You read the question.
In Civ 1, I took my time, I usually kept less then ten cities and could easily keep up in techs, I normally played on Prince and won maybe 1/3 of the games I played. I usually got to 3 or 4 cities as quick as possible then dug in and made my cities really nice.
In Civ 3, I now expand as fast as I possibly can. On a good start, I can outexpand the other countries on Regent untill my borders run against theirs, in my latest game I had 5 cities when most had 3/4. Of course finding settlers in goody huts helps a LOT, particularly if you get one on the third turn. In my latest game, I quickly became the #1 civ and have stayed there, and will now wait untill I build Sun Tzus before building a large offensive military and wiping the floor with the Indians. Everyone is on par in the tech race, but I have a slight lead along with the Russians (A few turns, enough so everyone else buys most of their tech from me, and I have been making loads of money as a result). If I hadn't accidentaly blown a settler by promptly readding it to my capital I would have grown even faster and probably had a bit more land area.
While I do try to expand fast, the first thing I always do is get a warrior in the city. I tend to not escort my settlers, because it takes too long, and I prefer to have defended cities. I lose em occasionally, but it is better then having all of my gold stolen from me. One time a barbarian attacked, and I kept getting messages saying they ransacked the city, the total was over a thousand gold
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I haven't played Civ 3 at King yet, I beat Civ 1 on it once, and I am sure I can ebat Civ 3 on it, but I just don't feel comfortable using my military very early on, probably because I am so focused on expansion at the beginning. I usually don't start warring at all untill the industrial age, and I often don't really start kicking ass untill the end of the game, when I usually wipe out entire civs in a decade or so, using scores of modern tanks (Attacking most any city outright with 30+ tanks will demolish it unless they defend their cities like I defend my main offensive point city before an attack
)
So basically my normal build order at the expansion part of the game is scout (Only in capital city, outer ones don't make scouts, and I generally only use 2-3 of them), warrior, settler, spearmen, settler, worker, temple, settler, or something like that, it keeps most of my cities defended and lets me grow fairly quickly. In border cities early in the game I usually do warrior, settler, warrior, settler, pikemen, worker, settler or something like that again. This basic build pattern works good for me, and if I get a nice starting place I can outexpand the uninhibited computer fairly easily.
But still, I just love that settler in a hut in the first 20 turns or so, I usually just start the city within 1-2 spaces of the place I get the settler and immeadeatly build warrior->settler out of it too, it can really give you a huge advantage to have nearly twice the production power of everyone else in the game so early on.
In Civ 1, I took my time, I usually kept less then ten cities and could easily keep up in techs, I normally played on Prince and won maybe 1/3 of the games I played. I usually got to 3 or 4 cities as quick as possible then dug in and made my cities really nice.
In Civ 3, I now expand as fast as I possibly can. On a good start, I can outexpand the other countries on Regent untill my borders run against theirs, in my latest game I had 5 cities when most had 3/4. Of course finding settlers in goody huts helps a LOT, particularly if you get one on the third turn. In my latest game, I quickly became the #1 civ and have stayed there, and will now wait untill I build Sun Tzus before building a large offensive military and wiping the floor with the Indians. Everyone is on par in the tech race, but I have a slight lead along with the Russians (A few turns, enough so everyone else buys most of their tech from me, and I have been making loads of money as a result). If I hadn't accidentaly blown a settler by promptly readding it to my capital I would have grown even faster and probably had a bit more land area.
While I do try to expand fast, the first thing I always do is get a warrior in the city. I tend to not escort my settlers, because it takes too long, and I prefer to have defended cities. I lose em occasionally, but it is better then having all of my gold stolen from me. One time a barbarian attacked, and I kept getting messages saying they ransacked the city, the total was over a thousand gold

I haven't played Civ 3 at King yet, I beat Civ 1 on it once, and I am sure I can ebat Civ 3 on it, but I just don't feel comfortable using my military very early on, probably because I am so focused on expansion at the beginning. I usually don't start warring at all untill the industrial age, and I often don't really start kicking ass untill the end of the game, when I usually wipe out entire civs in a decade or so, using scores of modern tanks (Attacking most any city outright with 30+ tanks will demolish it unless they defend their cities like I defend my main offensive point city before an attack

So basically my normal build order at the expansion part of the game is scout (Only in capital city, outer ones don't make scouts, and I generally only use 2-3 of them), warrior, settler, spearmen, settler, worker, temple, settler, or something like that, it keeps most of my cities defended and lets me grow fairly quickly. In border cities early in the game I usually do warrior, settler, warrior, settler, pikemen, worker, settler or something like that again. This basic build pattern works good for me, and if I get a nice starting place I can outexpand the uninhibited computer fairly easily.
But still, I just love that settler in a hut in the first 20 turns or so, I usually just start the city within 1-2 spaces of the place I get the settler and immeadeatly build warrior->settler out of it too, it can really give you a huge advantage to have nearly twice the production power of everyone else in the game so early on.