In college, my friends and I would get into board gaming spells that would result in us playing a single game exclusively. I used to hang out at Games of Westwood after school hours and could almost guarantee getting a board game in nearly every other night. One of my favorite board games is called Settlers of Catan. Since Settlers is a quick game (2-3 hours) and the gaming store had an irregular cycle of players, I got the opportunity for many games against repeat and one off players. I must have played it at least 40 or 50 times and developed a small reputation for being a very strong opponent. Before I get into some of my strategies, let’s talk a little bit about the game.
The basic game consists of 19 hexagonal tiles that represent the island of Catan. Each tile, except for the sole desert tile, produces a single type of resource- grain, sheep, clay, ore, and wood. These resources are used to build settlements, roads, cities, and development cards. Each settlement and city is worth points, with bonus points for the longest road, largest army, and certain development cards. The first player to 10 points wins. What makes the game interesting, from a strategic point, are two elements. First the game has a turn-wise random but game-wise static probability distribution to distribute new resources within the game, and secondly the players have the ability to trade resources forming a functional market with specific spot prices.
Each player places their game tokens at the intersection of three hexagonal board pieces. Each board piece has a number that when rolled produces that resource for anyone on the intersection. The possible numbers for each board section range from 2 to 12 (with no 7); this coincides with the sum of two six sided dice. There are four board sections for grain, sheep, and wood and three board sections for clay and ore. The 18 numbered board sections have two numbers from 3 to 11 and only a single 2 or 12. The basic game has a set number for each board section, but most players play with a random drop of tiles and then follow the assigned drop of numbers. This makes sure that you can never have a 6 by and 8 (the two best numbers), and that the 2 and 12 are diametrically opposite of each other. Surrounding the land is the Sea of Catan that contains trade ports that allow players to exchange certain resources for others in more favorable ratios.
What is very interesting about this setup is that you have certain amount of probability that can be determined at the start of each game. The sum of two 6 sided dice has 36 distinct combinations with 7 being the most possible combo (1 in 6 or 6 in 36) and 2 and 12 the least possible at (1 in 36). Since it’s very easy to think in parts of 36, I like to think of each board section in their respective probability. A board section with a 6 has a 5 (in 36) probability of being rolled each turn and a 2 has a 1 (in 36) chance of being rolled. The creators made sure to give this value to everyone as each number is listed with 1 to 5 circles depending upon the probability of being rolled per turn. Most players are savvy enough to realize this and determine their city placement by trying to get sections with the 6 and 8. You’ll notice in the section (since placement proceeds in a circle), each of the four players has a single city on a 6 or an 8 intersection. White probably was the fourth placement and got to place both cities at the same time. This is probably why it has two 6 placements.
While this is an effective strategy, what most players miss is that the clay and ore board sections are rarer than the others. While they may have lower values, their ‘trade value’ is actually much higher than other resources. I like to multiply their value by a 1/3 (+33%) to represent their true trade value. If you look at the blue player’s placement, his two choices have a combined value of 10 and 9. This is lower than other players’ cities on the 6 and 8 board sections which have a combined value of around 11. What isn’t usually calculated is that the blue player has the clay and ore sections and you should internally multiply their value by 1/3. If we do this, the left placement comes out to a trade-weighted value of 11 and the right placement has a trade weighted value of 10.5. This raises his placement value significantly. If you calculate the un-modified values, the red player has a placement value of 22 and all of the others are at 19. Red definitely has the best placement, but no other player has a disadvantage. If you recalculate the trade-weighted value of the placements, Red has placement value of 23.6, Blue is second at 21.5, Orange is at 21.3, and White is far behind at 19.3. Even though white was able to capture two 6’s (the best placement), his trade-weighted placement puts him far behind the others. He probably has the worst chance of winning of all of the players. I would also subjectively raise the value of blue’s ore positions, since the third ore spot is a twelve which no one has. If you want you could instead think of the ore values with a 50% bonus. In this case, red and blue are the clear outliers and placed strongly with placement values of 24 and 22.5 respectively.
… to be continued in Settler’s of Catan Strategies Part 2.