Hnnnng...it hurts so much to settle on a resource. Old habits die hard, I guess.
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You and your Mansas..lol...great leader though
It depends on the resource really. First off, as has been noticed there can be benefit in settling on certain resources or tile yields to provide instant bonus to the default yield of the city center tile. I call it "what you see is what you get". Like a plains hill has 2 hammers, so your city tile will have 2H vs. the 1H. In the case of resources you are sacrificing that later resource yield for an earlier boost to commerce, hammers, or food. As I've stated in our other discussion, Civ IV is about more stuff/more soonerer (sic).
Actually improving a single dye tile will likely not come for quite some later in the game, probably closer to 100 turns or so unless it is deemed worthy to tech Calendar yourself earlier (rare).
So take that bonus now. Also, you bananas are another good tile to settle on as it increased your food output in the city, which not only speeds growth but speeds up that first worker.
However, we must also talk about analyzing the start. The first thing is analyzing what you see, food specials, etc.. Then one must decide where to move the warrior/scout Turn 0 to offer provide most information to make a final settling decision. Look around the fog. Notice trees in the fog (generally we can assume no resources there).
So with unit move, my thinking unfolds like so: a) provide information of what I may lose if inclined to move settler the opposite direction b) reveal enough to feel secure in current settling decision. In this case, the unit move is not of huge value from what I see, but since, as Pangaea noted, I think settling 1SE on dyes is best move, I would move warrior 1W or 1NW to just view those areas I would otherwise miss out on. (or 1SW
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Next, I usually want the best situation for a possible Bureau cap. That mean rivers. In this case, moving 1SE looks to actually increase the number of river tiles for the city, as that river flows to the SE. So that is a positive. So with more river tiles for cottages, plus the remaining dyes available, this could be a pretty good Bureau cap.
Yes, your spiral idea is along the right lines of scouting for the initial unit. Generally, a ten tile radius around the city center. Your goal is to reveal as much land in this radius to find potential city spots. Then set that unit up in a spawnbust position, usually nearest to what you think will be you next city. Further scouting can be perform later by subsequent units, but your first few warriors will spawnbust for now.