In Settlers of Catan, how do you overcome bad initial settlement placement? In a lot of games of Catan I've played, initial settlement placement seems to really make or break the game for a player. Are there any good strategies for overcoming a weak starting placement?
I think the main thing you need to do is correctly identify your strengths and weaknesses, and don't try to force a strategy you're not set up for. If you don't have abundant brick and wood, don't even bother going for Longest Road.
Even the worst placement will have some resources they are rich in. Try to get a port that capitalizes on your resources, and make the necessary trades with other players to get the resources you're poor in.
If you're rich in...
Brick or Wood -- try for longest road and build plenty of settlements
Grain or Ore -- upgrade your starting settlements to cities and buy development cards
Sheep -- go for Largest Army via development cards, or depending on your next best resource, you'll probably follow one of the other two basic strategies
Of course even with all of this, sometimes the dice just won't drop your way :)
If your initial placement is bad, hopefully you can still build a little.
The first couple road placements are critical. By then you should be able to figure out which commodities are in short supply this game. Either because they haven't been rolled yet, or they're sitting on a 3 and an 11.
Use your first two roads to build for that scare resource, claim it, and then see who will overtrade you for it!
If you find you're often badly placed, initially, it may be that you're either making errors there, or misjudging where other players are going to place their initial settlements. It's easy to pick your optimal placement when in a four player game you place fourth-fifth, and you can usually figure where the fourth player to play will go when you place third-sixth. If you go first you usually grab one of the two best producing junctions, and should aim for brick and wood since if you have those two with your first settlement, if your options are limited when it gets back to you at least you're able to move, and other players are often hungry for brick and wood early in the game, meaning you're the trading king. Going second-seventh is often the toughest slot, since the first player to go typically grabs the best brick and wood combination (assuming there is one), and there often isn't another good brick and wood combo on the table. Then, of course, by the time it gets back to you pickings tend to be slim.
Still and all, given the good advice people have offered, above, you really shouldn't run into setup situations too often at the beginning of the game that seriously handicap you. One of the three main lines of play should be open to you. It's unusual to be stuck with setups where all you get are ore, sheep, and brick; or wheat, sheep, and wood; those triumvirates that leave you unable to move, unable to build, and unable to pick up development cards. Avoid those scenarios if you possibly can, since you're absolutely dependent on the tender mercies of other traders to bail you out and let you progress. Even so, if that's the best situation available to you, you may need to try to build to the nearest 2:1 port of a resource you're rich in, just to get the flexibility that'll get you back in the game.
Diplomacy. During the mid game, constantly point out how badly you are doing, encouraging others to trade with you in preference to other players - even offering you better deals. This can allow you to develop a couple of settlements and get back in the game while the others are playing stop-the-leader.
When there is a valuable resource(the average amount of pips for each resource is 11.6) that has less than 10 pips, and there is no red hex corresponding to that resource, and there is only a 4 pip for that resource(ie there is only a 9,3, and 12 hex for wheat, then try to claim the 9 and block other people from it) and don't trade with people for that resource unless it's 3:1(and usually if you want to trade 3:1 they have a harbor, else usually at least 4:1). So if you don't have that resource as initial placement, you should try to get a port and trade what you have(for example you have 2 cities and they correspond to a 8 and a 9 for sheep, get a sheep port) with the bank.
I made up something I haven't really tested thoroughly, but if you have enough tiles you could build a complete hidden map(tiles upsidedown) underneath your visible map and and have a player pay a wood and ore to make a shovel to dig for new ground beneath the "bad" tile and wait one round with a blank tile.)
It's an addition, you may or may not like, but hey.
(We usually remove the 2's and 12's and you're able to revise one of the numbers drawn so the gamble is more to the strategy than lady fortune smiling upon you.)