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

[shallow_thought]

If anyone wants to accuse me of indecision, vacillation and wasting valuable lurker time, I will reply "fair cop". MS has burnt Black Corridors, leaving RFS-81's only spear badly injured. My sentry gets 96.9%. Now, I could just take the kill - he'll struggle to replace it. But what if we do go full out, now that forking is not an option? He's not reinforced Rocky Paths - he's built walls. Now, his axe behind those walls gets good odds against a C1 sword, but against three, possibly promoted shock, backed by axes and Immortals? He's still got to cover his cap to some extent, and anything he moves over will be unfortified. Because I pulled back last turn any real attack is 3t away. But let's go the spear kill, make the moves, and see what happens.




Hah! Flawless win. At least I've started out OK...

AA can spit out a settler for the razed area in 5t+travel time, but I can get the guy headed for a filler spot back in 4-5 total. He must be one tired settler, wandering back and forth across the empire, but he's on his way.

We have the first spread of Hinduism in the world - and it's to Deadpool, Superdeath's city north of Evil End. I'm kind of irate with the RNG right now. Wonder how much that affected my decision to go (back) to war?

[shallow_thought]

While hanging around in turn-split hell, a quick diversion, which takes us a step closer to being able to evaluate the payback time for a bank. While I started from a different point, this largely turns into a re-hash of T-Hawk's findings (unsurprisingly).

The rule: build wealth rather than research, given the option.

Why? The intuitive answer is that, while neither wealth nor research get multipliers, building wealth lets you move the slider, and the "freed" commerce is then multiplied through science buildings. But is there anything else? Let's see.

What matters is the break-even science rate. In detail, the coarseness of the slider, rounding errors and tactical considerations complicate things, but not in a way that matters at scale.

Consider, for simplicity, a one-city empire.

Definitions:
s = break even beakers per turn
g = break even gold per turn
r = beakers from research per turn
w = gold from wealth per turn
m = base gold from other non-commerce sources per turn (merchants - hence "m", shrines)
L = base beakers from other non-commerce sources per turn (scientists - think "labs"; capitalised to avoid clash with numeral one)
u = science multiplier rate (think "university")
b = commerce multiplier rate (think "bank")
e = expenses per turn
c = total commerce
p = break-even slider position, 0 all gold, 1 all science
h = extra hammers, available for more research or wealth
ds = change in beakers per turn (and similar for changes in other terms)

(1) s = u.(p.c + L) + r         [science = multiplied commerce + multiplied scientists + research]

So, if we put the extra hammers into research, the change is (obviously):

ds = h

There is a similar equation for break-even gold.

(2) e = b.( (1-p).c + m ) + w     [ expenses = multiplied commerce + multiplied merchants + wealth ]

So, what happens if we put the hammers into wealth instead?

Solve (2) for p to get the break-even slider position (this only holds for p <= 1).

(3) p = 1 + (b.m + w - e) / b.c

This has a couple of counter-intuitive implications. First, it implies that building banks to process the gold from merchants doesn't directly affect the slider position. However, if you consider that the point is to replace gold-from-commerce with gold-from-merchants, and they share the same multiplier, then this makes sense. Building a bank still reduces the fraction of commerce needed to reach break-even, but, in the way I've arranged the equation, does so by reducing the impact of the expenses. For those who've read T-Hawk's articles, this should be ringing a bell ... we'll get back to that later.

Second, it implies that building a bank reduces the impact of each wealth-hammer on the slider. I think that the point is that, with the bank in place, it is less efficient to build wealth, and more efficient to put gold through the bank. If you are having to build wealth to pay off expenses rather than just using the slider you capture less of the gain from building the cash multipler than if you can fund your expenses through commerce, so the bank is not as good.

Anyway, substitute into (1) and simplify to give:

(3) s = r + u(L + c + m) + w.u/b - e.u/b

At first glance, this appears to disagrees with T-Hawk's article about specialists. It suggests that running merchants and scientists is equivalent. This is because of the simplifying assumption that this is a one-city empire. If you can run merchants in low-science multiplier cities to boost commerce in high-science multiplier cities, you make a net gain.

However, even in the simplified example, you can see that the wealth outperforms research if the science multiplier exceeds the gold multiplier. So, what about a real empire? The gold from wealth is independent of which city it's built in, so all we care about is the average multiplier. I think that for a real empire this can be calculated as:

(beakers at 100%) - (beakers at 0%) / ( (gold at 0%) - (gold at 100%) )

This certainly holds true for empires without shrines, specialists, wealth or research, where the negative terms are zero. I haven't done a detailed analysis to support my intuition, nor to confirm that this matches T-Hawk's definition (which he base on a single "step" of the slider). For much of the game, this is likely to be greater than unity, but there are cases when it may not be. An empire that has built markets everywhere for happiness but few libraries could, in theory, be better off running research, because it is more efficient to use commerce through the multiplier to pay expenses than to use wealth.

This diversion is not particularly interesting in itself, but equation (3) gives us a tool to analyse the changes that building a bank makes to an economy, and hence to calculate its payback time.

[shallow_thought]

So, I moved into position last turn, and this turn RFS-81 has played early, which helps me. Things to note about his turn:
 - 3 minutes
 - no whip in Rocky Paths
 - archer in north moved aimlessly, not into either city.
 
He did whip walls in Space Love, giving me only a 50-50 against the warrior (with a 10% withdrawal chance). It's a trap! I may yet decide to strike and take the gamble -  there's a reason RFS-81 has seemingly thrown in the towel. OT4E has declared on him, and with his Praetorian-fueled power spike, that's GG. Despite the political risks,I'd like to deny him the city.

In the main theatre, the lack of a spear opens the door to wearing down archers and axes with Immortals before using the swords, and taking the city this turn. So, let's throw some Immortals away to preserve our swords

17% v Archer - Win !
18% v Archer - Loss.
65% v Archer - Win.
35% v Axe (no C1 on this Immortal) - Win !

Well, that was embarrassingly lucky. Our swords didn't even get to see combat.




We get a granary for our (limited ) pains. The four turn resistance may, however, turn out to be a problem. I moved the Immortal to see what was near Space Love (and to have the option of pillaging the hamlet), and then left it to the last move of the turn. And then I snuck in and razed the city from under OT4E's nose (still lucky). I left the Immortal there to sate OT4E's rage (hah - as if!).

In the end, I rated the chance of cash and denial value more than a few turns more of "goodwill". Once OT4E had marched into RFS-81's capital he would have found our new flatland city a tasty target regardless. So, we need to be prepared to stave off those AGG Praetorians, in the hands of an expert. I know he's not exactly invested in this game, but that is still scary. He has another stack similar in size to the one in the screenshot (apologies - I thought I'd captured in a pic, but no...) heading fora replanted RFS-81 city ENE of RFS-81's cap, as well as some visible support, so ~12-15 units in the theatre. So we're outnumbered and slightly behind in quality. Our Immortals have done us proud, but their time is almost over. Speaking of that power spike...







In overall demos we're still not too bad. Charriu still being ahead of us in military is mixed news - it does restrict OT4E a little. Magic Science is actually the top GNP right now, despite Superdeath having built the Great Lighthouse.

The good (great!) news is that the cash from the captures and razing will fuel us to Currency in 2t with some left over. Construction for cats, followed by HBR for wellies is what we need. I'm not too worried about our former border, given that we can get walls up and have plenty of whip capacity, but holding Jacques S could be hard. Let's hope the city is luckier than the character.

Oh, and in case our recent tactical success should give anyone the wrong idea about my base competence, take a look at this.




That's an unescorted, wandering settler. It's the result of me agonising over paths and destinations for so long my finger slipped. I can't even honestly call it a simple mis-click, just pure indecision and brain freeze. I think this guy is safe, even from a worker-chariot combo from Magic Science, but it's still . And as for where to put him so that OT4E can't just rush the city, I have no idea.

Anyway, plan is to try and pillage as much of the road network as I sensibly can to protect JS. The cash means that a small bunch of military builds are back on. We may have to hard-whip the eastern border, as so much of our production is in the west. And really - I want to be whipping cats, not axes. Even with walls, we'd be lucky to go axe-for-Praetorian.

[shallow_thought]

Razing a city under OT4E's nose produced the predictable response. One dead Immortal, and this.




Much as I'd love to be playing these critical turns with my full attention, the turn split, the fact that the turn is obviously rolling at a terrible time for RFS-81 (he's playing 12+ hours in) and it being the first weekend my wife has had off in weeks is forcing me to rush things.

Still, I logged in early and took the quick peek above, and had a chance for a very brief chat with Hitru. I ran the odds of defending against shock Praetorians on flatland through a calculator . We've therefore retreated to the copper hill. If OTE4 decides the risk of a counter-attack is too high (swords will eat his troops in a fresh flatland city pretty well) and we've manged to push him into a raze ... then I'll try a plant in the hills with our wandering settler to grab at least one sugar second ring and offer peace.

I've offered peace to RFS-81, whipped another axe early out of DQ and am getting ready to put hammers into walls at various cities (ironically, I'm struggling to avoid getting overflow into them). Interesting times.

Poor Jacques S. The name, at least, is thematic. Apologies for spoilers if you haven't read the books/watched the series.

[shallow_thought]

We have cunningly persuaded OT4E to do our work for us by razing the original, flatland Jaques Snicket (alternative interpretations of the events of the previous few turns are available). Unable to face our enemy on the plains, we are doing what IMP does best and re-settling the empty land. On hills. With 1t walls thanks to prepared chops.




If OT4E had accepted a treaty we'd have push onto the copper instead, but he didn't. He offered a ceasefire, which we've taken. Once we get a border pop and calendar we'll have two food-poor but survivable cities, but right now JS2 and DQ are having to share one, dry wheat.

We also have eyes on a hill plant on the coast 3E of GG that will be freed up when (if?) OT4E takes RFS-81's capital. Grabbing it safely will be ... interesting, as there is no easy chop to line up for walls. We might be able to do something sneaky, we'll see.

We could also go for RFS-81's whale island, currently empty. Our galley was actually trapped there when RFS-81 accepted peace .

Economically, Currency has brought us up to 30-40% break even. We must expand more! Judging from the graph, we're not alone in enjoying its benefits (although SD could just be having fun with the Great Lighthouse and have more to come).

[shallow_thought]

OT4E has made peace with RFS-81. That's actually quite annoying. OT4E's stacks are still hanging around - Hitru expects a settler inbound soon for that hill. In the meantime, he's sent his GNP rocketing - I suspect Construction, which will probably spell final doom for RFS-81, although if that were a treaty, not a cease-fire, he has a little time.




Superdeath has offered fish-fish, which is nice as he has been building units. I think he's established OBs with Charriu, and hence with us. Being back on the global trade network does boost our commerce a bit. We're on track for Construction in 6t, at which point some stashed overflow and delayed chops will probably get put into catapults. So, our other borders are looking pretty peaceful right now. Charriu has power, but almost all his units anywhere near us are defensive, while Magic Science faces us at the border where most of our mobile army is hanging out, and lags in raw numbers. I do need to scout MS out though - I'd actually forgotten that we had OB, I've been so focused on the skirmishing .







So, perhaps this is a point to take stock?  Our GNP is a little less exciting than last turn, now that we're back to saving cash, but overall our demos are still fairly strong. I'd say we're definitely still in the pack with Superdeath and Charriu, and not that far ahead of Magic Science, but probably at the front of that pack on average. OT4E is ahead, and still within range, but I think that will change when he settles the land he's grabbed, and moves on to kill RFS-81. We can look to grab scraps around the edges (we've still got two filler sites, and hopes to grab both mainland and island sites from RFS-81's territory), but we're going to need a bolder move, luck or both to progress much more.




Graphs below, including that terrifying power edge. (FAKE EDIT - I may be doing MS a disservice looking at those graphs; there's really not a huge amount in it for the four of us).

I did take screenshots of every city this turn, so I'll try to put together some sort of commentary around that, if I get time.

[shallow_thought]

We have a Copper-Copper offer from Charriu. This is intriguing...

He's war-peaced RFS-81, so I think this is an attempt to try to hit OT4E (I doubt he wants to hit Superdeath with OT4E sitting there). I'm definitely sympathetic, but I just don't think it can be done just yet. OT4E has settled two cities near us (the screenshot is actually from last turn - we're now at 112), but the key one is on a hill. We could strike against the flat, but I suspect that puts our army horribly out of position.




For reference, I can easily see two praetorians, 9 axes, 2 spears and an archer in the city or guarding workers nearby. Against that we have 4 swords, 6 axes and 2-3 Immortals available to move. And our swords would get 25% against those fortified axes on the hill - without walls. The power graph makes it look almost plausible, but for the moment, no.

We're banned from using gold countdown timers or such tricks as including cities on the target border in the offer, so there's not a lot we can do. Fish-fish? Stone-stone? I have no idea what the latter would mean, but might try it anyway ("I agree, but not just yet"?).




I have concentrated what force we have, and I've begun shuffling some units from the Superdeath border across, although that is also to support our settling push into the filler space. We are 2t from Construction, which might change things, but realistically we're 7-8t away from getting any into an attack position. Even then, it would probably only be three, four at most. Enough to mess up an attack on us if used well, but for an offensive?

Charriu is right in that we have to do something. By the time we get cats in numbers (10t?) I suspect OT4 will have them, and will have been able to use that stone he's grabbed to get walls up. It's possible that there is already no reasonably thing to do but a "hail mary" attack, but it's not clear to me that we're at that point yet. Aside from anything else, if we can get HBR we can match Praetorians in base strength; get that and archery and we have fast units that are strong enough to count. And I do think that we can get there before OT4E has a chance to pull too far ahead. He'll have them too, but nothing better and not in hugely greater numbers. Charriu should also be able to do that, as his GNP is much improved.

[shallow_thought]

Last night I dreamt that we had just built our first pair of longbows, and installed them as garrisons in our border cities with OT4E. It made me feel warm and safe. This game may be getting to me; it's still a shame it wasn't real .

So, sleep and some calm advice from Hitru have reinforced my natural cautious instincts. We need to focus on expansion and getting our economy ticking over better. OT4E is ahead in land, but not by that much. We don't need to panic. The one risk I am taking is mining the copper. We'll also be roading it, which OT4E might consider a tad aggressive. But if he pushes hard in the next few turns we can meet him with a cat or two...




Offensively the terrain around Rome favours OT4E. Option A is to stage at JS2 and attack across the copper in 2t. However, he has sight of the city centre from roaded tiles, even after we pop borders. Also, we end up sitting on flatland outside the city and attacking from there. Hmm. Option B is to stage on the tile where we are now, out of sight. It then takes 3t to attack, and we still end up attacking from the flat. Option C is to go around and try to attack from the mined hill in RFS-81's (current) territory. If we had OB with RFS-81 we could approach (with worker support) without ever having to spend a full turn on flatland. Sadly some of the approach cannot be hidden (roading the hill W of the "grab" sign for example, will always be visible). And it leaves our army very badly placed to respond to a counter-atatck. So, more thinking required. And more troops, and better tech.

I also took a look around Charriu's far border. If that's the stack he was considering hitting OT4E, I'm glad we didn't try it.




Hitru also had time to come in and fix up the tile micro, which helps the economy a bit. We get Construction next turn. We're currently second in all the demos, but not by a lot, except the gap to OT4E's soldiers. However, I think different people are actually in first in each key category, so that's not too bad at all overall. Another reason not to panic. Once Construction is in, the plan is a quick diversion to Meditation, and chop a monastery and a missionary out of CC, followed by some more missionaries. Get a Monastery at the cap for science, and start spreading this so far worse than useless religion to key cultural pressure points (EE first - still want those gems - they are now at 51/48 [sic.]). We also founded a filler city. It's basically all about getting culture and a hill fort into the space between us and Superdeath/Magic Science. I hope we can get the second ring tiles quickly; it's not a great city, but does have chops for a quick start. We'll be getting a settler out for the banana site, and then one to go try pinch the island.




Pinching the island will require us to declare on RFS-81. I do wonder if OT4E can be fooled into thinking I'm actually planning to take the capital, and offer us an opportunity? I doubt it. Much more likely  is that Charriu will think that is our plan, try it himself, lose a bunch of power and get stomped by OT4E. But I could be wrong.

I still owe the lurkers a city breakdown from a few turns ago, and the third part of my diversion about working out the payback time for a bank. Hopefully I'll get round to that soon...

[shallow_thought]

Magic Science has gone for a Golden Age and converted to Hereditary Rule. Seems a bit early to me, but it does mean he's ahead of us along the Feudalism/Civil Service/Guilds track. Charriu has converted to Judaism without the benefit of a GA or SPI. Hmm. And OT4E has built the Great Wall. A slightly odd set of turns all round there to my mind, but what do I know?

We finally got a Hinduism spread, and it's to the capital, which is good news. EE would have been even better, but this probably means we can skip building a monastery at CC and just build one at the cap instead. Right now the diversion to pick up Polytheism is really not working out. But we needed stone anyway, it wasn't much of a cost on top of that and we should be able to start to finally make use of it at some point in the next 10 turns or so.

However, we do have other things we'd like to do with the cap... the big pointy stone tomb markers are still available, and worth a lot of failgold, so we're going to put the whip overflow from the market into them, and then a similar thing if we do manage to start building a monastery. Failgold is the aim, but if by some miracle we did land them Representation could really suit us.

Annoyingly anything more than just putting immediate overflow into the 'mids may have to wait: the cap is probably going to need to build wealth within the next couple of turns. I've crashed the economy, again, so we're struggling to get to Calendar. With our core cities busy building we 're running at about 10-20% break even. Moai finishes EOT, so BeaB can start pumping money, and the cap will have a market from next turn, both of which should help. In a BTS game I'd be rather crudely lining up 2- or even 3-pop whips of markets, but in RtR, and on a lowish food map by PB standards? Hmm.

So, can we afford this latest city? It's deeply sad, particularly as the delay on calendar means that we're probably going to have to farm the bananas, but we should be able to get a barracks out of it quite quickly and start getting some culture spread. It's primarily a defense guarding our core. The extra maintenance is going to hurt though.




It does feel that we're going a little backwards here at the moment. We're still right up there in crop yield, but it feels as if our larger number of poorer cities is failing to keep up in GNP. And we can't easily turn our food and queues into an army and do anything useful, because we're behing OT4E. After a few turns of seeming to catch up, he's off again. I'm wondering if that Mfg spike implies forges. And then there's the ever climbing power. We do have cats in build queues - one or two will be popping out in the next couple of turns - but we're not going to be able to go on any offensive any time soon for fear of Rome .










Oh, and you'll notice the lack of the other posts I keep promising. Sorry again.

[shallow_thought]

A quiet few turns up to 119. Technically we are at war with RFS-81, but only because he refused us OB. His cap is too well defended for us to fancy trying to take it. More precisely, it would be a big investment in hitters that could soon be obsolete, and risks losing a bunch of cats (which we don't actually have yet) for no guaranteed gain - OT4E and Charriu would be unlikely to sit on the sidelines. (Screenshot from t117)




So, we're bringing our galleys back, and loading one with a settler and an axe. If RFS-81 is feeling bored and vicious he could build a galley and load a couple of axes. Or two, and load four ... with nothing else to do it is a risk. But not mitigated much by sending one or two more garrison units, so we'll probably gamble. We'll then need peace to get trade routes to it, of course, which is not guaranteed. I'm not sure I'll offer full peace again, and would RFS-81 go for another ceasefire? We'll see. (Screenshot from t118)




You'll notice the rather significant drop in Calendar research time between the first screenshot and the next one. Wealth builds are fun, particularly with Moai online. Having the cap rigged for growth and commerce is also a help. In fact, I was so surprised with the speed that I've almost completely failed to get workers into position to work on two of the key tiles (circled). The silk near BeaB is getting a single turn of pre-chopping, the dyes near CC none at all. I'm better place for getting the bananas done, but we're going to have a couple of cities going unhappy until the first plantation comes online.




Those bananas are critical for the new city of Lemony S (briefly called Proximate Peril because I got ahead of my self without noticing), but those happy resources are worth three faces at the cap. And it could get better. We're at 50/50 on the gems tile so can hope to grab it soon. I've actually walked a worker onto the tile to start roading - let's hope that doesn't annoy Superdeath too much . We've also got sugar in the second ring of JS2. Whether we'll be able to grab it is ... questionable. Both our city and Antium (I think) will expand next turn, and while we're chopping a monument to match OT4E's free one (damn Stonehenge) he'll probably be building an AGG barracks himself to match ours. He doesn't have the chops we have though, so we could invest in another building. Ideally it would be a monastery, as a library is not very useful here, but I don't know if we can afford the delay while we get religion spread. Meditation will be our next tech, and the cap will push for a monastery and some missionaries straight after, possibly whipping for overflow into Pyramids on the way, making use of our new happy to gain hammers in the short term.