&B supports city-city-road-field (#8 & #16) and city-city-field-road (#10 & #14) even better and also offers the only city-road-field-field tile (#2). (The opposite, road-city-field-field tile was remarkably neglected until King & Scout.)

Blocking is an acceptable and often good strategy in Carcassonne, but ensured blockage, with no chance of a tile draw for release can be very frustrating.

Decreasing Stealing. Finally the classic Carcassonne supplements managed to make it harder to steal someone else's terrain by putting a meeple diagonally adjacent, then building in.

This was never a problem with roads, since there was so many tees. However, with the original Carcassonne it was impossible to keep someone out of your field if they placed diagonally, except by making the space in between impossible to fill (which is actually an OK strategy for fields, since you don't need to close them). For cities, there were two adjacent double-cap tiles in the main set (#14), but that was the only way to keep someone diagonally adjacent out of your city, and here you don't want to block out the space usually.

As already noted the classic supplements introduced four elongated city segments, which could be used to block off diagonal fields. Much more notable were the city dividers, each of which could be used to create multiple adjacent cities. There are 9 in the two classic supplements (I&C #3, #4, and #6; T&B #6, #7, #9, #13, #18, and #23) bringing the ratio from 2/72 to 11/114, tripling the tile percentage from 3% to 9%.

The notable increases both overall and from I&C to T&B suggest that the designer saw the overease of capturing other peoples terrain as a continuing issue.

Later Expansions: I'd originally thought that I didn't need to talk about the newer supplements when looking at tile distribution. After all, the aforementioned problems were largely fixed by the classic Carcassonne sets, and thus the newer ones didn't need to worry much about changing the tile distributions.

I was surprised when I crunched a few numbers to see that the newer supplements in general go backward on all of the issues I mention above (other than blocking). If you add in The Princess & The Dragon and The Tower fields start getting larger again, and it starts to get easier to get into other players terrains once more.

The follow chart shows how field/tile ratio, and the percentage of separator tiles have changed from major release to major release:

F/T Ratio1.752.262.361.802.06
Full Tile %1.4%11.1%8.3%0.0%0.0%
Field Sep. %0.0%5.5%12.5%3.3%5.5%
City Sep. %2.7%16.7%25%6.6%11.1%

The field to tile ratio is acceptable in The Tower but everything else is moving notably back toward the tile distributions of the original game, and the attendant problems.


One of the reasons that I like the classic Carcassonne supplements, meaning Inns & Cathedrals and Traders & Builders, is that they were all about tweaking the base game. The original Carcassonne was clearly a good game, else it wouldn't have won the SdJ, but it had balance problems both in scoring and in tile distribution. These first supplements largely fixed those issues via a number of different and clever mechanisms.

In my next article in this series I'm going to look more at how cooperation, competition, and theme, and start to show how later Carcassonne supplements have dramatically changed the direction of the game.


Anonymous said...

When discussing new tiles, you said: "city-city-road-field (#8)". I think it's #9, right?

Shannon Appelcline said...

I'm actually pretty curious how H&G stacks up too. It was my favorite game too, until The City came out. I'm planning to plot out some of these same numbers for the other games, but that's in part five of the series, which will probably post in May or June(!).

I somewhat agree with your thoughts on the extra tiles making the game too long. I think I may mention that in one of the next couple of parts. I don't think it's over the top with I&C plus T&B, but it's right at my limit.

Doug Orleans said...

You (and Chris Farrell) seem to assume that each expansion requires all the previous expansions. But you could easily just pick one expansion to add to the base game. In theory you could even just choose a few expansions and leave out the basic tiles altogether!

Anonymous said...

Great post. I would love to know what you think about the revisions that were made to the scoring system in the German version of the game. Do you see these as improvements in terms of balance or are they only there to make the scoring easier?

Anonymous said...

I&C is excellent expansion, tweaks rules slightly but adds a lot of fun (+ city splitters). T&B completly ruins value of fields, which are the best element of carcassone.