The Hills Send Back The Cry [SPOILERS]

[Alhazard]

You could write a primer on how to use Solver in Excel to figure out pop? Pop guessing is the worst part of C&D .

[El Grillo]

Sure, and it's great to see a new lurker post in here My method has a lot of limitations, mainly because of how much information you need to already have to get reliable results. Let's look at the numbers for the most recent turn as an example.

I'll have to spoiler this for length

First and foremost, you have to know the population figure for the player you're analyzing. In practice, this is only feasible for the Rival Best and Rival Worst - I've tried to back into the Rival Average for the third player in this game, and that led to the problems I was having earlier.



In this case, and in most games, the Rival Best (868000) and Rival Worst (807000) are relatively close, so there's some guesswork involved.



We're going to use the Top 5 Cities screen to fill in some blanks.





Let's start by assuming that the Rival Best population is Adrien, from previous turns.



Adrien has 7 cities. From the Top 5 screen, we know that he Timbuktu is a size 6 city. Furthermore, I personally know that he planted Tadmekka last turn, so it has to be size 1. We can then fill in the first two rows.



Like so. Ideally, we'd have more knowledge, but at a certain point this becomes self-defeating :D Now, let's put Solver to work:



We set the objective to be the derived population, the variable cells being whether each city is or isn't a particular size. The constraints are effectively that each city is one and only one size. Use the Simplex LP method - the other two that come with the default Solver plugin are not great for this kind of network simulation. So now, let's try it.



We have a possible solution. However, this is where we need to double-check: does the data fit another player, or is this a unique fit? Furthermore, from past analysis, do the results make sense? This is what was troubling me earlier - normally cities either stay the same size, increase by 1, or decrease by some number. If your result says a city grew 2 or more sizes, throw it out and try again using different assumptions.



For example, let's test if Adrien fits the Rival Worst population of 807000.



Lo and behold, we find a solution... but wait! This result says that Adrien has a size-9 city, but from the Top 5 Cities screen and previous-turns tracking and from the gamestate in general, we know that can't be possible. This is where you have to exercise your judgment. In fact, after double-checking, the Rival Best numbers don't match Adrien either! I know from previous turns that two cities couldn't have grown that large. Before you despair, the good news is that each population total has only one pop distribution corresponding to it, provided you know the number of cities.

So this means Adrien is neither the Rival Best nor the Rival Worst in population. Now, since this is a four-player game, let's try him using a population figure derived from the Rival Average: Average * 3 - (Best + Worst) = Other. In this case, 847000 * 3 - 868000 - 807000 = 866000.



Success! This matches the data from previous turns in a way that the other two results don't, so I feel confident in stating that is in fact Adrien's population distribution on T62. Let's check this postgame, for science!

Now we can match the other two players:



Khan has 8 cities. From our wars, I have vision on a few:



I also know that his most recent city in the center, Mount Pleasant, is size 1. Let's test him as the Rival Best at 868000. We can then fill in the first 4 rows for his table:



We get this result:


Again, the size-9 city disqualifies this result. Let's try him as Rival Worst at 807000.


Success!

That means Ginger is Rival Best at 868000. He has 6 cities, and we know 2 of them are size-7 from the Top 5 Cities. I highly suspect his newest city is still size-1, but I'm not sure, so I'll leave that one blank.


Results in:


This fits with the previous turn's distribution, as we'd expect (since it's the last one we're calculating).

As you can see, this method relies on having a couple of good turns where you can confidently assign a population distribution to each player - this makes it possible to confidently rule out erroneous distributions in the future. In general, I'd recommend it in a PBEM setting with few players, where ideally you have city visibility (through war, open borders, map trade) for one or more players, but before you have visibility on all players' cities. Furthermore, it's a lot more work than I first expected, due to the interpretation and trial-and-error. I also don't have the expertise to make use of the data well enough to justify doing it every turn, especially if we keep this turn pace up!

For the rest of you lurkers, here's each player's pop total:

Adrien: 35
Khan: 33
Ginger: 31
Me: 28 (after whipping away 5 pop)

[El Grillo]

T63:



In the north, there's no sign of a Khan city yet. That could mean a few things, in decreasing order of likelihood:
1) His Settler moved onto the Galley last turn, so this turn he could only unload it.
2) He preemptively dropped off military units to secure the landing, and is going back for his Settler now.
3) The Galley was empty. Perhaps he wanted to confirm that it was indeed Stone on all of the islands, or he wanted me to know that he had a Galley.

If scenario 2 plays out and he dropped off 2 Skirmishers, then we won't be able to force him off, but we can prevent him from hooking nets. I do believe we've banned blockades, and my Galley can't get there in time to take a coin-flip on sinking his Settler, so if he has a Settler lined up, then this was quite well played by him.

If scenario 1 plays out, then I can load up either Axe/Impi or Axe/Axe and go for the raze - his Galley could potentially bring reinforcements in before I can attack, but I can keep the Galley out of sight next turn, and I always have the option of declining combat if I see 2+ units in there.

In either case, my Settler from Silent Walk is on its way, either to board the Galley or to head north for the Gold/Fur site.




In the south, Ginger has finally approached my borders with a Chariot, presumably to scout while we still have Open Borders. I may build and send a Missionary his way to return the favor.




For a domestic summary: I'm 1-turning Archers out of Onramp to garrison my new cities and free up some Impi, Stuntsheet One and Tossing&Turning will hook their Fishes next turn, and my Settler will arrive in the north in 3t.

Graphs:

[ReallyEvilMuffin]

T63:



In the north, there's no sign of a Khan city yet. That could mean a few things, in decreasing order of likelihood:
1) His Settler moved onto the Galley last turn, so this turn he could only unload it.
2) He preemptively dropped off military units to secure the landing, and is going back for his Settler now.
3) The Galley was empty. Perhaps he wanted to confirm that it was indeed Stone on all of the islands, or he wanted me to know that he had a Galley.

If scenario 2 plays out and he dropped off 2 Skirmishers, then we won't be able to force him off, but we can prevent him from hooking nets. I do believe we've banned blockades, and my Galley can't get there in time to take a coin-flip on sinking his Settler, so if he has a Settler lined up, then this was quite well played by him.

If scenario 1 plays out, then I can load up either Axe/Impi or Axe/Axe and go for the raze - his Galley could potentially bring reinforcements in before I can attack, but I can keep the Galley out of sight next turn, and I always have the option of declining combat if I see 2+ units in there.

In either case, my Settler from Silent Walk is on its way, either to board the Galley or to head north for the Gold/Fur site.




In the south, Ginger has finally approached my borders with a Chariot, presumably to scout while we still have Open Borders. I may build and send a Missionary his way to return the favor.




For a domestic summary: I'm 1-turning Archers out of Onramp to garrison my new cities and free up some Impi, Stuntsheet One and Tossing&Turning will hook their Fishes next turn, and my Settler will arrive in the north in 3t.

Graphs:

If Khan has nothing there, how many turns till you settle it?

[El Grillo]

The Settler ended its turn in Onramp. If I were certain that Khan had no units there or en route, I could load it from the plains hill W-NW of Onramp on T65 and settle on T67. Of course, that opens me up to Khan bringing 2 units and going for a raze, so a more cautious play would bring 2 units over and then settle on T69.

[El Grillo]

Khan sent me an email saying that he had to work late, but would play the turn in the morning (in about 3-4 hours), so I'll stay up and play it. While we're waiting, my friend and I had a chat about our medium-term plans.




The first question concerns the GPP accumulating in Initial 64. We currently have 38 Prophet points and 6 Merchant points, increasing by 2 Prophet points per turn, and we need 134 GPP. With no changes, it won't get there for 45 turns, which means we could push another city in front of it like we did with the Merchant at Onramp. That would give us the opportunity to generate a Scientist, Artist, or Merchant at near-100% odds from another city. Alternatively, we could hire lots of specialists in Initial 64, accepting a ~35% chance of a Prophet. Lastly, we could build cheap SPI Temples for additional Priest slots, hire Priests, and accelerate out a high-odds Great Prophet.

From a planning perspective, we'd both favor more certainty, and we're not keen on wasting the accumulated Prophet points, which leaves us with the third option - finishing a Confucian Temple, bringing over a Jewish or Hindu Missionary (we'll want more religions for Monasteries at some point, once we have the Worker labor to put down Cottages and the satellite cities to grow them) and then hiring 2 Priests to get a Prophet in ~15 turns.

The question then becomes: what do we do with a Great Prophet 15 turns from now? The options are the Confucian shrine, bulbing Theology, and starting a Golden Age (settling it seems strictly worse than building a shrine). The shrine is the safe, incremental option, worth ~15-18 gpt from the cities I plan on settling, and maybe more if I can spread Confucianism to Ginger. We know he already has at least one Buddhist city, but he hasn't converted. Theology is a 502b tech that unlocks a useful civic, a much-diminished-value religion, the AP, which would have a reasonable payoff time, and Hagia Sophia, which I would skip, unless I can find some truly broken thing to do with 200% effective Serfdom/HS Workers. Finally, a Golden Age would come at a time when most of my cities have their basic Granary/Courthouse/Lighthouse infrastructure, and I'd have 3 cities with large food surpluses capable of generating Great People 3, 4, and 5 (Silent Walk, Stuntsheet One, and Tossing&Turning). Truth be told, I have little experience or comfort with knowing when to trigger Golden Ages and how best to make use of them.




The second question concerns our disposition towards Khan. It seems all but certain that he'll be the first target of our war efforts, especially if we can seize the naval base in our contested sea. We also have a ticking cultural time bomb at work at Marchup Cadence - there will be a window where we'll gain control of his city's first-ring tiles, forcing him to withdraw or face a catapult-backed alpha strike. The duration of the timing window will depend on whether or not Khan gets more sources of culture into Halton, but we estimate that it will open in ~20-25 turns. It will then remain open for at most ~25-30 turns, until his Monument catches up and pops his 3rd-ring borders. That essentially dictates the terms and tech level of our attack - Horse Archers, Catapults, Impi, and Axes. My friend and I both agree that we should make the most of this opportunity, but we differ on the extent of our war goals.




My friend wants to research HBR, Construction, and Calendar, and set up a blitz on Mount Pleasant, Khan's Marble city. The goal would be to build a road up to the city, capture it (and hook Marble, despite resistance, counter-intuitively), and use it to build the Mausoleum in one turn. This could be done by chopping all five of the remaining Forests at Initial 64 and getting 34h from overflow and production.

On the other hand, I think Khan will build the Mausoleum himself in his core, and that should be our goal - a conquest/partition of his corner of the map. My friend argues that Khan won't feel secure enough to build a Wonder when he's also aware of our timing window at Halton, and that an all-out war benefits Adrien far more than it does us. My reply is that a flashy claim of the Mausoleum puts a far larger target on our back, has a high opportunity cost, and carries much more risk overall. I can definitely see both sides of this argument, and I'm sure we'll revisit it as time goes on.

[El Grillo]

Other plans of varying seriousness/feasibility include:
A) Tech Meditation and Aesthetics. Chop out Shwedagon Paya, use the Prophet for a Golden Age, swap to Rep/Caste/Pacifism and use bulbs to tech to Guilds, then swap to Vassalage/Theocracy for 9xp Knights. Segues into Banking for Rep/Caste/Merc.
B) Bulb Theology, build the Apostolic Palace, tech Paper, build the University of Sankore, and spam Temples and Monasteries. Divine Right/Spiral Minaret optional.
C) Skip the attack entirely, tech Monarchy->Feudalism->Civil Service, use the Prophet for a shrine, and build in peace.
D) Tech Theology. Skip Monarchy. Use the Prophet to bulb Civil Service.
E) Build a fleet of Galleys on the outer sea and launch a four-pronged invasion of Khan.

[ReallyEvilMuffin]

Nice culture play there. How much do you feel he values that front city?

[El Grillo]

Quick update, no screenshots until later tonight:

My read on the situation with Khan is that we've reached an uneasy stalemate, given our current military tech, at the border, and we've both decided to expand elsewhere - Khan into the center of the map, and us onto the outer coast and inner islands. The difference is that we now have one militarized front, and Khan has three. That's why I feel safe taking the northern island from him. Now, on land, I'm not as confident about predicting what he'll prioritize defending, but perhaps if he recognizes that Halton is indefensible relative to his other fronts, and arguably less valuable, then he'll give it up without too much of a struggle.

My friend played the turn and says that Khan settled the island, that there are currently no units visible there, but that his Galley is in a position where it could reinforce the city next turn with one or two units. He doesn't have visibility on our Galley. Fingers crossed that his Galley's empty or only carrying one Skirmisher, which wouldn't get any fortify bonus on our next turn.

[El Grillo]

My friend played another turn. Khan dropped off 2 Skirmishers and moved his Galley NE of the city to block off our approach, so the attack is off. We withdrew our Galley back to Sproul Steps. Beaten by a turn, and we could've made it by starting the Galley immediately at Sproul Steps, instead of putting hammers into the Granary. Lesson learned - make sure you know what you want, and then do it.

Any attack on Khan will be risky while he holds that city. My friend says he's going to run some sims with Horse Archers, but I don't believe you get withdrawal odds when attacking off a boat, so it's definitely going to be messy. Might even have to wait for Knights :S