How Fast Should an Empire Grow?

[TheMeInTeam]

@ TMIT - It's a standard random Fractal map, not doctored in any way. It's quite an unusually easy one, I grant you, but it's a good exercise map for what I'm interested in here, which is: what is optimal expansion when there is plenty of space?

By the way, when I played this map, all the AIs but one formed a massive Buddhist block (to which the human was not invited) and got to friendly with each other, so in spite of the massive amount of land available it was quite challenging to keep apace with the collective AI tech rate (especially after hitting WFYABTA). Also, I got nearly as many cities peacefully on your IU Cathy game as I did on this map (I got 14 on Cathy, 15 on this one including barb cities).

Spoiler :

I poached flood plains+stone and fur to the east near charlie before he could get there (he has like 2-3 cities LOL), so I anticipate getting more on this map. I only see 2 other AI right now - ragnar and charlie. I will meet more soon because 1) I have EP on them and 2) a chariot is going through to check things out. I see no reason for getting 0 buddhist cities, although currently only ragnar's in it.

 

[shyuhe]

Optimal tech rate depends on whether you plan on playing peacefully all game or eventually going to bash heads. For vicawoo's map, you can easily settle 10-ish cities using just the capital and nearby floodplains (cottaged) to pay for the cities while you beeline monarchy and code of laws (can't tell which Caesar so I don't know if they're half price).

My general metric (pre-currency) for when to plant cities is if my slider is greater than 50%. Unless I have alphabet or I desperately need to complete a block, I won't settle any more cities at that point without currency. Otherwise it takes too long to get the necessary economic techs to recover long term.

 

[NihilZero]

Spoiler :

I poached flood plains+stone and fur to the east near charlie before he could get there (he has like 2-3 cities LOL), so I anticipate getting more on this map. I only see 2 other AI right now - ragnar and charlie. I will meet more soon because 1) I have EP on them and 2) a chariot is going through to check things out. I see no reason for getting 0 buddhist cities, although currently only ragnar's in it.

Spoiler :

Charlie is very sluggish on this map, unusually for him. By the way - how does the EP thing work whereby you can tell if there are other AIs to meet? (if I'm understanding you correctly) I seem to remember you mentioning that in one of your videos and I wondered about it.

 

[vicawoo]

At 10 cities on standard, number of city maintenance alone will increase by 6.

In a research race the criteria is turns to break even, which will depend on the expected mid-range economic output and technically the output of all the turns in between.

Spoiler unfinished :

Say maintenance increase is M, initial output (trade routes, city tile, initial tile) is C0, assume linear growth, t*(t-1)*average commerce growth/2 = (M-C0)*t.
breakeven = (M-C0)*2/commerce growth, this is a rough estimate.

 

[TheMeInTeam]

AI will split its EP distribution between you and other civs early game. If you've met 1-2 civs and have an EP advantage on them, it's because they've met somebody (and allocated points towards him/her/them) such that you have more allocated vs them than they have vs you. This is an excellent way to tell if there are additional civs that you'll be able to contact in the near future.

 

[TheMeInTeam]

At 10 cities on standard, number of city maintenance alone will increase by 6.

In a research race the criteria is turns to break even, which will depend on the expected mid-range economic output and technically the output of all the turns in between.

Spoiler unfinished :

Say maintenance increase is M, initial output (trade routes, city tile, initial tile) is C0, assume linear growth, t*(t-1)*average commerce growth/2 = (M-C0)*t.
breakeven = (M-C0)*2/commerce growth, this is a rough estimate.

That's pretty clear other than "commerce growth". Obviously that's going to differ between city specializations, and are you rating it on the combination of trade routes, intended cottage turns, etc? Seems like a lot of time investment for an analysis, but possibly necessary.

 

[NihilZero]

AI will split its EP distribution between you and other civs early game. If you've met 1-2 civs and have an EP advantage on them, it's because they've met somebody (and allocated points towards him/her/them) such that you have more allocated vs them than they have vs you. This is an excellent way to tell if there are additional civs that you'll be able to contact in the near future.

Excellent, thanks for that.

 

[vicawoo]

That's pretty clear other than "commerce growth". Obviously that's going to differ between city specializations, and are you rating it on the combination of trade routes, intended cottage turns, etc? Seems like a lot of time investment for an analysis, but possibly necessary.

Being more awake, I can write more coherently and intelligently on the issue. What I mean by commerce increase is your city should produce more commerce from trade routes/tiles as it grows, that's all.

We can just assume it increase linearly over time, say you gain one cottage every 8 turns. Then the time it takes to grow to match your maintenance is when you're in the negative, say n turns. The n+1 turn you'll gain just as much as you lost in the n-1st turn

So the break-even point is about twice the number of turns it takes for commerce output = empire-wide maintenance increase. If you're racing for a tech, do it if you can reach the break-even point before you reach your goal.

Example: Your maintenance increase is 6 from # cities, 3 from distance. Say you have currency, so starting with trade routes you start with 3 commerce. Say you grow to another cottage every 5 turns, so in 15 turns you grow to size 4 and have 3 cottages to net 9 commerce per turn.
That means in 2 x 15 = 30 turns, you should break even. Round down liberally due to cottage growth and when foreign trade routes kick in.

 

[TheMeInTeam]

Being more awake, I can write more coherently and intelligently on the issue. What I mean by commerce increase is your city should produce more commerce from trade routes/tiles as it grows, that's all.

We can just assume it increase linearly over time, say you gain one cottage every 8 turns. Then the time it takes to grow to match your maintenance is when you're in the negative, say n turns. The n+1 turn you'll gain just as much as you lost in the n-1st turn

So the break-even point is about twice the number of turns it takes for commerce output = empire-wide maintenance increase. If you're racing for a tech, do it if you can reach the break-even point before you reach your goal.

Example: Your maintenance increase is 6 from # cities, 3 from distance. Say you have currency, so starting with trade routes you start with 3 commerce. Say you grow to another cottage every 5 turns, so in 15 turns you grow to size 4 and have 3 cottages to net 9 commerce per turn.
That means in 2 x 15 = 30 turns, you should break even. Round down liberally due to cottage growth and when foreign trade routes kick in.

Excellent. Now one of the harder things to decide in this game is that investment vs others. There isn't just the city, but the hammers/food into the settler, and compared against other options. If it has the best payback time out of all options, founding another city is obvious. I bet that rarely happens with large swaths of land outside city #2 or #3, so now we evaluate additional cities vs other things and it gets harder. Do you have a rule of thumb for how many turns something should take to pay back, or is that a "feel it out" thing, or do you just repeatedly pick the best ROI? Obviously my qualification here is that we have way-too-much-land and are trying to settle it ahead of the AI or find a way to beat the AI if we do not settle it. Which approach has a better outcome on average?

 

[vicawoo]

Hmmmm, my personal decision making process would be having a comparable research rate (hard to measure objectively, probably some GNP comparison) to the AIs, assuming I'm not in pursuit of some tech goal. If I can invest while not falling behind, I'll do it. I feel the fundamental decision is, which is a more cost efficient investment, peacefully expanding now, attacking (spending hammers), or teching then attacking (spending hammers).

The dave cottage justification was that taking land was always better, but if you're stalemated, cottage investments break the stalemate. Peacefully expanding is like a cottage investment, you get bigger which will help you break the stalemate.

If I have too much land and am competing with the AI, of course the first thing I do is send settlers to the spots closer to the opponent to block/force him into worse locations. If they are a poor investment, I'll skip turn repeatedly until settling them at the last possible moment (assuming they are even somewhat affordable). I usually assume it's more cost efficient on higher levels to peacefully take it than sending dozens of units, although people disagree with cuirassiers.
Now the land behind the border cities, that's where decision making comes into play, and where I usually feel for the average tech rate, and I guess I go backwards from fastest (edit: best) investment return (strongest commerce cities vs maintenance) until I hit the average tech rate, stop, wait for investment to compensate, repeat. I'm not entirely sure how to rate high food cities though, since they require longer investments but have bigger returns.

 

[iggymnrr]

I'm only an emperor level play and simply am not comfortable until the economy is 10 %. Anything higher than that ... wait a second. <evil laugh>

 

[TheMeInTeam]

Hmmmm, my personal decision making process would be having a comparable research rate (hard to measure objectively, probably some GNP comparison) to the AIs, assuming I'm not in pursuit of some tech goal. If I can invest while not falling behind, I'll do it. I feel the fundamental decision is, which is a more cost efficient investment, peacefully expanding now, attacking (spending hammers), or teching then attacking (spending hammers).

The dave cottage justification was that taking land was always better, but if you're stalemated, cottage investments break the stalemate. Peacefully expanding is like a cottage investment, you get bigger which will help you break the stalemate.

If I have too much land and am competing with the AI, of course the first thing I do is send settlers to the spots closer to the opponent to block/force him into worse locations. If they are a poor investment, I'll skip turn repeatedly until settling them at the last possible moment (assuming they are even somewhat affordable). I usually assume it's more cost efficient on higher levels to peacefully take it than sending dozens of units, although people disagree with cuirassiers.
Now the land behind the border cities, that's where decision making comes into play, and where I usually feel for the average tech rate, and I guess I go backwards from fastest (edit: best) investment return (strongest commerce cities vs maintenance) until I hit the average tech rate, stop, wait for investment to compensate, repeat. I'm not entirely sure how to rate high food cities though, since they require longer investments but have bigger returns.

You're missing my question a little bit. When it's relatively easy to block that kind of makes the decision for us.

The hard one is when it's just a massive amount of flatland where the AI pays a joke fraction of the cost on land that we do. It's not a question of settling towards them ---> they can easily just go around unless we gobble up ALL the land near them. However, if we DON'T settle the land it turns into 30 AI cities 10 human or so.

Possibly, there is no good answer there and it's just "well, that sucks and on high levels you'll usually lose", but before I concede that, it's useful to explore approaches to dealing with it.

 

[yanner39]

I spawn busted to the side with the good land. There was a barb warrior who was conveniently spawn busting archers from my left side

Spoiler :

But the chariots (2 from the second city) did keep me safe. Once I saw charlemagne settle east of my cow city, I could recall my chariot to the west side, and I made an additional chariot in my capital.

There wasn't a great impetus to grow past size 2 before expanding, since the plains hill gave us a a warrior at size 2, and other than getting the imperialistic bonus, all our tiles are inferior to an expansion resource. Settler then growing to mines will give you more yield than growing to mines then settling.

This is interesting. So just to be clear, a settler at size 2 was a good idea because there were no other expansion resources (high food/hammer yields) in the BFC? If there was a corn or wheat resource in the BFC as well, I guess the settler would wait until the second food resource was improved?

I'm just wondering because, typically, I grow to the cap and spam all may workers and settlers in one shot. However, I do have the spawnbusters in place. These are usually all warriors but getting a settler out earlier could allow me to sink hammers in Axes or Chariots instead.

 

[Aoxomoxoa]

While every game is as different as the map, what I've settled on as a 'typical' start with any Civ that begins with mining usually goes like this... study whatever needed to improve or if that's covered go with bronzeworking.

Worker first, improving the best 'bonus' tile, typically food... improves next best tile favoring a hill (and/or forest if BW is in) of some sort then moves to third. If bronzeworking is in already then I'll chop (or prechop) so that the chop goes to the settler. If the chop doesn't push him I will whip. > Warrior>Warrior. I want the city at size 3 before starting the settler so I will put hammers into a 3rd warrior, but then switch to the settler at size 3. First warrior goes to fogbust in the opposite direction of the beginning warrior or scout... the second goes to spawnbust the first expansion.. Settler2>Warrior>Worker>Settler3...

Water start with seafood that doesn't start with Fishing.. worker until fishing is in, then switch to workboat, then back to worker.. after that I'm still shooting for size 3 although the vast majority of the time I still get at least one warrior before the settler.

There are nuances that can change some of the specifics... but that's the gist of what typically happens.