[Spoilers] Shallow Thought and Hitru's series of (unfortunate?) events

[shallow_thought]

Charriu has already taken a city - and I think a mature one.

Also, Hitru understands the line-of-sight rules and has pointed out that we can stage 1E of HH out-of-sight. That means that an Immortal attack could be on the cards ... even sooner. Particularly as RFS-81 has stripped his garrisons to a warrior and - nothing.

His power remains high, at least as high as ours. He must have something, somewhere. I gues we'll find out.

[shallow_thought]

We're gearing up for war. Our overall power is was only around that of RFS-81 a couple of turns ago, but things are different now. It's nice to see Charriu paying for his gains.




So, staging troops near GG. I messed up and put a sentry Immortal in the city, which may give RFS-81 a clue that something is up - it should have been left on the rear staging tile. Nonetheless, next turn we can hit with a tiny strike force of 2 Imms, backed with the sentry and an axe, which was more than enough the last time we saw the city. I will probably wait one more turn though. That would double our first strike strength, as well as bringing us closer to having a second wave whipped out of the border cities. Also, there is something pleasing about declaring war on t100.




Economically, we get a Great Scientist next turn who wil provide an academy. We're getting a three-commerce trade route from each of Superdeath and Charriu, which is nice. I guess I should try to provide a t100 overview at the weekend, but I'm hoping we're going to be busy...

[shallow_thought]

So, I failed to count correctly last turn, and thought I needed an extra road to get an Immortal into position for t100, when I didn't. So my workers were out of position for the t99 strike with 2 imms. Which is a shame, as RFS-81 left an axe and an archer on flatland which we could have hit. Still there could be advantages to a stronger intial push, and this doubles the force. We finish our (EDIT: this snuck in at some point during editing - it's not in the first draft. What did we finish? Our academy? My attempt to pretend I have a grasp of the English language? Answers on a postcard...).




There's plenty of clues for RFS-81 to pick up on: the worker chop should have finished this turn if I hadn't started a road, there's an axe missing from GG and the Imm now there isn't a sentry, and has no moves. Whether he will have been able to do much about it is the question. He struck back hard at Charriu last turn, taking a city. Whether that was a re-take or a counterstrike I forgot to check *.

In other news, Hypatia founded an Academy in Bad Beginning. 2t to Masonry, then perhaps science back on. Currency is the natural target, but with a war on Construction could be tempting. I'm hoping not to need it against RFS-81, but as a counter to Charriu or anyone else vulturing in, it could be significant. For those counting minor errors I also forgot to sweep the world for bridges this turn*. Couerva or Superdeath have been ahead in GNP for a while, so could have it.

*Unlike the worker error I could always fix these by logging back in and looking around, but I'm trying not to focus RFS-81's attention.

Question for experienced lurkers about turn splits: we're planning to keep the pattern of the last few turns, and play after RFS-81 (avoiding his last-minute whips) but ahead of Charriu. We're obvious going to be in an official turn split with RFS-81 next turn, but at what point do we need to start considering ourselves in an official split with our "ally" (and point that out to him)? We certainly don't want to lose a chance to take any juicy core cities out from under his nose .

[Old Harry]

What did you finish?  (paragraph one)

I'd say you don't need to worry about the turn split until you see your ally's units,  but at that point you're probably locked in so sticking with the turn order now would be safer.

[shallow_thought]

So, I start my MP combat career at RB by taking advantage of a friend's troubles to get in a vicious backstab. This is normal, right?

Or, rather it would have been a vicious backstab if RFS-81 hadn't got a spear there. It's got 5% fortify, so either arrived last turn, or just maybe the turn before with its last move. The pop level doesn't suggest major whipping, which carries the nasty implication that he could also whip walls there if he wanted - or a second spear. The other troops (axe, two archers) seem unfortified. If we had been able to hit two turns ago he could have been in trouble, but that was never an option. Last turn? We'd have hurt him, possibly captured the city if we didn't go for the flatland units, but almost certainly lost it on the counter. Might still have been worth it if he'd lost hammers invested into that damn spear. Oh well.




We declared anyway and took the opportunity to run our sentry Immortals through his lands. This got us sight of his capital, where he has five archers and three axes. We wouldn't be taking that any time soon. Charriu? Let's hope not. The strategic issue is that he's down to four cities, so we're poking directly at his core. We're running our Immortals up to DQ and trying to at least threaten Black Corridors, trying to force him to split his troops. The terrain doesn't really favour speed much though, with all those woods and hills. In 5t we'll have three swords available to have another look, two on the southern front, one on the north. Feint north, swing to Rocky Paths again, see what we can do? His power has stabilised, but he's got enough to stall us.




We've offered a cease-fire, but I doubt he'll take it. Offering peace would let him defend against Charriu better if no-one else piles in, but it would tie our hands if Magic Science or Couerva/OT4E did take an interest.

Speaking of Magic Science, he has a couple of chariots hanging around near DQ, but not near enough to hit the city. He has offered OB, which we've now offered back. He hopefully just wants to scout a bit.

Superdeath's Impi near DQ was significantly more annoying - I wanted to empty the city, sending the axe to support the new sword as it moves towards RFS-81, but if SD had declared and teleported to the wrong tile he could have raised it. Not worth the risk. Hopefully he's not feeling frisky, as there is a worker on his border he can hit with a chariot. It's covered with an axe, on a jungled hill, but he'd still have good odds. We'll get an Immortal back on that border soon, but we're now delaying some unit builds, with an eye to pushing for Currency ASAP.

Oh, doesn't look like anyone has Construction yet, which is good, as that should mean RFS-81 stays alive a while.

[shallow_thought]

In a break from your scheduled programming, another of Shallow Thought's rules of thumb.

The rule: build buildings; the designers put them in the game for a reason.

Well, even by my standards that is an exaggeration. Even at my worst I rarely built coliseums in BTS. But everything else? Sure - every city used to get a library, grocer, even an aqueduct if it had any health issues at all. I tended to be at peace until I'd built a sizeable tech edge over the AI (low level play, remember); what else was I going to do with those hammers?

So, why is this rule wrong? Lots of reasons. Some are truly obvious: you need to build settlers and workers to expand and improve tiles; even if you were playing "always peace" you'd need troops for MP and scouting. But even when you've enough units, buildings compete for hammers with research and wealth building. This can be tricky to quantify, but there is one simple case - multiplier buildings, with other side effects ignored. In this case you can calculate how long it will take before a building "pays back". Other people sometimes seem to do this differently, which confuses me, but I'll explain my thinking.

First, if you're going to talk generally, you need to make some simplifying assumptions. In a real game you need to think about likely changes ("in 5t I will swap the silver back to this city, which increases the value of having a bank here"). Similarly timing matters - if you need a defender in a city in three turns, finishing a forge to build it more efficiently doesn't work well if it then takes 4t to get there. However, for the purposes of this discussion we will be assuming that nothing changes during the calculation window, and that hammers, gold and beakers are worth as much at the end as at the beginning. I'm also going to ignore overflow, rounding and such like.

In that case, lets be needlessly abstract. What we want out of the city in question is "useful" stuff, produced at a rate of "a" per turn without putting production into it and "a+b" per turn if it's actually being produced . This can be hammers for units, wealth, research, culture - whatever.

There exists a building that would adds "m" to the useful stuff per turn. This may be a simple multiplier on "a", but might not be (for example, it could actually add culture). It will take "x" turns to build.

So, we set up two parallel timelines, one where we build the building and then focus on "stuff", and one where we just produce "stuff". We calculate the total quantity of useful stuff at turn "x+y" from now, such that it's the same for the timelines. That is the definition of payback time - "x+y". After that point, we have more total stuff in the timeline where we built the building.

EDIT: restating definitions for clarity.
x: turns to complete building
y: turns after building complete until payback
a: amount of stuff generated per turn, excluding production (that is, ignoring wealth, research or culture builds), before building complete
b: amount of stuff generated per turn through production (hammers, wealth, research, build culture, as appropriate), before building complete
m: change production of stuff after building complete - the gain, or delta

Timeline A: s = (x + y).(a + b)
Timeline B: s = y.(a + b + m) + x.a

=> x.a + x.b + y.a + y.b = y.a + y.b + y.m + x.a (1)
=> x.b = y.m
=> y = x.b/m
Payback time = x + y

Note that the "background", non-production rate of gain per turn ("a") drops out, as you intuitively expect. Note also that you don't have to directly consider the complexities of different multipliers for hammers depending on what's being built. It's simply the time it takes to build the multiplier building, and the rate of production of useful stuff before and after the new multiplier takes effect.

So, an example. Consider a city making 40 gpt without building wealth + 20gpt from building wealth, that will take 10t to build a bank. That makes "m" 20 gpt - 50% of the 40gpt. The formula says that y is 20.10/20, or 10t, or a payback time of 20t.

Consider timeline A: in 20t, we get 1200 gold. In timeline B, we get bank and 400 gold in 10t, and an additional 800 in the next 10, for 1200 gold.

You can make the calculation a bit more complicated by saying that you change "b" after building; that is, in timeline A you build wealth until t10, and in B you build the bank, then in both you build knights instead. But that only affects the y.b terms in line (1) above, and in the same way on each timeline, so that they still cancel.

So, this boils down to if "it takes take me 10t to build a forge, and it gains me 2 hammers per turn, it pays back in 5t, after it's built". Or, if "it takes me 10t to build a library, and it gains me 3 beakers, and I could get 9 beakers a turn through research, it pays back in 30t, after it's built". The errors I tend to see are people forgetting the "after it's built" part when faced with a long payback time, or getting caught up in unnecessary complexity worrying about the difference that Organised Religion or IND makes to exact hammer numbers when building a forge.

This is so basic that I'm probably wasting your valuable time. However, there is one final tweak. If the building is a cash multiplier, one of the the assumptions is not valid. The thing is, you don't usually want cash in Civ IV (maybe if you're upgrading units, or trading with the AI). You actually want beakers. So you have to redefine "useful stuff" in the formula above - your "m" is not your gain in gold-per-turn, but in beakers-per-turn; similarly, your "b" is not wealth, but the extra beakers you gain from building wealth. The relationship there is quite complex - as explained by T-Hawk in his articles at http://www.dos486.com/civ4/index/economy.shtml and http://www.dos486.com/civ4/index/bank.shtml. So, what's does that mean for the payback time for that bank? We'll get into that in a bit.

[Bacchus]

Your forge example is very strange in terms of concrete numbers, but the formula is right - the forge pays back at 1 + 4 times it's completion time because it yields a quarter of production. Where m is a multiplier of b, you don't need to get to absolute yields, unless there are forecasted changes to them. OrgRel is relevant because it worsens the forge effect for buildings to 1 + 5 times completion, so if you are choosing to build a forge ahead of a wonder, that's what you should look at. IND, of course, pushes that even further to 1 + 6, but then the completion time is halved, so normally still better.

All of those are actually better, of course, because production grows over time. Growth is a big feature of the game that it really shouldn't be abstracted from, its what catches people out with courthouses. You need to start building them so that they are worth it once complete, so well before the current maintenance justifies it.

[mackoti]

Your forge example is very strange in terms of concrete numbers, but the formula is right - the forge pays back at 1 + 4 times it's completion time because it yields a quarter of production. Where m is a multiplier of b, you don't need to get to absolute yields, unless there are forecasted changes to them. OrgRel is relevant because it worsens the forge effect for buildings to 1 + 5 times completion, so if you are choosing to build a forge ahead of a wonder, that's what you should look at. IND, of course, pushes that even further to 1 + 6, but then the completion time is halved, so normally still better.

All of those are actually better, of course, because production grows over time. Growth is a big feature of the game that it really shouldn't be abstracted from, its what catches people out with courthouses. You need to start building them so that they are worth it once complete, so well before the current maintenance justifies it.

Or just to be ORG and finish them in 1-2 turns.

[shallow_thought]

Your forge example is very strange in terms of concrete numbers, but the formula is right - the forge pays back at 1 + 4 times it's completion time because it yields a quarter of production. Where m is a multiplier of b, you don't need to get to absolute yields, unless there are forecasted changes to them. OrgRel is relevant because it worsens the forge effect for buildings to 1 + 5 times completion, so if you are choosing to build a forge ahead of a wonder, that's what you should look at. IND, of course, pushes that even further to 1 + 6, but then the completion time is halved, so normally still better.

All of those are actually better, of course, because production grows over time. Growth is a big feature of the game that it really shouldn't be abstracted from, its what catches people out with courthouses. You need to start building them so that they are worth it once complete, so well before the current maintenance justifies it.

Yes, the numbers were pulled completely out of thin air. I've had a great deal of fun over the last couple of days trying to establish a formula for calculating the payback time for cash buildings. I managed to prove to myself that T-Hawk was (unsuprisingly) correct in what he had said, turned up one minor wrinkle (banks are worth less if you're already building wealth than otherwise) and utterly failed to generalise the formula beyond a one-city empire. I'll post what I did manage to sort out soon.

Sadly, the game itself is not going so well. I have several grumbles.

Grumble. I'm an idiot. I neglected to check the event log last turn because I was so excited. Charriu had already made peace before our move. Actually, in a better-to-be-lucky-than-good moment, I gained from declaring and sending sentries into RFS-81's territory, as I got vision and he accepted the ceasefire. Sorry friend (no quotation marks, dammit, we have a shared history of MOO and Civ SGs here), but if you don't do something about your ungarrisoned city to the north, I'll be chewing on it in a few turns. If I beat Magic Science to it that is. He has two chariots, I have four Immortals, and axe and a sword. I'd win that, but he may have more units I can't see.

Grumble. It's annoying. A pause last turn has left RFS-81 playing late, and thus me later. I had to delay until after my parents had been and gone for dinner. I love them, but I don't invite them round and stay sober. So, this turn I have tried to signal to Superdeath that my worker activity on his border, including a road is harmless, by sending crab-crab. I think that made sense, but cannot be sure.

Final grumble. Charriu is settling the plains cows in our neutral zone. I have tried to signal that I think this is a bad idea by cancelling our crab-crab deal and sending a new one. Even if I'd managed it, that's not a clear signal. As it is, the PB diplo interface and a defeated me in my weakened state and I have no idea what I've actually done. I think that he would have paid no attention anyway.




Get Construction and kill them all . But we're going for Currency first (9t, hopefully less if I can get some more research builds going).

Let's not overstate the grumbling. Still first in crop yield, competitive in Mfg, OK in GNP, decent in power. I just feel that I've missed a chance to improve in the last few turns...

[shallow_thought]

Normal service more or less resumes. I'm still a bit down after t100's non-event, but the sulking is nearly over. The world is at peace, open borders almost everywhere. This implies that either Charriu has alpha, or both Magic Science and Superdeath have it. I think the latter, given the GNP graphs and Charriu's recent activity. At a player level, OT4E has been left in a very uncomfortable position, with Couerva having stepped aside completely (according to the tech thread). From a leading position he could probably stomp this field in his sleep, but that would be no fun for anyone, so he's left just ticking the turns over. Hopefully we'll be able to get someone into his place soon. Personally I'd even settle for one of the dedlurkers if the skill level was appropriate. I don't think there are too many huge secrets in this game.




I do think RFS-81 made the most of little in his defence. He's moved his spear, probably heading for Black Corridors, and 2-pop whipped both his cap and Rocky Paths. I expect more spears. I also suspect that I've missed a window to strike immediately after the cease-fire, but we've now exchanged messages confirming that the turnsplit is over, and my forces are out of position. In fact, I've pulled them back further than is visible in this screenshot, with the Immortals moving behind DQ out of Magic Science's immediate sight.




Speaking of Magic Science, he's doing some slightly brave out-of-border chopping there. I imagine a pop is timed for next turn. Even so, a more aggressive player than me should really be teaching him a lesson right now...




I guess I should try to put an empire overview together. There's no real news; it's that uncomfortable time I run into in games pre-Currency when I can never work out what to whip as my cities grow. Currency will help that (markets) as would Calendar (more happy) but I think that we'll be going Construction before the latter. The whip will crack, the cats will roll. But that's ~15t away, I think, maybe a bit sooner. A lot could change elsewhere in that time. I'd hope to beat both Charriu and RFS-81 to Construction, given the graphs, spoilered below, but either could have chosen to beeline it.

There should be an overall demo screenshot here, but I ended up with two of the power graph instead. Next time, maybe.

Overall, not too bad. However, Charriu's land gains will soon start to appear. Need to get that tech edge working, either through outright having cats when he doesn't, or being able to support more troops and cities while still making progress.