Initial Setup
EARLY GAME
1) Grow!
How fast you grow is exponential, not linear. In a linear growth mode, you would receive (on the average) the same amount of resources each turn. In Settler's, "investing" production to build more production centers (settlements and cities) leads to an exponential growth rate. It's how compound interest works, and why if you invest a little early on in the game you can get a huge advantage later. Even a small numerical advantage in production in the beginning of the game can result in an inordinately large production compared to other players later in the game. (Note that the rate of exponential growth decreases as the game progresses, as the "best" intersections are settled or converted to cities, leaving only the lower-value intersections remaining for new production centers. Even though the rate of exponential growth decreases, this growth is still exponential and should be taken into account.) You have probably noticed where in a lot of games the leader(s) move out farther and farther ahead, and those behind can't seem to catch up. This is why.
I would argue this is the MOST important concept of the game. It is a major factor (arguably the most important factor) in the initial setup, and also determines what your first few turns look like. Simply put, BUILD PRODUCTION CENTERS in the first few turns, and build them in areas that are relatively high in production value. You do not want to be caught behind another player in the exponential growth race.
In the early game, don't bother with constructing the longest road, building the largest army, exploring unknown hexes in Seefahrers scenarios, etc. Your main goal at the beginning should be to increase production. (Note that if building production centers cannot be done in your turn, it may be advantageous to buy cards, build roads for future use, start exploring, etc., just to keep the robber away from an ever-increasing hand. However, this should be treated as a fallback plan.)
For example, consider the player who wants to go to a single-hex island early in the game, to get the extra victory points. In one Seefahrers scenario it costs three ships to get to a single-hex island, and then you need to build a settlement that only borders on that one hex. That is a total card cost of ten (six for the three ships, and four for the settlement). Let's see, say the hex produces on a ten, that is once every 12 turns. That means you will get back your investment in 120 turns. Not a good idea early in the game. The moral is keep your eye on production the first few turns.
2) Contrary to popular belief, the numbers thrown on the dice do not "even out" over the course of the game (well maybe literally, but not in their effect).
Numbers coming up early in the game are much more important than later in the game, due to the exponential growth rate. That resource you get early on, if invested into more production, will result in even more resources. This means the robber is also more important early in the game. If the robber lands on someone early in the game, its effect can be far worse than later; it takes not only that particular resource, but robs that player of all the future resources it would have led to if invested.
3) "Clumping" of numbers
Numbers on the dice always seem to clump together at times, and never seem to be rolled at other times . A famous example of clumping in real life (and how we perceive it) can be demonstrated by convincing two of your friends to perform a little experiment. Have one toss a coin 100 times and write down the results. Have the other write up a "random" assortment of 100 heads and tails that they came up with in their head. Don't let them tell you which person used which method, instead tell them you will figure it out. Ninety-five percent of the time, the person flipping the coin will generate a series of seven or more heads or tails in a row. You almost never see this in the list the other person makes up, as they invariable think that seven or more in a row will never happen. (This works even better in large groups of people, like beginning statistics classes.)
In terms of what to expect in the game, similar clumping of production numbers will occur. Just like the person making up the heads/tails, this will seem extremely unlikely (or really bad/good luck), but it isn't; what seems to be really strange clumping is in fact quite common. You usually only remember clumping if it is really bad for you (or someone whines a lot about it), but watch your next few games carefully. It will happen in practically every one. If this clumping works against you in the early game, you can really be screwed, because you can fall way behind in the exponential growth race.
You have to assume weird clumping will happen, and plan for it. Consider spreading out your production centers in the early game onto different numbers so this has less of a chance of happening to you. Personally, I don't pay too much attention to this myself as I think other factors are usually more important, but others swear by it. I think it would be more important if you are playing a strategy that emphasizes cities (i.e. the ore-grain strategy), as you will have less production centers (and by extension, be located next to fewer production numbers) to begin with, and therefore are at a greater risk from clumping.
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