Sunday, March 04, 2007

Data and Observations from Games 1-3: Development Cards Are Nice.

Game #1
In Thursday night’s game of The Settlers of Catan, played with Cinderella, FD&C Yellow Dye #4, and Eto Camoe, I recorded the resources produced by the board, as well as the trades made with the bank, discarded resources from 7 being rolled, cards taken from the bank on “Year of Plenty” cards, and the cards used in concert with Discovery counters obtained from the jungle.* The resources produced were 48 wood, 14 brick, 53 wheat, 47 sheep, 31 ore, and 5 discovery counters. Only once did a player (me) have to discard resources on a seven; I threw away 3 wood and a sheep. The “Year of Plenty” was used to produce two ore, which were used on that turn to construct a city—a typical use of a YoP. The discovery counters were used alone once, then two were used with a wheat once.

Without a port, trading with the bank requires trading four resources of one type for one of another. This steep cost means that many players are unable or unwilling to make such a trade. However, three times, wood was traded for brick, and once each was wood traded for sheep, wheat for brick, and wheat for sheep. The four “generic” ports allow 3:1 trading, and it was used once to trade brick for ore. (Notably, this came immediately after Cinderella used a “Monopoly” card to take everyone’s brick. Otherwise, giving up three bricks, even to get a valuable ore, would not have made sense.) Resource-specific ports played a very large role in the game; unsurprising in a game with so little brick and ore. Yellow Dye #4 started play with the “Sheep-O-Matic” strategy; he had settlements next to two great pastures: 6 and 8. Obviously, having the sheep port helped YD4 greatly. Trading two sheep for another resource happened often: four times each for brick and ore, twice for wheat, and once for wood. Cinderella soon built the wheat port, which she used thrice for Brick, and once each for wood, ore, and sheep. I built the ore port, but never used it. YD4 also built the wood port, and used it to get ore three times. In total, 22 wood, 3 brick, 20 wheat, 22 sheep, and no ore were traded to the bank for 2 wood, 11 brick, 2 wheat, 3 sheep, and 9 ore.

When combined with the previous instances, this sums to 25 wood, 3 brick, 21 wheat, 23 sheep, and 0 ore were sent to the bank and 2 wood, 11 brick, 2 grain, 3 sheep, and 11 ore were collected from the bank through the decisions of the players. Knowing how players chose to give and take cards from the bank shows the difference between optimal and actual resource production. Obviously, in a game like this, the players believed that wood was produced far too much when compared with its perfect complement, brick. (Not a surprise.) This lack of road-building material drove up the production of cities and development cards through a substitution effect. Since players couldn’t build as many roads, they built other things. By the end of the game, an unusually high 14 development cards were bought, Eto Camoe and YD4 had built all four of their allowed cities (and one more settlement each), and I had built three cities. Cinderella, who had taken brick with a monopoly card, had no ore production, so she used her wheat port primarily to buttress road and settlement building, and finished with only one city, but used all five of her settlements.** Since her strategy ran contrary to the city-building of the rest of us, it was not difficult for her to expand over much of one side of the board and gain the Longest Road.

In this game, ore was the most valuable resource, used for the cities and development cards that often prove useful. Only slightly less valuable was brick, the perfect compliment to the plentiful wood. Trading to get brick is also easier to immediately use than ore, in many cases; if a player would like to build a city, it takes three ore; to build a road, only one brick and one of the plentiful wood are needed. Since wheat and sheep were also plentiful, the same circumstances apply to settlement-building. This made bricks valuable in the early game, when building only one road was often enough to get to a new settlement site. Later, though, when the best sites were taken and Cinderella had Monopolized brick, the other players focused on cities.

The other resources were far less valuable, but wheat was still more valuable than sheep and wood, likely because of its many possible uses; everything but roads requires wheat. Sheep were actually slightly more valuable than wood in this game, but it took wood being produced at about three and a half times the rate of brick for this to happen. Although wood is usually more common than brick (since there are three hills and four forests in a 4-player game), it is usually less than even the 33% difference that would be randomly predicted, because players will recognize the relative scarcity of brick while placing their initial settlements.

I managed to eke out a victory in the game—10 points to the 9 of every other player, on 3 cities, Largest Army (five soldiers [one unplayed]), and two victory point cards. Eto Camoe and YD4 had 4 cities and a settlement, and Cinderella had a city, five settlements, and Longest Road. Close game, fun game. I always enjoy playing with people that know what they’re doing. This game also highlighted the importance of buying development cards; the eight I purchased were vital. Cinderella’s “Monopoly” kept Eto Camoe from winning on his next turn at that point of the game. Moral of the story: development cards are awesome. When you’ve got four points, start considering the purchase of development cards. When you’ve got five points, start buying if you haven’t yet. When you’ve got six, development cards need to be your top priority.***

*We played a variant that involved a “jungle” tile, rather than a desert. The jungle doesn’t produce resource cards; when the number on its chit is rolled, it produces a counter that can be used as a wild card for wheat, sheep, or ore when purchasing a development card. They may not be traded or used to purchase any other item.

**Each player has only four cities, five settlements, and 15 roads. Using all of the roads is rare, but it is relatively common for a player to have all of their city or settlement pieces in play. When a player has built all of their cities, they may not upgrade another settlement; when they have built five settlements, they must upgrade one to a city in order to once again be able to place a settlement.

***Unless you’re playing the road-building strategy. Then you’ve got to start thinking about cities once you’ve got three settlements, and making it a priority when you’ve got four settlements, because once you’ve got five, you’re a bit stuck. The way to win here is five settlements, Longest Road, a city, and a victory point. (Or a second city instead of one of those settlements.) The problem with this strategy is that the points are obvious to every other player, which attracts attention. If you play this way, you need to be an expert politically, able to convince other players that the development cards face-down in front of card-building players like The Franchise are victory points.

Game #2
Friday, Cinderella and I played with her younger siblings. This game had far more statistical balance: 31 Wood, 35 Brick, 50 Wheat, 36 Sheep, and 35 Ore. Wheat was something of an outlier, but due to its value, its frequency was welcome. In a game like this, with relatively equal production amounts, the trades made with the bank were more due to short-term trends than the overall production during the game, in serious contrast to Thursday’s game. This game was standard Settlers, without any variant rules. Most of the resources that players elected to give or take from the bank were in port trades, but I once gave 4 wood to the bank on a 7,* and gained 2 wheat from a “Year of Plenty” card.

CindyBro chose to start the game with the wheat port, so the port trades in the early game were mostly conducted by him, trading to get brick and wood once each, and ore four times. Cinderella built the brick port, and traded for brick thrice, wheat twice, and ore once. CindySis built the sheep port, but since she had low sheep production, and built the port when I was shifting my focus to development cards, so demand for sheep had increased. As such, she used the sheep port once each to get wheat and brick. Strangely, she used the ore port more frequently, twice for wheat, and also for brick and wood. Cinderella once used a generic port to trade sheep for wheat. 4:1 trades, which were not present on Thursday, were relatively common, as players traded sheep for wood, wood for wheat, and sheep for wheat.

In sum 4 wood (8 including discards), 12 brick, 12 wheat, 15 sheep, and 8 ore were exchanged for 6 wood, 3 brick, 8 wheat (10 including “Year of Plenty”), no sheep, and 5 ore. Clearly, sheep were the least valuable resource; no player needed to trade for sheep at any point. Despite the outsized wheat production in the game, it still seems to have been slightly more valuable than ore. Unsurprisingly, in a game that had roughly equal production of wood and brick, the two were roughly equal in value; with the slightly rarer wood having a slightly higher value over the course of the game.

CindyBro and CindySis played balanced strategies; she had 3 cities and 2 settlements, he had 2 of each. Cinderella played a road-building strategy, with a city, 4 settlements, and Longest Road. If I had not won on my turn, she would have had enough to build a city on her turn and win. At the start of my final turn, I had three cities, a settlement, and Largest Army. I had bought six development cards (four soldiers, [one unplayed] a “Year of Plenty,” and an unplayed “Road Building”), and each of the other players had one soldier.

Conclusions: once again, it was clear to me that whenever possible, one should start buying development cards when at about 5 VPs. This game strongly suggests wheat is the most valuable resource; even when it was considerably more common than other resources, it was still in high demand by most players, as evidenced by it being the most common objective of elective bank transactions. Wood, ore, and brick were of similar values, with only very slight differences in value, but seem to be valued in that order, likely due to wood’s slight scarcity. Relatively new players also seem to have a greater predilection for road-building, which likely increased the value of wood and brick to Brother and Sister, who were each playing in their third game.

*On my final turn, I had a wood, 2 brick, 2 wheat, 2 sheep, and 3 ore when I rolled a 7. Since I could win by either building a settlement or a city, and could do either one, I am omitting my choice from the data. Either way, a brick and a sheep would have been discarded, but the other three cards would depend on what I would use to win. Either way, I would definitely keep a wheat (probably both).

Game #3
We had another game Saturday afternoon. Same cast as the last one, except with Cinderella’s Dad as well. Only his second game, but the guy has a mind like a steel trap, so I was not surprised that he became the strongest opponent. I ended up having to throw him under the bus to ensure my win, encouraging CindyBro to get Longest Road. (Sorry about that one, CindyDad.) Playing with 5-6 players requires a larger island, so there are two more of each productive land type, and another desert. Or jungle, in this case, as I love that variant, since it means that more development cards are in play, which makes the game more complex. Always a good thing, I think. (It also strengthens my “card builder” strategy, so I’m always in support of it…) There are also more ports on a 5-6 player map; in addition to the five resource-specific and four generic ports of the standard game, there’s a second sheep port and a fifth generic port. Large games also allow players a “special build phase” between players as well, when they can build if they have the exact resources needed, but they may not trade with other players or the bank. Largely, this rule is to help players from having to discard too frequently when sevens are rolled, but it also introduces some odd side effects.*

Unlike the last game, this match saw a return of uneven production, with 51 wood, 36 brick, 56 wheat, 71 sheep, 23 ore, and 19 discovery counters. Thus, it is no surprise that ore was the most sought-after resource in the game, as players needed it badly to produce development cards and cities. With a larger map and more players, trading with the bank was also rarer, as people were more likely to get what they needed from one another.

Trades with the bank were mainly to obtain ore. Cindy had sheep ports, so she traded in sheep often; six times for ore, thrice each for brick and wood, and twice for wheat. CindyDad’s wheat port was used once, for ore. He also made 4:1 trades with sheep and wood to get ore. In sum, 4 wood, no brick, 2 wheat, 32 sheep, and no ore were traded for 3 wood, 3 brick, 2 wheat, no sheep, and 9 ore. On sevens, 6 wood, a wheat, and 3 sheep were discarded, and CindyBro once used a “Year of Plenty” to get wheat and wood. In total, 10 wood, no brick, 3 wheat, 35 sheep, and no ore were voluntarily given to the bank, and players elected to collect 4 wood, 3 brick, 3 wheat, no sheep, and 9 ore.

CindyBro and I were the ones built by the jungle, so we frequently used discovery counters to buy more development cards. When development cards were purchased with a mix of counters and cards, four times it was a wheat and 2 counters, and once each it was a wheat, a sheep, and a counter; a sheep, an ore, and a counter; and a sheep and 2 counters. In mixed sets, counters were used for 2 wheat, 4 sheep, and 6 ore. I’m still not sure how to account for this data in relation to the resources given/chosen model, but it’s definitely important, especially in further highlighting the value of ore during this game. The mild surprise here is that sheep were not the least-substituted of the resources, but this was largely due to my unusually high wheat production during the endgame, when I was buying a development card approximately once per turn, (I had a city on one jungle and two settlements on the other, so I would get two counters on such rolls, and could spend them very rapidly) and CindyBro’s predilection for only getting development cards once he had three counters.

When ore is produced at such a low rate by the board, it is unsurprising players used most of their bank exchanges to augment their ore supplies. Having jungles in such circumstances is highly useful for producing development cards, which saves the valuable ore for use in city-building. Having jungles makes a “card building” strategy very effective, even when wheat or ore are relatively rare.

On the opening of my last turn, I had 2 cities, 2 settlements, Largest Army (6 soldiers), and a Victory Point card. CindyDad had a city and five settlements; Cindy had 2 cities, 3 settlements, and a VP card; CindyBro had a city, 3 settlements, and Longest Road (9 segments); and CindySis had 2 cities and 2 settlements.

When I placed settlements for this game, I had no access to brick or wood, (I bordered two fields, a pasture, two mountains, and a jungle) but strangely, it was not especially difficult to expand to two additional sites. The ease with which I did so was largely because of my access to wheat and ore—wheat due to its value to all strategies, and ore because of how rare it was in this game. As a result, it was quite easy to get 1:1 trades with other players to collect building materials, and combined with early use of soldiers, which allowed more access to more resources, I was able to keep the robber away from my own productive sites and even, on occasion, steal the resources I needed to expand. I had actually intended to upgrade my first expansion site to a city before worrying about the second, but when I managed to get the wood and brick I needed without having to overpay, I did, which had the added effect of denying other players a solid expansion site.

*Players cannot use a development card purchased during that turn, but they can buy a card during the build phase immediately before that turn, then use the card before rolling. (Of course, using a non-soldier card does not offer a benefit.)



At 8:11 PM, March 04, 2007, Blogger Th. said...


I smell a PhD dissertation coming on....


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