Oddly, I am still able to play all of the OpenDev scenarios.  I like this.

Abstract

I read most Scenario 3 (Hold the Fort) threads here and on Steam, to about page 4.  Some OpenDevils (heh) said they counterattacked early, captured both Angkor and Tenochtitlan, and explored the entire map, to the far NW corner.  I replicated that.  It's not even hard, given that you "cheat" by knowing the AI's exact order of battle.  Basically, survive 1 big showdown battle at Oxeneford, and heal as you walk SW toward Angkor.

I have delved deeply into the Stability and Food numbers, and reverse-engineered their formulae (+/- 1 due to round-offs, grumble).

Stability scales linearly(?) with population and attached territories.

Food scales quadratically with population only.

I'll go over this, and what it means for your large-city layout planning.  Basically, we continue to build +Stability and +Food all game long, or we'll grow +1 pop and drop down -2 tiers from Growth to Starvation.  (Corollary: Beware of triggering Agrarian Mother's Milk! It isn't free!)

Finally, HK's Extensions also have adjacency bonuses, and Infrastructures add to them.  We haven't explored this much, given that the time-limited scenarios guided our attention elsewhere.  I'll doodle some preliminary geometric solutions to HK's adjacencies.  Briefly: small triangles?

First I shall elaborate on HK's math. Then I'll apply it to a Scenario 3 replay, and we'll explore to the NW corner.

1.  Stability, Population, and Attaching Territories

Stability is new to EL/ES players.  In OpenDev, there are only 3 tiers of Stability:

00-29: Unrest

50: baseline for all cities

30-90: Under Control. No bonuses or maluses.

91+: [edit] Reliable. (see post #5 in this thread)

I suspect the full badness of the Unrest tier was not implemented in OpenDev.  You can (ahem) exploit that.

Population and attached territories lower stability.  These maluses are summed as the "City:" line in the Stability tooltip.

• -(3 to 7) Stability per 1 population (see table)
• -20 Stability per attached territory.  This is the major cost of attachments!  It's a fair trade: You expect +1 territory to bring 1 full hex ring of FIMS, plus its luxury and strategic resources.  Oxeneford's Horses territory gives +55 FIMS, while Londonia's Marble territory gives +88(!) FIMS.  -20 Stability is the price you pay.

I tabulated the actual numbers for population 10-12 and 14-15 in Scenario 3, and population 1-6 in Scenario 1 Towers of Babylon, then reverse-engineered a progression.  Italics are interpolated numbers from my progression, while bold are from actual HK game play.

(text-editor fume: it does not display a table's Header row -- I must type it in again as a normal row.  I shake my fist at it)

I confess I reverse-engineered the strides to make the sums come out exact.  The bobble at 4-5 population could be accumulated round-off errors from a true value of -4.5 or so.  This might be a very wide parabola, so that it looks only slightly supra-linear.  EDIT: Added population 13.

The tech tree teases us with several +Stability buildables.  I'll abbreviate Ancient/Classical/Medieval to I / II / III, indicating Era.

We're seeing only a fraction of each Era, esp. Era III.  I expect many more techs and rearrangements.

+2 per territory: Public Hygiene (Infrastructure) { L1 = I.Irrigation.Public Fountain, L2 = II.Hydrology.Aqueduct }

These each give you a -10% discount on the -20 per territory Stability malus of attaching the territory in the first place.

(Ob. joke: if you complete them all through Era X, you get -20 +20 = 0 per territory, and then you attach the rest of the universe with no further malus.  Legend has it that this is what black holes are: ancient civilizations that have completed Era X.)

+5 per adjacent Extension (of any type): I.Calendar.Commons Quarter.  Crazy good if you (literally) build around it. Put it in the center of a hex ring of Extensions, and it generates max. +32 Stability by itself, +6 more for the 1 Public Servant slot if you assign 1 pop to it.  But the opportunity cost is high: if that center Extension were mono-type (identical to the 6 around it), it could have produced 12 adjacencies instead (6 inward, 6 outward).  Choose!

In Amplitude's own example, in the thread HUMANKIND - Synthesis tables and tips for Open Dev, entry Exemple of proximity bonuses scheme, you can see they also put a Commons Quarter in the center of a hex ring of Extensions, for +32 Stablity.

+1 to adjacency bonus: Entertainment { L1 = II.Rehtoric.Theater } ... maybe it shall go to L5 = VII.Internet.Cat Videos

This is a subtle, but recurring, pattern in HK's economic model, so we should promote it to 1st-class and learn it now.  HK is not Endless Legends (EL), and shall handle adjacency differently from EL. In particular, many Extensions have an adjacency bonus of +k (usually +1 per adjacent Extension of identical type).  A triangle of 3 identical Extensions would give each Extension +2 income from adjacency (because each vertex in a triangle has 2 neighbors). In turn, some Infrastructures give +b to a specific adjacency bonus.  That scales linearly over the number of adjacencies you've built. Commons Quarter has k = 5, and Theater gives k += 1.  Presumably, additional levels of the Entertainment family will boost this further, up to maybe a max of k = 5+5 = 10 at L5. Then 1 Commons Quarter might give 2 + 60 + the 1 Public Servant slot = 68 Stability, and you could keep maybe Edo or Rome in the Under Control band.

This two-tiered model is very intriguing, and makes me want to buy HK just to play without turn limits.  You must build geometric adjacencies on the map, and build Infrastructure families to increase the multipliers. Think of it as a pinball machine, hehe. Keep the ball alive to amass bonus, and go for specific targets to collect bonus multipliers. I'll revisit this in a later post on adjacencies.

+5 per luxury resource, on all cities (not just the one it's attached to). Since most territories will have 0 or 1 luxury resource(-- ?), this might average out to +3 Stability per territory, or a -15% discount to the Stability attachment malus.

+5 per Repeatable on City Center: III.Rhetoric.Games. Repeatables are another HK pattern. You can build any number of these (at increasing industry cost). The gains are mild, but unbounded, limited only by competition for each city's single build queue.

+3 per Castle -- really?  Heh!  II.Standing Army.City Watch springs this surprise upon us.  Terminology is significant!  It seems that you attach territories to a city, grit teeth and build Castle (or English Stronghold?) in each non-city territory, and then -- this tech pays you for having built those Castles. In that case, it's yet another mild discount of -15% to the Stability malus of attachment.  I guess your City Center isn't a Castle, and so you don't get this bonus in your city. That's OK, since your city center already has the Repeatable.

To summarize: Stability decreases roughly linearly with population and attachments.  Dropping into the lower band of Unrest will likely be a bad thing.  Thus, every city will feel a small pressure to build ahead of that curve.

Next: Food pressure is even worse!

2.  Food and Population

In HK, food and growth rate are handled as a two-stage pipeline.  Food puts you into a growth tier, and the tier gives your growth rate.

2.1  Growth Rate Tiers

There are 6 tiers of growth rate, based solely on your city's total Food:

-21 and lower: Starvation.  -50 Stability malus.  It says: Population value will decrease, but for OpenDev it gives zero population change(--?).

-20 to -1: Threat of Starvation. -50 Stability malus and zero population change.

0 to 9: Stagnation.  Zero population change.

10 to 50: Growth.  +1 population every 8 turns.

51 and higher: Super Growth. +1 population every 4 turns (= 2x the Growth rate).

In Endless Legends (EL hereafter), Food directly gave your growth rate.  This was fun to abuse at the end of games, when you generate +4-5k food per turn, use it to grow +1 pop per turn, and discard the rest.  That's probably exactly why Humankind doesn't do it that way.

2.2  Food Consumption Rate

Population eat food, but at a (roughly) quadratic rate (see table). That's a refreshing shock to those of us accustomed to the "-2 Food per population" rule in many other 4Xes (including EL itself).  Throughout Scenario 1, you may have felt that food was an afterthought, and why bother.  That's indeed true from about 1 to 5 population.  But then in Scenario 3, you activate Agrarian Mother's Milk for 10 +2 = 12 population in Londonia, and pow! Your Food drops by -60! That's the new normal in Humankind. Anticipate this curve, and you can expect to keep building +Food improvements all game long, as your cities keep growing.

I reverse-engineered a two-step progression, which gives a parabola.  I'll borrow the terms acceleration (~constant) and velocity (= the sum of acceleration) to emphasize this.  Then food consumption corresponds to position (= the sum of velocity).  This is shown as the "City: -N Food" line in each city's Food tooltip. EDIT: Added population 13.

With this growth rate in mind, Agrarian Mother's Milk can give you 2 (or even 3!) food consumption increments all at once.  That can drop you from 1 (Stagnation) to -101 (Starvation) with one click!  We're all surprised by it once.  Later, we'll know to build many +Food sources, and choose our growth rate.  (In my Scenario 3 replay, I attached both territories and abstained from Mother's Milk for 6 turns, until its bonus grew to +3 Londonia/+2 Oxeneford. So I could skip only from 11 to 14 or from 12 to 15, and I lack data for 13 population. I shall predict -184 :) EDIT: Confirmed!

2.3  +Food Buildables: Adjacencies and Multipliers

Food is part of FIMS, which you exploit from tiles.  In addition, various buildables give +Food.

+5 per territory: I.Calendar.Granary.  Generally, this category of Infrastructure rewards you for attaching territories (and is dead weight if you don't).  You also get +4 Food, +4 Industry, and +2 Money per territory for the 3 tier-0 techs (which are not in the tech tree).

+1, +1 per same adjacent: 0.Farmers Quarter. (Ob. joke: What's the Roman numeral for 0?)  Anyways, this reflexive (self-) adjacency immediately suggests small triangles of 3 = 3 + 2*3 = 9 Food, full hex-rings of 7 = 7 + 3*6 (every perimeter hex has 3 neighbors) + 6 (the center hex has 6 neighbors) = 31 Food, or any subset of a full hex-ring.

+1 on a Quarter, +1 on its adjacency bonus: The Animal Husbandry Infrastructure family is your bonus multiplier for Food.  Elsewhere in the tech tree, the Coal Energy family is the multiplier for Makers Quarter and Industry.  Both families work the same way: Each level(--?) adds +1x to your entire hex-ring's intrinsic production (= ignoring all tile FIMS). That is:

- At L1 = I.Domestication.Animal Barns (or L1 = 1.Bronze-Working.Forge), each Quarter earns 1+1 = 2 by itself, and each same-adjacency earns 1+1 = 2.  So you get 2x of the entire intrinsic production.  Your full hex-ring of 7 now generates 31 * 2 = 62 intrinsically, not counting whatever it harvests from free tiles.

- At L2 = II.Craftsmanship.Charcoal Kiln, you get (1+2)x = 3x = 93 Industry!

- At L3 = III.Furnace Steel.High Furnace, you get (1+3)x = 4x = 124 Industry!

- ... At L6 = VII.Grand Unified Theory.Coal Fusion (haha), you get (1+6)x = 7x = 217!  After that, I guess we drop coal into miniature black holes.  It's still Coal Energy!

Corollary 1: If you have only 1-2 Quarters in play, these Infrastructure families aren't worth their build cost.  So in Scenario 1, they're a bad idea.

Corollary 2: When you've built 8-15 Quarters, then you also must devote some of your build queue to these families.

You can't maximize the product a*b by keeping b = 1 forever.  So at some tipping point, Corollary 1 gives way to Corollary 2.  I look forward to exploring the timing of that transition in my own huge cities :)

I think this two-part stacked economy is HK's subtle genius, and is already a contribution to the 4X genre.  At first, I was not impressed by II.Craftsmanship.Charcoal Kiln's "payoff": it's a tier-2 tech that requires 1 strategic, and that's "all" you get?  But think of it as the "3X" bonus multiplier on a pinball machine, and then it makes sense.  In fact, it's a neat way for you to pack economic density into a city's constrained layout.  When you can't build wide(r), you can keep building taller, by making your existing Quarters more powerful.

This is already very different from Galactic Civilization III's adjacency bonuses, which is probably a good thing for both games.  It's also different from, and much more generous than, Endless Legends' relatively rigid 2xN stick city layout as the optimal (and thus sole) solution. Large HK cities will look utterly different than EL cities.

2.4  Super Growth in Babylon

In my Scenario 1 replay, I built 2 Farmers Quarters (side-by-side, of course :), and first reached Super Growth on turn 17.  So I grew to 2 population on turn 9, 3 on turn 17, 4 on turn 21, 5 on turn 24, and 6 on turn 29.  It may be possible to improve on that, if you aggressively use Money to buy out Farmers Quarters.

[_] Challenge: Get 7 population in Scenario 1 (Towers of Babylon).

3.  Scenario 3: Attach to the Fort!

Aside from Scenario 3's value as an exercise in siege warfare, it's also a tantalizing sneak peek at the Medieval (Era III) economy.  You can build 2 Extensions + 2-3 Infrastructures in Londonia in between Longbowmen (hah), and explore their FIMS impact.  Is Londonia, in fact, a good city layout?  What would you have done differently?

At start of scenario (on turn 120), there are already interesting, landscape-altering decisions to make:

• Attach the outpost territories to the cities?  Briefly: Yes, attach 1-2 territories to every city. This is the current general solution, given what we've seen in OpenDev.
• What shall each city build 2nd?  (1st is always Longbowmen, of course)

The Stability and Food data can partially inform our decisions; but there's more to learn.  In this post, I shall deeply explore the FIMS benefit of attaching the outposts.  Then we can simplify it to a rule.  I trust it will be illuminating to work out one specific example in detail, so that you appreciate exactly where the benefits come from.

Disclaimer: I got the inspiration of attaching territories on Turn 120 from a previous poster.  Alas, the OpenDev Scenario 1, 2, 3 threads have been unstickied.  When I find that thread, I'll add a citation.

3.a  Start of Scenario Inventory

At start of scenario (turn 120), you own:

• Londonia (10 population, 2 territories), -270 Money to attach a 3rd territory
• a Marble territory north of Londonia (the Artisans Quarter on Marble is not yet built)
• Oxeneford (1 population, 1 territory), -135 Money to attach a 2nd territory
• a Horses territory south of Oxeneford (the Horses is being ransacked by Khmer AI, but you can rebuild it later)

• -m Money as a one-time fee. This is shown in the Attach tooltip. Anyways, almost every Outpost action has a Money cost.
• -20 Stability in the city, per territory, permanently (described previously).
• Full hex ring of FIMS.  The Outpost instantly becomes an Administrative Center, which is an Industry Extension, creating 2 Industry even if the tile previously had no yield. All 6 adjacent tiles become Exploitations (but see next). Like a City Center, it harvests all 4 FIMS resources from its Exploitations.
• Every built Artisans Quarter on a Luxury Deposit, or Mine on a Stategic Deposit, is also an Extension, which harvests its own tile's FIMS (but not its adjacent tiles). This supercedes the previous item, so if a Deposit was adjacent to an Outpost, then its hex is counted as an Extension, not an Exploitation.  In that case, the Administrative Center would have only 5 (or fewer) Exploitations.  Corollary: Prefer to build your Outposts not adjacent to any Deposits, so that they nab a full 6 Exploitations each.
• Merged build queue. Your city can (and must) build any unbuilt Mines and Artisans Quarters using Industry instead of Money.  (This could be a reason to not attach immediately!)
• +1/+2 Extensions and cap. Your City gains +2(?) Extensions to its Extensions cap (shown in its city menu, directly below its name). Then the Administrative Center promptly consumes +1 Extension from the raised cap. So if your city was at 8/8 Extensions and cap before attaching, it goes to 9/10, and you can build 1 more Extension of your choice later. Note that Artisans Quarters and Mines count as +0 Extensions against your cap, so you can build all of them without affecting your cap.
• More space to build. Since you must construct an Extension in an Exploitation hex, and your new territory gains 6 (or fewer) Exploitations, it follows that you can immediately build new Extensions in your new territory. This can give you better FIMS, more space for a new full hex ring (hehe), access to special hexes, and so on. Corollary: Plan ahead for this when building (or relocating) the Outpost!
• +1 Farmer, +1 Worker, +1 Trader, and +1 Researcher slots in your city. If you've assigned maximum population to Money (for example), your max just went up.

3.b  Londonia Attaches Unbuilt Marble

Summary: Londonia gains +88 FIMS, from 233 FIMS to 321 FIMS, or a stupendous +37.8%. I'll take that for only -20 Stability!

In more detail:

40f, 101i, 44m, 48s = 233 FIMS (with a 1-4-3-1-1 population assignment, in B-F-I-M-S order) before attaching.

52f, 139i, 44m, 86s = 321 FIMS (with a 1-1-3-0-5 population assignment) after attaching.

Note that the max. 5/5 Researchers wasn't even possible before attaching (because attaching added +1 Researcher slot), so direct comparisons are not possible.

Now we walk through every point of that FIMS gain.  This analysis should be done at least once, and hopefully not again.

"Population:" +2 FIMS.  I proritize Science, to finish Heavy Infantry ASAP for Great Swordsmen, so I shift the new maximum 5/5 Researchers into Science. I moved -3 Farmers x 4 Food each and -1 Trader x 6 Money to +4 Researchers x 5 Science, which is a net gain of +2 FIMS.

"Infrastructure:" +18 FIMS.  These are further subdivided into:

• Per-territory.  +9 Food (Millstone, Granary), +4 Industry (Pottery Workshop), +2 Money (Tanning Racks). I exclude +2 Stability (Public Fountains) because Stability isn't in FIMS.
• Global.  +3 Science (Alchemist's Workshop*).  * This teaser is not in the OpenDev tech tree.  It also seems to miscalculate 10% of 86 Science = "+7", not +8.  Peeking further ahead, I think the 86 we see is actually (100% + 10% + 15%) = 125% of a base value of 69 Science, and we get +10% here and +15% later.
  

"Extensions:" +14 FIMS from +3 Extensions:

• +2 Industry Extensions for +9 Industry.  These are exactly the Administrative Center (+2i) and the Iron Mine (+7i, but it's hidden behind the Iron Mine icon). The 7 Industry is further broken down as { +1i on Exploitation (Lumber Yard), +1i on Mountain, +5i on Strategic Deposit (Stoneworks) }. But does Lumber Yard apply to an Extension hex?
• +1 Science Extension for +5 Science.  This is also the same Iron Mine. As an Extension, it harvests all FIMS in its hex. The 5 Science is intrinsic to all Strategic Deposits(-- ?).

"Exploitations:" +43 FIMS from +17 Exploitations:

• +14 Food from +6 Food Exploitations.  12 Food in 5 Exploitations are around the Administrative Center, including the unbuilt Marble because it's not an Extension yet, but excluding the Iron Mine because it has no Food.  On the map, you count only 8 Food in 5 Exploitations, but in their tooltips you see it's actually 12 Food.  I think the +1f adjacent to a river (Flood Irrigation) is not displayed on the map, which is an OpenDev visual display bug, affecting the 4 hexes adjacent to the river (including the 2 river hexes themselves, since they're adjacent to each other, haha).  The 6th hex is subtle, but makes total sense: it's due north of Londonia, adjacent to its city walls.  Before we attached the Marble territory, this hex was clipped by the territory boundary!  But now that it's all one big happy region, this hex is included.  And it also shows the same bug: it displays 1f on the map, but it's adjacent to the river inside the city walls, and its tooltip properly says "2 Food".
• +20 Industry from +5 Industry Exploitations.  These are the 5 Exploitations around the Administrative Center, including the unbuilt Marble, whose 3i is mostly hidden behind the Marble icon.  OpenDev visual display bug: on the map, the 2 river hexes show "3i" each, and the 5 hexes sum to 18i, but these 2 hexes' tooltips show "4 Industry" from +1i on River (Watermill), which brings the total to 20i.
• +4 Money from +1 Money Exploitation.  This is the unbuilt Marble hex.
• +5 Science from +5 Science Exploitations.  These are the 5 Exploitations around the Administrative Center, from +1s on Exploitation (Library).

"Civilization Bonus:" +11 FIMS = +2 Food, +5 Industry, +4 Science.  These don't correspond to anything in the tech tree or Londonia's completed constructions.  More deeply, comparing total (not incremental) bonus to each resouce's total without the bonus, this is +7 of 45 Food, +20 of 119 Industry, +6 of 38 Money, and +12 of 79 Science.  So I deduce that English get +15% FIMS as one of their traits.

And that exactly adds up to the +88 FIMS gained.  Now we shall grotesquely simplify this down to a Too-Simple Rule:

• Roughly half of the gain (43 of 88) come from the new Exploitations.
• The other half comes from +1 Extension, +1 territory, and traits.
• Therefore, attaching a territory and finishing most or all of its Deposits gives roughly double its FIMS hex ring in total FIMS.

In a real game, the English player probably should have attached a 3rd territory around turn 20, instead of waiting until turn 120 for us to do it.  The gain would have started out smaller, but it would have paid off over 100 more turns.  Lesson (for HKEA): Attach early.

3.c  Londonia Builds upon Pearls!

Before attaching the Marble territory, you may notice that Londonia's Constructions menu contains Artisans Quarter for 168 Industry.  (Or, if you attach the territory and build the Marble first, Artisans Quarter remains in your queue with its cost increased to 192 Industry.)  This means Londonia does, in fact, have 1 unbuilt Luxury Deposit that isn't the Marble!  This didn't even confuse me for 1 full week: my mind quietly blipped over it without even wondering why.  I finally thought to go panning for it.  Scroll down to the bottom edge of the map, in the harbor just above 47.0 on the yardstick.  Londonia has unbuilt Pearls in the water!  You can build that for another +2 Money, +5 Stability in each of your cities.

Lesson: If you can build it, you have it somewhere.

Next: Oxeneford attaches Ransacked Horses (In the Second That the Greatsword Hits)

Appendix A.  Yardstick Coordinate System (YCS)

For a coordinate system, I shall use the existing yardsticks along the borders of the map.

First we must agree on how to read both the yardstick itself, and then each hex border. I adopt the same convention as a physical ruler, yardstick, or tape measure.

• Every yardstick box begins at its left vertical separator (respectively, its bottom horizontal separator), and goes until the next separator. Thus, its number label is located at its own x.5 (or y.5) coordinate.
• Yardstick boxes are 0-origin, with [00,00] in the lower left corner of the map.  We shall use the bottom edge yardstick only.  Do not use the top edge yardstick, for it is inconsistent with the bottom edge yardstick, by -1.0 dx.
• Each hex uses its leftmost edge for its x-coordinate.  When it's perfectly(*) aligned with a yardstick box's left separator, that's an x.0 coordinate (and an odd row).  If it's perfectly aligned with the numeral, that' an x.5 (and an even row).
• Each hex uses its lower chord (a line segment through its lower-left and lower-right vertices) to align with a vertical yardstick box's numeral. (Equivalently, we could say that the hex's bottom vertex is a little bit above the box's lower separator. But I find lining up the numeral with the chord to be more natural.)
• Caveat: The HK map itself has a 3D depth of z = -1.0 or so, to allow for tall terrain to grow upward.  As you zoom in and out, the camera angle tilts.  Then the hex borders may not align perfectly with the yardstick separators, due to parallax.  You can see this for hex [01,01] hex in the figure.
• The lower-left most hex would perfectly align with the "0" numeral in the lower-left corner of the yardstick, if it were printed.  So this hex is at coordinate [00.5, 00].  It follows that every hex in an even row will have the x + 0.5 offset.  (It's a hex map, after all.) To simplify the notation, I shall adopt the convention that we elide all 0.5 coordinates. Then you shall remember the mnemonic that even rows implicitly have x += 0.5.
• A map coordinate is then a 7-character string of the form [xx,yy], with leading 0s as needed, and no space after the comma.

In the following examples, I'll label (some) hexes and edges with their YCS numbers.  I shall also give whimsical names to certain hexes of interest.  We have:

• [47,07] = Londonia
• [43,08] = west stronghold = Westmoor (because attackers from the west bog down in the rivers :)
• [49,10] = east stronghold = Eastgate
• [37,12] = Oxeneford

Alas, I can't now look up Angkor and Tenochtitlan's coordinates.  Steam has finally "updated" my HKOD folder to empty.  I shall leave this Appendix here, because I expect that it will be re-usable in HKEA and HK Release.

4.  AI's Order of Battle (But It's Over Now)

I did manage to finish 1 full Scenario 3 playthrough last night, and pull off my gimmick build path for maximum Industry.  This must have been nearly the last possible opportunity.  This morning, Steam has updated HKOD to empty, which means there's no longer an .exe to run.  Alas, I have screenshots of the battles only, which are relatively uninteresting now.  For the record, here they are.

• [43,08] Westmoor: 3K = 3 Knights
• [49,07] in Londonia: 2L = 2 Longbowmen
• On T120, build a 3rd Longbowmen (and 2L becomes 3L).  It suffices; you need nothing else.

You can use all remaining turns to build other things; see post after next.

The AI attacks Londonia piecemeal with the following small groups.  Generally, intercept them and Attack first, or immediately Sortie to break any siege.  You will always have numerical advantage.

• Turn 120: Aztec J2 = 2 Jaguar Warriors near Eastgate.  Attack first at 172-66 Combat Strength.
• 
• Turn 122: Khmer K2, K1 = 2 + 1 Knights from the west.  Sortie at 312-108.  (You're stronger because you finished the 3rd Longbowmen.)
• 
• Turn 123: Aztec C2 = 2 Crossbowmen at Londonia Falls.  Attack at 203-62.
• 
• Turn 123 or 124: Aztec J3 = 3 Jaguar Warriors near Eastgate.  Sortie at 204-99.  (My 3K group was still in Westmoor, too far away to reinforce.)
• 
• Turn 124: Khmer G2 = 2 Great Swordsmen, near Westmoor.  Preview-attack, move 3L into battle board, then Attack at 207-70.  Note that my 3L are on the high ground just north of Londonia city center, so that D1 = 1 Dhanvi-Gaja doesn't take that hex for itself.
• 
  
• Turn 125: Khmer D1 = 1 Dhanvi-Gaja sieges Londonia from the north.  Sortie at 243-42 and shoot it down.  (no image)
• Turn 125 or 126: Aztec P3 = 3 Pikemen sieges Londonia from near Eastgate. Sortie at 243-93. (no image)
• Turn 126: Aztec N3 = 3 Knights, near or in Londonia Falls. Attack at 208-108, the same way we handled C2.
• 
• Turn 128-129: Aztec J5 = 5 Jaguar Warriors.  Normally they loop east near Tenochtitlan (hidden by fog of war to the north) and sneak south through Coffee Road, so you can head north early and meet them on the way.  But if they get pinned in place by the siege at Oxeneford, they might come due south to Westmoor instead.  Anyways, attack.  (No image)

• Aztec P4 = 4 Pikemen.  They have advantage over both your Knights and Longbowmen.  Don't let them have high ground.
• Tenochtitlan, Aztec C4 = 4 Citizens. Killing them captures Tenochtitlan, and reduces its population from 5 to 1.

4.b  Sieges at Oxeneford

Oxeneford basically fights only twice.  Both fights could go extra time, needing 1-2 extra turns to mop up.

You start with:

• [37,08] 3P = 3 Pikemen, on high ground NE of your Horses
• [38,10] 2B = 2 Longbowmen, in the valley just south of Oxeneford's city walls
• Build 3 Longbowmen (which takes 5 turns).  Then rebuild your Horses for its FIMS, and a 4th Longbowmen if you expect to take 1 casualty and need the reinforcement.

• Turn 123: Aztec C1, JK = 1 Crossbowmen, 2 Knights, 4 Jaguar Warriors. The Crossbowmen initiate the siege from the north plateau river hex. Sortie immediately. I put 1 Pikemen at [37,14] = the north plateau hex that isn't a river. They defend the slopes from enemy melee troops running downhill.
• 
• Turn 126: Khmer D2 = 5 Great Swordsmen, 5 Crossbowmen, 2 Dhanvi-Gaja, 2 Pikemen.  This is the stuff of legend! These are 3 separate army groups (due to unit slot limits), and sometimes you get them only 1 or 2 at a time, which is of course easier.  In this playthrough, I got the full house all at once.  The Sortie says 335-341, but with all of Khmer's reinforcements it becomes 326-473.
• 
• I did manage to stand on 1 reinforcement flag on the northern plateau, which denied 3 Great Swordsmen.  I had  3 Pikemen, 5 Longbowmen (-1 died), 3 Peasants (-1 died), and I built a 6th Longbowmen during the siege (on turn 127).  He does immediately appear as a new reinforcement on turn 127 round 1, which is a useful game mechanic to know.
• On turn 126, I killed 2/2 Great Swordsmen, 2/5 Crossbowmen and dinged a 3rd to 7 hp, 1 Pikeman and injured the other to 30 hp, and damaged the Dhanvi-Gajas to 11 and 85 hp.  I killed off the survivors by turn 127 round 3, and chose not to let the 3 Great Swordsmen out of their flag, so it ended like that. I had Longbowmen at 8 and 41 hp, Pikemen at 16 and 34, and I don't care about Peasants' hp because you get fresh ones on every new siege.

And that's it for Oxeneford's attacks.  Scenario 3 was actually two sub-Scenarios at once, with numerical advantage in Londonia and without it in Oxeneford.

Promptly move your survivors SW and explore for Curiosities.  You can heal a bit as you walk by staying in your Horses region.

• Angkor, Khmer A4 = 4 Citizens (no image). Winning  this fight captures Angkor, but you don't get its Construction Queue, and its 1-population assignment is locked.  I captured it on T132, and by T138 it was still locked, so I could never attach a territory to it.

5.  High Furnace for 4X Industry

Londonia spends only 2 turns building 1 Longbowmen.  From T122 to T138, its build queue is free to ... experiment.  I resolved to maximize Industry, as a test of HKOD's two-stage Extensions adjacencies x Infrastructures multiplier model.

5.a  Londonia's Extensions

Consider Londonia's layout at start of Scenario 3, on T120.  It has 12 Extensions:

• 6 Farmers Quarters, grouped into a circle of 5 and an isolated 1.  The 5 Farmers Quarters to the east have 2, 2, 3, 3, and 4 neighbors, respectively, for a total of 14 adjacencies, so they score 19 Food for self + adjacencies.  N.B. this is the optimal number of adjacencies for 5 Quarters.  The 1 Farmers Quarter to the west has 0 adjacencies, so it adds 1 Food for self + adjacencies.
• Londonia has I.Domestication.Animal Barns for L1 in Animal Husbandry (which is the maximum in OpenDev).  This gives 2X to the self + adjacencies production of Farmers Quarters, so the 6 Farmers Quarters gain +19 and +1 Food, respectively.  Note that the 5 Farmers Quarters average 3.8 Food each before multipliers, while the 1 isolated Farmers Quarter averages 1.0 Food by itself.  That's the power of adjacencies, and the Infrastructure families that multiply them.
• 1 Research Quarter.  It does gain +2 Science in adjacency bonus from the 2 Makers Quarters, but they gain nothing from it.
• 1 Money Quarter.  It gets and gives zero adjacency bonus.
• 2 Makers Quarters, as a pair.  They each have 1 neighbor, so they each score 1+1 Industry for self + adjacencies (which is optimal for 2 Quarters).  Londonia has I.Coal Energy.Forge for 2X this amount, so they each score 4 Industry from self, adjacencies, and multipliers.  Both have a base value of 1 Industry from Stone Field, so they display as 5i, 5i on the map.
• 2 Strongholds. These count against your Extensions cap, but contribute no FIMS.

•  the 2nd Quarter adds +1 edge, so +2 adjacencies;
• every new Quarter from 3 to 6 adds +2 edges each, so their adjacencies increase by +4 per Quarter
• the 7th Quarter, which completes the full hex ring, adds +3 edges, so it adds +6 adjacencies.

Geometry matters!  Good geometric layout is up to four times more productive than a set of isolated Quarters.

• You can't always build full hex rings, due to your city's Extensions cap and the exponential(!) cost of Extensions.  But you want to at least create triangles.
• Farmers and Makers Quarters pay only for self-adjacencies, i.e. to Quarters of the same type.
• Research and Market Quarters, and the Distribution and Education Infrastructure families, pay for cross-adjacencies (to Quarters of different type).  I think a simple way to envision this is to abut your triangles so that they share common sides. But I've never worked out a full city design.
• Finally, recall that the Infrastructure families multiply this entire amount.  You can get up to 5X (and more --?) of your 4.43x! Both parts matter.  Build!
• Nomenclature: I hereby coin the HK term "SAX" for self, adjacency, and multiplier. Then we can say Makers Quarters have a "base SAX amount", and that the Coal Energy family multiplies its SAX. This cute acronym is a counterpart to FIMS, which come from the tile. SAX should be a first-class acronym separate from FIMS, because SAX income is disjoint from FIMS tile income.

As a lark, on turn 138, the last turn of Scenario 3:

• I bought out III.Military Architecture.Fort for -667 Money.
• Then I queued up a 4th(!) Makers Quarter at [47,04], in the forest hex SE of the existing Makers Quarter.  (The other candidate hex is the woodland cul-de-sac at [48,06], due south of the 2 Farmers Quarters, but it was worse by -1 Industry tile FIMS, and they're symmetric in SAX.  Plus, [48,06] really wants to be a 7th Farmers Quarters, to complete a length-3 triangle.)  With one more click, I bought it out for -1,108 Money, leaving me with 19 Money. After juggling mild Generals upkeep for a few turns, and discovering 11 Old Hoard for ~720 Money, plus all of my savings, it was that close!

• T126: Finish III.Heavy Infantry.  (This is why I prioritized Science above everything else.)
• T127: Win at Oxeneford, start running west. Don't ransack the Copper Mine on your way through! If you leave it intact, you annex it intact!
• T131: Finish III.Furnace Steel 1 turn early via Curiosity Discoveries.
• T132: Longbowmen arrive and Ransack Outpost, which destroys it, even though the English have researched II.Conquest.Outpost Assimilation.  (Outpost capture was not in OpenDev, else Khmer AI would have captured your Horses, so don't complain.)
• T133: Longbowmen create a new Outpost in that territory.  Instantly, the existing Copper Mine joins your empire.  Londonia builds High Furnace.

• T120: Londonia assigns 1 Farmer = 52 Food (Super Growth).  Then it grows +1 population exactly when the Agrarian Affinity meter fills up.
• T124: +1 = 11 population in Londonia.  Mother's Milk for +3 = 14 population, move the Farmer into Industry. +4 population in 1 turn drops Londonia from 52 Food (Super Growth) to -68 Food (Starvation).  I ignored that, and put 5/5 Science and 9/9 Industry.
• T128: Starvation -4 = 10 population! Easy come, easy go :( It seems -- abrupt, but at least it was implemented. Hilarious: Londonia rebounds to 48 Food, so +1 Farmer = 52 for Super Growth, and we'll do it again! I didn't bother to activate Mother's Milk a 2nd time, though.