Hittites on Fertile Crescent, and Other Hard Lessons

[Gilmoy]

Scholar, random victory conditions (no edits).
I kill Canaanites outright! So I inherit their entire swath of land.
That gives me the economy to outgrind Babylonians and Assyrians concurrently.

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Easy Empires: Nice Guy Pays Off
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I used to play as the Nice Guy, and try to make a picturesquely perfect economy.
This actually works with some Easy empires, hence I got some of those achievements.

Nice Guy vs. Easy:
0. Buy Food (100%) until you have about +30 (per turn).
Research more Research (recursively), then whatever.

1. Turn off Food (0%) and start saving Wealth.
2. Reduce Wealth/Knowledge/Food Waste, all L1 and L2.
3. Buy 1st army and +1 Power.
4. Reduce Power Waste, L1 and L2.
5. Buy 2nd army and +few Power.

But ultimately, it's a bunch of bad habits. Hard empires teach me that lesson!

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Medium Empires: Choose a Direction and Go
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On Fertile Crescent, Elamites (SE) might get boxed into a small corner
by Babylonians expanding due east over the swath of hills, and south to the desert.
Then you lose on economy by having simply Fewer Tiles, and you can't buy military.

On turn 1, carefully study your tech tree and surrounding terrain, and make a plan.
I found the plan of being Hill God, and swarming due north over hills.
Hills cost extra food to take, but hill techs are amazingly cheap.
This had the benefit of forcing Babylonians north to meet Assyrians.

Medium Guy vs. Medium:
0. Buy Food until the merge (i.e. you're contiguous with your neighbor).
This prioritizes an expansion phase, so that you're not 2nd-best through dilly-dallying.
Cease buying around $30 (per turn), and save for a unit.

Research more Research, etc.

1. Buy 1st unit.
2. Thereafter, juggle it with Power spurts and Waste reduction.

You can't meekly sit at home and play SimBeanCount.
Economies are swung by armies changing borders, and you must go get your share.
Hence, the 1st army is more important than reducing some Waste steps.
Capture territory and cities, and your winnings and land pay for Waste reduction later.

This works, and outraces Babylonians.
They still get the entire desert (which is exactly how I won with them).
But my hills were untouchable, and my economy was nearly equal.
Then Babylonians are stuck in the middle, squeezed from 3 sides.

Yet the Medium Guy mentality is still too dainty.
I had to lose a few more games to the AI's military swarming to grasp that.

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Hard Empires: Gambit and Blitz
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0. Buy Food and expand aggressively, until contiguous.
1. Research more Research, then whichever you have most tiles in.

If you have 16 Grasslands, go for Grasslands Food, then Grasslands Money.
16 of anything is a winner.

2. Don't spend on premature Wealth optimization.
The best way to not waste K/W/F is to simply spend it all, every turn.
Then your waste is negligible, deep into the midgame.

3. Your 1st spare $100 shall buy 1st army, and maybe a 2nd.
Aggressively seize the initiative, and you can capture 3-6 tiles uncontested.
Plus you get ahead in Power racing, and can reliably press an assault, even 2v4.

This conquest focus wins more tiles for a bigger economy.
Then your future earnings pay for details like Waste.

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Hard Hittites on Fertile Crescent
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I had to lose to Babylonians in the desert about 3 times.
Then I fought them to a draw and didn't die, but they still won on V.C.s another 2-3 times.

- I tried being Hill God and expanding NW, away from everybody.
It sucketh. Too meek, no space, no economy, it doesn't pay off.

- I tried expanding east along rivers into Assyrians.
But then Babylonians laugh, and eat us both.

+ This game, I finally envisioned the Grass God Gambit.
Splurge Research yolk on (gasp) Grassland flags, to warp-drive my expansion.
I knew this would trash my early Research, but I prioritize moar tiles.

It works very well. Sweep south through grasslands and plains, to the desert.
Let Assyrians have some rivers between you.
Soon enough, Babylonians and Assyrians will stare each other down.

+ Meanwhile, my vast tiles gave me a big economy.
Research more Research, then every yield from 14(!) Grassland.
That pays for some Desert yield, which pays for Sea yield.

+ 1st army rampages uncontested by Canaanites.
Its economy never gets going vs. mine.

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Unit Trough-to-Peak Spending
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The AI reacts to threatened tiles. It doesn't necessarily react to your armies.

Tile capture has a natural 2-turn cadence.
Grasp how the AI reacts during this, and you can time your spending to fit.

turn t+0: No tiles are under threat. Your army sits on a border.
The AI may ignore you, and rush elsewhere.

This is a perfect downbeat to spend Wealth, and let your Power drop.
Keep just enough residual Power to threaten a tile.
Assume you must beat the enemy's nearby city strength + tile power, but 0 armies.

turn t+1: You threaten 1+ tiles. Your army must stay there to finish the attack.
The AI will surely swoop 1-5 armies into the threatened zone, to defend it.

On this turn, spend max (100%) Wealth on +Power.
This is your trump card, hammer stone, and dunk shot.
The AI's reaction may be calibrated to beat your current Power, visible this turn.
It can underestimate your max power for next turn.

turn t+2: Your extra spending beats the AI's just-enough swooping. (It wasn't enough.)
You capture 1+ tiles. Repeat.

This finally taught me the right time to buy a k-th army, or a Power Waste reduction.
Spend on those things in the turn in which you will threaten, but haven't yet.
You don't need to burn cash to threaten empty tiles.
Threaten for cheap, while the AI heeds you not.
Then as the AI panics, finish it with your wallet.

Sometimes the AI defends 2-deep and 2-wide, stacking 5 units adjacent to 1 city tile.
That's tough to beat, but you can undermine its endpoints and gradually take edge tiles.

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Killing Canaanites, and Victory
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My 1st army, alone, executes a perfect trough-to-peak spend cycle twice, to power 7.
Canaanite AI has no economy, only 1 city at size 2, and only 1 army at power 2.
I capture its sole city outright, eliminating it early, only about turn 16(!).

I smoothly take over the entire SW desert, and have moar tiles.
I max out at 4 armies, with steady peak spending (90%) up to Power 14.
This suffices to hold Babylonians to a stalemate.
I pivot north and grind 1 city from Assyrians.

I don't even glance at the Victory Conditions until about turn 25.
If your military can't hold a line, all V.C.s are moot.
If you can grind space, you have time to cherry-pick your winning crown combo.
So first I get economy, then I grind to stop Babylonians, then I finally take a peek.

I win on 7 natural crowns, almost a boring combination. It's only turn 29!!
Babylonians have 2-3 crowns (it fluctuates), Assyrians 2, Elamites 0.

0/3 Temple of Artemis: 7/18 Power techs -- I like the 1st of each, I hate the 2nd+
0/2 Colossus: 4/7 armies -- there was never a pause to buy a 5th
0/2 Pyramids: 28/30 city pop -- I was 1 turn away
0/2 Mausoleum: 2/3 cities captured -- probably 3 turns away

I won too fast for myself If not these crowns, then surely those.

3/3 Statue of Zeus: 18/18 Power
3/3 Great Lighthouse: 131/120 spaces (about 1/3 of the map)
1/1 Hanging Gardens: 382/300 Wealth

They're all interconnected. Having moar tiles gives moar wealth (about $270 per turn).
I end with 2is 8ri 18gr 10pl 22hi 1fo 48de 14se 8ci tiles = 131.
Yes, 48 desert tiles, earning 1/2/1 each. I am the Desert God, after all.

My 90% peak spending (with 4 armies) buys +7 Power.
At -50% Waste, this attains an equilibrium level at 14 Power.
Inevitably, you get a sequence of mercenary opportunities in consecutive turns.
I get 4 in 4 turns, which lifts me to a new equilibrium level at 18-20 Power.

The 382 Wealth is an artifact of my peak spending granularity.
Even spending 100%, the remnant unspent, plus 1 turn's new income, is 382.
I'm this-close to taking a 2nd city from Assyrians, but I earn these crowns too dang fast.

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Very Hard: Winning as Canaanites
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I've lost with Canaanites before.
I always expand south into desert and hills, but it's still a small economy.

Here's a silly thought: Perhaps the gambit is to go north and eliminate Hittites.
Wouldn't that be a punch line!

[Gilmoy]

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Very Hard: Canaanites as Plains God?!
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I gave it a shot. Turn 1, spend all research yolk on ... Hill flags, yes. And go north.
The concept is to hem Hittites in by aggressively imposing a border.
Hittites and Assyrians squabble over rivers, it leaves all plains to me, I do keep it small.

Then build a desert fence due south to halt Babylonians, or they'll sweep SW and take it all.
I stabilize with a thinner slice of the west, about 1/4 map width, about 3/4 tall.
It's ... almost enough to compete.

Alas, Hittites get 1 army out about 10 turns before I do, and thereafter it's a grind, no blitz.
I could "easily" crush Hittites (and did), but then Assyrians wins.
If I pivot and stop Assyrians, Babylonians wins.
I can't make them fight each other, and I can't beat all 3 at the same time.

The key gambit of going north does seem to work.

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Easy: Oxus in Asia (badge)
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I test out my newfangled emphasis on fast expansion to keep neighbors small.

0. Plains God, ghastly 7 + 10 + 12 of my 30 Research yolk on all 3 Plains flags
1. Decent expansion south to desert, east to steppes.

Harappans are trapped between me and Kuru (India), squeezed for space,
doomed to have a small economy all game long.
But nothing corks Kuru in its bottle, and it smoothly accretes all of the SW seas.
I thought Kuru would win on largest economy.

Just-in-time shift to military + decent trough-to-peak spending buys Power 8-11.
Harappans never has the tiles to beat me in a spending race, maxing out around Power 5.
Flagging most of Harappan's territory vaults me from 9th to 2nd.

Oddly, Kuru has only 1 army + 1 fleet in play, at only Power 6.
My 3 army + 1 fleet at Power 14 roll like a topological sweep line.
From there, economy begets Power, which begets more economy, recur, repeat, sweep.

On turn 39, I finally study the Victory Conditions, and see a cute trick.
3/3 for 18 Power. I eventually attain 24 Power, it ebbs to 23.
2/2 captured 7/3 cities, currently threatening an 8th

0/1 for 4/5 units -- oh hey, I could build one right now
0/3 for 34/36 city pop
0/2 for 89/90 tiles

I build +1 army, click End Turn, and win with 11/7 crowns.
Taking that 1 threatened city gave me +2 pop and +1 tile.

All 8 AIs tied with 0 crowns each. Asia is too congested for any 1 of them to sprawl.

~~~~

I think I could win as Kuru, by repeating its Sea God gambit.
It follows that Harappans should win that way, too.

Perhaps Oxus could drill due south along the west edge of the map, and reach the sea.
But ultimately, focusing on the hill war vs. Harappans wins well enough.

[Gilmoy]

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Medium: Harappans on Asia
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Originally posted by Gilmoy:

I think I could win as Kuru, by repeating its Sea God gambit.
It follows that Harappans should win that way, too.

Briefly, early-game no, mid-game yes.

1st try: Mad Hill God, spending 5 + 10 + 15 = all 30 yolk on 3 Hill flags.
I did get 11 hills, but never had food. Kuru took the seas, Oxus killed me with plains.

2nd try: River Power Gambit!
Let's not meekly cede 2 precious food tiles on turn 1, fearing flag ties.
* 5 + 10 Research on 2 Hill flags.
* Boldly gambit 10(!) Research on +1 River power -- on turn 1!
That's what makes it a gambit.

It works.
+ Turn 1, I win the flag-tie for the 1 river hex bordering me and Kuru ...
+ ... and go north over hills.
+ Turn 3-4, I win another flag-tie for 1 river hex bordering my northern arm and Oxus.

I come this-close to bottling up Oxus like a pig in a blanket, within about a 6x8 tile corner.
Then you'd be easily 3:1 its tile size and economy, and roll over it.
Alas, it wins a plains tie along the north edge of the map (surely with +1 Plains power).
Nonetheless, I have viable food income.

[_] Double Gambit: 20/30 Research on +1 River +1 Grasslands power, and take both tiles?

I build a sea fence due south, hugging Kuru's west border.
By turn 20, my sea wall looks like Chile: tall, skinny, 1 tile wide, flanking Kuru like a vine.
This excellently stops Kuru from ever spreading west.

I outrace Oxus to 1st army, and soon cut it in half along the top edge of map.
West Oxus, with 1 city of pop 1, out-Powers me 6:5, and out-armies me 2:1.
But Huns attack from the east 2:0 and win East Oxus's city (pop 3).
Thereafter, Sole Oxus has no economy, drops to Power 2, and I win that.

There was a brief 3-turn window of angst, as Oxus West pushed me back,
while Kuru's 1 lone fleet captured 6 of my seas. Yet this was only ever papier-mâché.
I doggedly stick with my assault, even ceding 1:1 exchanges in uncontested tiles.
When East Oxus falls, I annex West Oxus like a loot drop.
Meanwhile, Kuru's fleet scampers east to defend its own tiles, and never returns.

I sweep 2a + 2f at Power 14 east through Kuru, capture 6-10 tiles per 2 turns for 12 turns.
Ultimately, the aggressive opening to keep Oxus small wins, after all.
It couldn't protect its geometric shape, and after I get its tiles, I attain critical mass.
That's more pro-active than a dainty stalemate, or a losing one.

~~~~

I learn that a turn 1 Power gambit can earn you 40 turns of production from 1 good tile.
It paid for itself, and when I did it, I win. That idea is surely worth something.

[Gilmoy]

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Medium: Kuru on Asia
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A strangely fun win.
I play like a strangler vine, wrapping tightly around neighbors' coasts.
This keeps them smol, which inevitably gets them killed later on.

Kuru is Ecological, with -2 cost per flag and -25% cost for food techs.

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1. River/Grassland Double Gambit
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+ Westward, Kuru and Harappans are jointly adjacent to 1 river 1 grassland.
+ Eastward, Kuru and Ban Chiang are jointly adjacent to 1 river.

Recalling my Harappans River Power gambit, I try a double gambit.
I pay 10 + 10 of my 40 yolk for +1 River +1 Grassland Power, and flag all 3 tiles.

a) Ban Chiang ducks, and I take that river uncontested.
b) Harappans duels with +1/+1 Power of its own :o

We flag-tie both tiles 4 turns in a row, wasting our early food.
I thought this was suicidal, and would get both of us killed.
But ultimately, it succeeded in keeping Harappans small, while Oxus spread unchecked.

I eventually use the game rule that adjacent owned tiles is a tiebreaker.

b1) I pay for a dead sea tile to get +1 adjacency to the river
b2) I take a hill tile for +1 adjacency to the grasslands

So I eventually do get all 3 tiles.

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2. Landlocking Harappans
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I ignore sea tiles with 0 early yield, and hoard my food for growth.
However, I prioritize encircling neighbors, and I'll take barren sea tiles for that.

Harappans is uniquely vulnerable to this attack vector.
Its capital (starting city) is at distance 2 from the sea.
By game rule, cities must be at least distance 2 from each other.
So it can never build a city on the shore, because it would be adjacent to its capital.

Then "all" you need to do is extend a tendril of sea tiles along its entire coast.
Boom, it's landlocked

It's not a complete lock because its capital is river-connected to the sea.
So it could, in principle, build a fleet in its capital, and fight its way out.
But I own the river adjacent to the sea, from #1.
Its armies never took that river tile from me, so a fleet would be equally helpless.

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3. Late Sea God
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Similarly, I make a sea fence eastward to cut off Ban Chiang.
Then I "own" the entire SW sea by default. No AI can see them to flag them!

I leave those tiles unclaimed for 20 turns to hoard early food.
As I finally research sea yield, I sweep them up at my leisure.
Kuru does eventually own 30+ sea tiles yielding 1/1/1 each, plus all of the SW islands.

Then Kuru is by far the #1 economy, and wins by the usual juggernasting.
("juggernast" = juggernaut + nasty like a lawnmower with tank treads)

Meanwhile, Harappans was tiny, only 1/3 the size of Oxus, and lost that war.

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4. Tactical Swooping
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I discover a further tactical refinement in 2-army coordination.

4.a) On any t+0, 1 army (East) projects a threat.
AIs see no threat yet, and run elsewhere.
Schedule your mild purchases now, esp. 1 waste reduction.
You don't need max wealth to project a threat vs. 0 defenders.

4.b) On t+1, you threaten 1 East zone. East AIs will swoop in to defend it.
West AIs are on your border, but have no threat yet.
Your West army is free to go! It swoops from West to East and joins the attack.

You can anticipate:
- West AIs will create a threat vs. you (but they're out of sync to actually capture it)
+ You double down on the East attack, and win on combined Power

4.c) On t+2, if West AIs created a threat, you swoop back West and defend it.

Then your 2 armies can beat 4 East armies and stalemate 3 West armies.
It's all in the timing. If East and West were in sync, you couldn't ever leave.
But when they're out of sync, you have time to go and return.

I add +1 fleet, and win by juggernasting.
Every endgame is the same, if you don't get crushed before then.

[Gilmoy]

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Medium: Gojoseon on Asia
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I peek across the map on turn 1.
Harappans AI does indeed execute a River/Grassland Power double gambit vs. Kuru AI.
It wins both of those tiles on turn 1, as meek Kuru doesn't rise to challenge it.
I wasn't dreaming when I saw Harappans AI do that to me. It must be scripted.

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1. Putting a Cork in Zhou('s Smol Botl)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Gojoseon has an obvious Grassland Gambit, spending 5+10 on 2 Grassland flags.
From turn 3-7, I accept a flag-tie duel vs. Zhou for the 1 Grassland due north of Zhou.
This is, of course, a terrible loss of early food. But I deem it worth the cost in the long run.

+ It utterly encircles Zhou, and keeps them small.
Zhou is (soon) bordered from the south, west, and northwest, and by sea to the east.
North is literally its sole remaining degree of freedom.
Capping it early is an inevitable win on sheer size.

It would be far worse to lose 1 turn of food in a tie, meekly duck,
and let Zhou win and break out north to the forest.
Then you'd lose 1 turn of food and be small yourself.

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2. Sea Tendrils Like a Seaweed Epiphyte
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Again, I avoid sea tiles while their yield is still 0, except for:

2.a) sea tile that hops me to an island tile
2.b) sea tiles that beeline south to Polynesians AI, to set the Voronoi border 'tween us

Around turn 20, I own my starting land, the north forest, the island chains,
and one single 1-wide corridor of sea tiles, 3 tiles tall, that extends due south.
There, I meet Polynesian AI's 1-wide corridor of sea tiles, 2 tiles tall, encroaching north.
From there, we both fan out like perfect mushroom caps, east and west until I cut it off.
My aggressive expansion is the perfect (and only) counter to the AI's own expansion.

This creates a decent interior of ~20 unowned sea tiles, which Polynesians AI can't see.
I collect all of them later, like Capablanca's ripe apples.

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3. Ozymandi-Go
~~~~~~~~~~~~~
Then I'm the #1 economy, and I juggernast Zhou, Polynesians, Dong Son, and Han
concurrently.

In other words, expansion is go (the ancient board game).
Build a fence to claim the space inside it.
Then fill it in with your (ahem) stones, and sweep your line over topology.

This will surely be the right mindset for 3-player Indus Valley and Aegean Sea.
Heck, it might even solve Canaanites on Fertile Crescent

[Gilmoy]

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Medium: Zhou on Asia
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Wow, does the AI ever have a blind spot.
It's the same generic AI playing every nation.
It follows that if a strategic principle is beyond its horizon once, it will always remain so.

On turn 1 on a congested map, study your tiles that you share with 1 neighbor.
You might be stuck flag-racing to get them first on a tiebreaker.
Then the +1 Power Gambit beats the Timid Strategy.

Nomenclature: I shall use (r, o'clock) polar coordinates

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Turn 1-2: River/Grass Double Gambit Corks Dong Son
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Turn 1: Dong Son and Zhou are mutually adjacent to 2 good tiles:
+ a River at my (6:45, 2)
+ a Grasslands at my (6:00, 2)

1.1) I spend (10 + 15)/40 on a River/Grasslands Power Gambit, and flag both.
1.2) I gambit (5 + 10) more on 2 Grassland flags(!).

I now overwhelmingly value extending my early food to seize land and get big early.
It's worth converting all of my Research yolk essentially into Food, just to take +3-5 tiles.
That's much more important than earning extra +Research in the first ~10 turns.
Be big, and you'll have thousands of Research, and win wars for more.
Be small, and +200 early Research won't save you.

3-5 early tiles is a quietly seismic deal, because it keeps AIs small.
Fencing them in early earns you 20+ turns, and eventually 45 turns, of being Bigger.

Dong Son does flag-duel both shared tiles, but ducks (= does not match my +1 Power).
+ I win both tiles, by the Power tiebreaker.

Turn 2: Dong Son did flag the forest at its (12:00, 2) / my (7:30, 2).
We are now both-adjacent to a river tile at my (9:00, 2).
We flag-tie it, and I win by the same tiebreaker.

This locks Dong Son out of expanding NW, for the rest of the game.
Also, I have +3 good food tiles, Dong Son wasted its food and 2 turns and still has 0.
It kneecaps its economy, just like that.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Turn 3: Same Grass Gambit Casks Huns
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Huns went west, and never took a Grasslands at my (11:15, 3).
We flag-tie it, and I win by the same tiebreaker.

This fences Huns from the east, and they never break through that.

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Turn 5-7: Forest Power Gambit Roofs Gojoseon
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As Gojoseon (see previous), I knew to cap Zhou from the north, and seize the forest.
As Zhou, I was frantically determined to not let that happen to me.

I beeline north myself, and do reach the forest first.
I spend 20 on a Delayed Forest Gambit to win a flag-tiebreaker vs. Gojoseon.
We do, indeed, flag-tie in forest, and I get all of them.
This fences Gojoseon to its west and north, leaving only barren sea.

It's the same simple trick every time, and it works 3 times in a row.
Then I'm the #1 economy, literally from Turn 1 onward.

This is the result:
https://steamcommunity.com/sharedfiles/filedetails/?id=3088340562
Taking those 2 good food tiles on Turn 1 surely outscores every other AI's Turn 1.
And this recurs, and accelerates.

[Gilmoy]

There should be a wiki named The Ozymandibus

[Gilmoy]

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Very Hard: Canaanites on Fertile Crescent
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I finally cheesed it in a mildly unsatisfying way.

+ Playing it "fair" (with random Victory Conditions), I actually attain a decent midgame.
Full research tree, I own the mid-NW Plains, perfect north-to-south desert wall.
My early-enough military steadily roll back Babylonians or Assyrians (but not both).

But there's simply no answer for the AIs' early Food.
Then their economies are Simply Larger, and they cruise to 30-36 city pop + 800 Wealth.
Even if you steadily capture 15-25 desert tiles from Babylonians, you can't touch its income.

I conclude that it's mathematically impossible for a fair human Canaanite economy
to out-Food Assyrians and Babylonians. You can out-fight them, but time runs out.

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Custom Victory Conditions
~~~~~~~~~~~~~~~~~~~~
Ergo, to win, edit Victory Conditions and delete the Wealth and City Population options.
This counters the AIs' hard-coded advantages in these areas.

I set Victory Conditions as follows:

7 crowns to win
4 crowns (max) for 175 tiles (about 1/2 the map, the most grueling setting for this task)
3 crowns (max) for 18 Power
3 crowns (max) for 5 cities captured

The only way to win is to get 3+4 crowns. In the end, you'll inevitably get all 10.

Thereafter, a human military victory is nearly assured.
In the sole area of peak Power, the human player has an insurmountable advantage.

+ The human player gets Opportunities, which can be Mercenaries for +Power.
- The AIs don't.

Then given two equal economies, the human player can inevitably buy more +Power.
This breaks any tie, and ensures that you win 1:1 or 5:5 line duels.

Thereafter, actually grinding out 30+ turns of line duels is even a tad repetitive.
It's actually not so fun to kick the AIs' teeth in, knowing that you're Simply Superior.
There's very little need for tactical brilliance or brilliant sacrificial combinations.
Line up, win your individual match-ups, roll forward.

~~~~~~~~~~~~~~~~~~~~~~
Peak Power Math: All Players
~~~~~~~~~~~~~~~~~~~~~~
The math for Power growth is mildly intriguing.
For all players, the endgame begins roughly when it finishes both of:

+ the Research tree (= all tile yields, +1 all Power), and
+ the Waste Reduction tree (= minimum Waste in all 4 categories).

and sets Wealth spending to 100% Power, since there's nothing else worth buying.

This implies that all players have the minimum -50% Power waste.
Then your total economy gives you +Wealth per turn.
Converting 100% of that into +Power gives you peak Power proportional to your size.

+ Let k be your +Power per turn. It depends on your empire size, and # of units.
+ Then your peak Power is simply 2k.
At this level, your +Power per turn matches your -50% Waste, attaining equilibrium.

Also, it takes 2-5 turns to grow from 0 Power to your peak Power.
For example, with k = +7 Power per turn, your growth rate will be:

+7 = 7
+4 = 11 (Waste always(?) truncates any fraction)
+2 = 13
+1 = 14, and it took 4 turns
=0 = 14 thereafter

Roughly, it takes log_2( 2k ) = log_2 k + 1 turns.
This can matter if you're 1-2 turns late to get your 1st Army out.

+ If you're below 2k, you gain +k per turn and Waste less than -k.
So you make a profit, and rise toward 2k.

- If you're above 2k (esp. if an AI player just lost a lot of tiles and city income),
your Waste exceeds your income, and your Power decays.

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Peak Power Math: Human Only
~~~~~~~~~~~~~~~~~~~~~~~~
The human player gets a bonus to the previous math.
We get Opportunity cards. From midgame onward, several of these are Mercenaries.

Mercenary offers last 1-5 turns each, for +3 to +1 Power per turn.
They stack with each other, for as long as their durations overlap.

The deeper point is that Mercenary +Power is added after this turn's Waste.
Next turn, you do pay Waste on it normally.

Let k = your +Power per turn from Wealth, as above.
Let m = your average +Power per turn from all Mercenary offers

Then your peak Power will attain equilibrium at 2(k + m), for the same reason.
At this level, your -Waste exactly balances your total +Power.
And the turns to reach your new 2nd peak is also the same: log_2 m + 1.

Continuing the previous example, let k = +7 Power per turn from Wealth.
Now let m = +2 Power per turn from Assassins offers, which last 1 turn each.

14 +7 -7 +2 = 16
16 +7 -8 +2 = 17
16 +7 -8 +2 = 18, and it took 3 turns
16 +7 -9 +2 = 18

For small m, the Waste truncation rule can add +1 turn to creep to equilibrium.

Things get a bit messier when we stack multiple Mercenaries with different durations.
But m is ultimately just the average over all of your offers.
Think of any 1 offer as contributing 1 row of a histogram.
Then sum (or integrate) the total area of the histogram, and divide by turns t.

In practice, you can often buy 5 Mercenaries in 5 turns, for m ~= +8 per turn.
But over 10 turns, you can't get 10 in a row, so your m is slightly lower, around +6.
Then your Human Peak Power is 2(7 + 6) ~= 26, with spikes up to 28 and dips to 23-24.

No AI can compete against that, regardless of their economies.
The Wealth cost of Power k is quadratic* in k.
(Edit: See proof in post #11, below.)
Even an AI with 2-3x your economy buys only +1 or +2 more k.
You can overwhelm that by buying Mercenaries.

You do have to buy enough Armies to create a 3-wide or 5-wide line of assault.
This counters the AI's tendency to defend in depth, stacking a 2-deep line.
Force it to defend 1-deep 5-wide, and it can't beat you 5:1 anywhere.
When you win 1:1 on math, you'll win 3:3 in the center of a 5-wide line.

After that, it's just a matter of grinding down the AIs, slowly rolling them back.
Along the way, you'll take every city in your path.

It's actually quite thoroughly anticlimactic.
There's no sense of ever being the underdog, and winning through guile or brilliance.
You're Simply Superior, as long as you don't get crushed in the opening.

[Gilmoy]

~~~~~~~~~~~~~~~~~~~~~~~~
Hard: Dholavira on Indus Valley
~~~~~~~~~~~~~~~~~~~~~~~~
3-player maps present yet another wrinkle.
With vast open space for unhindered expansion, all 3 players can get big fast.
Dholavira boasts an embarrassment of +Research to finish the entire yield tree early.

Yet the midgame challenge remains the same:
1. where to set the border, and
2. when to shift to military.

Lose to Harappans' midgame about twice in a row, and you'll appreciate #1.
Then this actually promotes to be the #0 priority, even on turn 1.

Hence we begin our pre-game analysis with the midgame vs. Harappans.
The Turn 1-3 gambit vs. your neighbor Mohenjo-Dara is simpler, and we'll defer it to #2.

~~~~~~~~~~~~~~~~
1. The Mideast Valley
~~~~~~~~~~~~~~~~
Look east of Dholavira's east border.
At 6 tiles ENE, there's a natural gap that goes:

Hill, Plains*, River
Plains, Plains, Forest

Harappans will expand south and southeast, and soon reach this Valley.
You can, and should, race southeast around the desert + hills, then northeast to the Valley.
With suitable maniacal focus, you can intercept Harappans in the Valley.
You get the Plains* tile, Harappans gets the River, +/- 1 tile either way.

All players' expansion can proceed only breadth-first.
Each turn, you can add at most +1 layer to the onion.
Counting tiles, Harappans is actually closer to the Plains* tile, at distance 6 vs. distance 8.
But you can count on Harappans AI to expand westward first, until it meets Mohenjo-Dara.
This costs it 2-3 turns of distraction.
Don't get distracted yourself, and you can outrace it to the Plains*.

From the Plains* tile, draw a diagonal line SE to the edge of the map. That's the border.
Now imagine it's the north border of a 3x8 parallelogram
that runs from the desert hills to the SE corner of the map.

- If you're slow in the east, Harappans will take this parallelogram and keep you small.
+ If you're fast in the east, you get this entire parallelogram for yourself.

You'll never keep Harappans small, but you can keep them small-er.
That buys you time in which they don't win on Food and Wealth.

Thus, I consider the #1 early-game priority to be to expand toward the Valley Plains* tile.
Every turn, without fail, take the 1 tile along that path. That's "all" there is to it.
This supercedes the need to encircle Mohenjo-Dara early. When in doubt, prefer east.

~~~~~~~~~~~~~~~~~~~
2. Turn 1-3 River Gambit
~~~~~~~~~~~~~~~~~~~
The eastward focus costs you only 1-2 tiles' worth of Food per turn, from turns 1-8.
Use the rest of your early Food in the usual way, to go west and seize good shared tiles.

I spend all of my 40 Research yolk on all 3 Plains + 3 Grassland flags, to grow fastest.
Also take at least 1 River tile, for your 1st River.
You start with 0 River tiles, and you can't buy River flags or Power while you have 0.

On Turn 2 or 3, you'll contest 1-2 shared tiles with Mohenjo-Dara coming SE.
You can gamble 10 Research on +1 Power in any of River, Grassland, or Plains,
to maybe win a flag-tie. I choose River, to guarantee winning an early River for +2 Food.

Thereafter, I follow Plains north until all 3 players meet.
Then I essentially cease all westward attention, and let Mohenjo-Dara have all hills.
Mohenjo-Dara never has Food, and is not a late-game threat to win, so I ignore it.
You must prepare your military thrust to roll back Harappans a bit.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
3. Early-Enough Military vs. Harappans
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To the SE, I follow the river.
But most of the emphasis is to seize the Valley from #1.
More deeply, you must set the mideast border vs. Harappans as far north as possible.

Dholavira is Ecological, so Units cost +20%.
Then your 1st army costs 48 instead of 40.
In particular, you cannot one-shot your 1st army in 1 turn. You must save for 2 turns.

To judge when to shift your Wealth to buy 1-2 unit(s),
the harshest way is to not do it, and lose to Harappans doing it to you.
Then your blunder was 2 turns earlier, when you didn't start hoarding Wealth for an army.

But this only makes you just-in-time to defend, which is a low bar, and too passive.
It's far more fun to be just-in-time to attack first.
That means you want to start saving 3 turns before Harappans do

My quick rule is: Whenever I research my first +Wealth tile yield, I turn off Food purchases.
Usually, this is 30 Research for +1 Wealth per Plains, when I have 14-16 Plains.
It's about the 5th thing I research, after more +Research and some +Food.

+ If I want +Food, I can research it directly.
+ Hence, when I research +Wealth, I'm not interested in converting it to more Food.

Wealth is to attack, and so it's the right time to shift to unit buying.

~~~~~~~~~~~~~~~~~~~~~~~~~
4. Too Many AI Armies Too Soon
~~~~~~~~~~~~~~~~~~~~~~~~~
The AI prefers to quickly buy 3-5 armies, even with an economy not better than yours.
This is mathematically feasible, and you could copy it if you wished (but I don't).

The first 5 armies cost 40, 70, 100, 130, and 160, or on average 100 each.

+ Any empire that earns +100 Wealth per turn could buy 5 in 5 turns (ignoring Waste).
- However, then it has $0 left each turn (on average) to buy +Power, so it buys =0 Power.

Then the 5 armies are Power 1 each, and a human could fight them 1v4 and win.
During the recruitment phase, while the AI is adding +1 army per turn, they're all weak.
So will yours be, if you do the same.

When the AI ceases recruiting and buys +Power instead,
it will attain its peak Power in the usual few turns. I sketch the math:

+ 5 armies costs -9 Wealth per base Power step.
+ Let the AI earn +180 Wealth per turn. Divide by 9 to get 20 steps' worth of Wealth.

+ Power steps then satisfy SUM{1, n} (i) = n(n+1)/2 < 20.
Solve or eyeball it to get n = 5 and SUM{1,5} (i) = 15 < 20.
SUM{1,6} (i) = 21 doesn't fit, barely. At +189 Wealth per turn, it does.

+ Then spending 100% Wealth on +Power buys +5 Power per turn,
with a peak at 10 Power (assuming -50% Power Waste). The growth rate is:

0 -0 +5 = 5 Power
5 -2 +5 = 8 Power
8 -4 +5 = 9 Power
9 -4 +5 = 10 Power, and it takes 4 turns = CEILING{ log_2 ( 5 )} + 1

Note that the very 1st turn of buying power gives a huge spike in on-field Power.
The AI's 5 armies will go from 5*1 = 5 Power total, to 5*5 = 25 Power.
That can stymie your 1-army attack if you're only at 10-12 peak Power yourself.

Anyways, the human player's solution is to bring 2 armies, and later 3.
Time your Power Waste reduction steps and new-army buys to coincide
with natural troughs in your attack cadence, esp. when you're threatening 0 tiles this turn.

All of these things happen against Harappans
+ I did attack first, and won 1 tile uncontested
+ Harappans AI did turbo-buy 3, then 4, then 6 armies
+ I was stronger 1:4, and then 3:5, than Harappans' impoverished Power spending

I let Mohenjo-Dara win a few tiles in the west. I can't defend everywhere at once.
I prefer to focus all 4 armies in the east to overwhelm Harappans and capture 2 cities.
Ultimately, I win on economy, as the two AIs combined never touch my production base.

To win as Harappans, obviously win the race to the Valley and push that border south.
To win as Mohenjo-Dara, maybe use a River Power Gambit in the center.
I don't know how it ever gets Food to compete vs. Harappans' east holdings.

[Gilmoy]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hard: Mohenjo-Dara on Indus Valley
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
First-try perfect! But I think I randomly got ideal anti-AI Victory Conditions.

+ Turn 1: Spend (5 + 8)/20 on 2 River flags. Save 7 to have 12 on Turn 2 for +1 Power!
+ Turn 2: Spend 12 on +1 River Power. This wins 2-3 River tile flag-ties from the 2 AIs.
+ Early: Invest in Plains/Grasslands flags, get as many as you can.

+ Midgame: All hill flags, go west over hills. Yields in the usual way, by bang-for-buck.
+ Dholavira AI and I turned off Wealth-to-Food on the same turn,
and created our 1st armies on the same turn.

+ I win an early skirmish, 1v2 but far superior in peak Power.
Driving due south to the shore, I cut off a 4-tile arm of Dholavira with 1 naked city west.
Its 2 armies were-defending from the east, get thrown east, and are now disjoint.
I easily take that city, and never lose it.

+ In the early endgame, the 2 AIs tag-team me (5 + 3) vs. 2.
They ignore each others' shared border, and attack only me.

+ Yet the V.C.s are utterly anti-AI.
The 3-crown options are: 18 Power, Capture 5 Cities, and 18 Power Techs.
AIs can never attain 18 Power, and can't out-fight me for Capture 5.

I somehow outfight them both without capturing a single city, and easily reach:
3/3: 18 Power -- using Mercenaries, of course
2/2: 30/30 city pop
1/1: 5/5 units (all armies)
1/1: 98/90 tiles

Both AIs had 4/7 crowns for the same bottom 3, but they'll never get any of the 3s.
So all I needed to do was to not-lose and hold the line.
800 Wealth was worth 2/2 crowns, but neither could afford that, and it still wouldn't win.

On T29, I grow the 30th pop, clinch 7/7 crowns, and then capture 1 city from Harappans.
I think we were zero-sum in trading tiles back and forth, other than that 1.

Mohenjo-Dara does get enough Food to not-lose.
Hills, some Desert, and some Sea are worth +1 Food at most, but that suffices.
AIs can't turn their ++Food advantage into peak Power on offense.

[Gilmoy]

~~~~~~~~~~~~~~~~~~~~~~~~~
Medium: Videha on Ganges Plain
Medium: Kosala on Ganges Plain
~~~~~~~~~~~~~~~~~~~~~~~~~
Ganges Plain introduces 1 new wrinkle, which is almost a newbie-trap.
All 4 players seem to start with very low Research.

• Videha's starter city has 1 pop x 2 Research = +2 Research per turn!
  
• Kosala's starter city has 2 pop x 2 Research = +4 Research per turn.

They both start with =0 Research per turn from all other tiles.
This can trap you at +2 or +4 for the entire early game, until you hit 20 for River Research.

Work-around: Continue to spend all Research yolk on flags and +1 Power, usually River.
Soon (by turn ~5), you'll be swimming in +Food from Rivers and Grasslands.
Shift your Wealth to buy Research at 100%, instead of more Food.
Then it takes only 2-3 turns to buy a +Research tile yield.

All else follows the usual methodology.
All players freely expand north and south to the edges of the map, and own 1/4 of land each.

Kosala is a tad more vexing because it borders 2, and possibly all 3, AIs, and they'll dogpile.
Pick one enemy, focus your Power, and stall or drive for V.C. crowns.

[Gilmoy]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Lemma: The Wealth cost of Power k for n units is linear in n and quadratic in k.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
From the How to Play, p. 5/5:
For example, if you have 1 unit, Power costs 5 for 1, 15 for 2 (5+10), and 30 for 3 (5+10+15).
However, if you have 6 units, 3 power costs 60 (10+20+30).

Let n denote the total number of units (armies + navies).
Then the base price of Power is (n+4).
n = 1 gives base price 5, and n = 6 gives base price 10.

Dividing the 2 examples by the base price, Power costs:

• (1+4) * (1) for 1, with n = 1
  
• (1+4) * (1+2) for 2
  
• (1+4) * (1+2+3) for 3
  
• (6+4) * (1+2+3) for 3, with n = 6

Let k denote total Power. We generalize the formula in the obvious way:

• = (base price) * (1 + 2 + 3 + ... + k)
  
• = (base price) * SUM{1,k} (i)
  
• = (n+4) * k(k+1)/2

This is linear in n and quadratic in k, as claimed.

[Gilmoy]

Using this formula, we can doodle out some typical benchmarks for peak Power.

A. Suppose we earn +240 Wealth per turn, and have 4 armies + 0 navies.
What's the maximum Power k we can buy per turn?
This is a typical Wealth level when you own about 1/4 of a map, with full tile yields.

Plugging in, we have 240 >= (4+4) * 1/2 * k(k+1), or 480 / (4+4) = 60 >= k(k+1).
Ignoring the +1, what's the largest perfect square smaller than 60?
7*7 = 49 fits, but 8*8 = 64 doesn't.
Now evaluate 7*8 = 56, and it still fits.

So we can buy +7 Power per turn, with a peak at 14 Power.

A.1) With +240 Wealth and 1 unit_, we have 480 / (1+4) = 96 >= k(k+1), and k = 9 fits.
A.2) With +240 Wealth and 2 units, we have 480 / (2+4) = 80 >= k(k+1), and k = 8 fits.
A.3) With +240 Wealth and 3 units, we have 480 / (3+4) = 68.6 >= k(k+1), and k = 7 fits.
A.5) With +240 Wealth and 5 units, we have 480 / (5+4) = 53.3 >= k(k+1), and k = 6 fits.

Note that k = 7 is the solution for both 3 units and 4 units.
Solving forward, at 3 units we pay 7*(56/2) = -192 of 240 per turn, with +48 surplus.
At 4 units, we pay 8*(56/2) = -224 of 240 per turn, with only +16 surplus.

[Gilmoy]

~~~~~~~~~~~~~~~~~~~
Hard: Ban Chiang on Asia
~~~~~~~~~~~~~~~~~~~
First-time perfect (or good enough).

Turn 1: River Power Gambit takes the shared west river tile from Kuru's east.
Harappans still runs its own Double Power Gambit to take 2 tiles from Kuru's west.
Inevitably, this kills Kuru's turn-1 economy, and probably dooms it to die.

No nearby tile type has enough multiplicity to justify flags, so 0 on flags.
With only 20 starting Research, I can't afford +1/+1 Power in 2 terrains.
I duck in the east, let Dong Son have the shared tiles, and go for non-shared Forest.

2 turns of Wealth => 100% Food to spread south ASAP.
Then shift Wealth => 100% Research for faster +Research yield.
I take most of the island chain south. On turn 10, I hoard Wealth for 1st army on turn 11.

The Asia map is full of Hill (+2 defensive bonus) and Forest (+1 defensive bonus) tiles.
AIs are content to have 1 early fleet at 3 Power for 10+ turns of midgame squabbles.
You can stymie that with 0 units, using only 1 city + Hill/Forest defensive bonus.
This let me ignore Dong Son + Polynesians' 1 fleet each for ~20 turns.

I patiently get 2 armies, push west into Kuru, cleave it twain, and flag its fallow hills.
I turn on sea yields and take 36 sea tiles, all the way to the SW corner.
Oxus kills Huns and takes some hills from my north, I eventually go 4-wide and push them.

Research patiently gets more +Research yield.
Wealth patiently buys a 2nd army, for 2v2 attacks to wipe out 1 weak neighbor.
Ignore your Waste steps until after you've established military progress.
I minimize -Food waste on barren sea tiles, except to build a sea fence to cut off Kuru.
Around turn 25, sea yield is the right time to flag seas en masse.

Finally, sometimes it's tactically justified to trade tiles.
Let an east or north neighbor take 2 of your NE tiles, as long as you take 2 west tiles.
You can't passively defend everything forever.
Better to focus your tile trades to kill an AI, and collect 1-2 cities and 5-20 tiles profit.

~~~~

Kuru AI will never self-modify its algorithm to run its own Power Gambit,
so that 1 book trick will work against it forever.
I do wonder how Harappans AI is scripted to always do it, and no other AIs ever do.
Maybe Harappans starts with 40 Research, which satisfies a precondition?

[Gilmoy]

~~~~~~~~~~~~~~~~~~~
Hard: Dong Son on Asia
~~~~~~~~~~~~~~~~~~~
Dong Son starts with 0 River tiles, so you cannot do a Turn 1 River Power Gambit vs. Zhou.
I go NE for the Grasslands instead, then NW into Hills with +1 Power, then south into islands.

Buy 2 turns of Food until your good Food tiles bootstrap, then buy Research for ~8 turns.
I outrace Zhou to 1 army, then to 2 armies, and soon kill Zhou and Ban Chiang.
After that, I have economy advantage and Power advantage.

~~~~~~~~~~~~~~~~~~~
Very Hard: Huns on Asia
~~~~~~~~~~~~~~~~~~~
Lost 1 while learning it, won the 2nd.
This was the most fun win I've had in the last 10+ games, oddly because it took a while.
I finally won on Turn 48, after an epic struggle.

Huns have an obvious Grasslands/Forest opening going east.
More curiously, it starts with 30 Research, with +7 income and -8 Waste.
Hence you must spend some Research on Turn 1, or you'll waste it all.
I choose 2 Hill flags for -15, and later +1 Hill Power to win 3 flag-ties.

There's almost zero chance of taking Zhou's adjacent River tile.
Even if Zhou leaves the river tile empty on Turn 1, on Turn 2 it will win it on adjacent tiles.
Huns can't buy +1 River Power on Turn 2, since you start with 0 River.

More deeply, Huns' early-game problem is never enough Food.
Buy 100% Food for about 5 turns, until you earn about +8 Food per turn,
which lets you flag 1 Hill per turn. Most AIs also flag 1 tile per turn, so it's good enough.

Then buy 100% Research for a few turns.
Huns are Militant, so 32 Wealth suffices for 1st army.
I time it correctly, outrace Zhou to 1 army, cut it in half, and take its northern city.
Then I push Gojoseon back to the hill tile above their city, but I can't beat its bonuses 1:1.

The most important thing to buy with ~60 Wealth is -- the 2nd army, for 2:1 dogpiling.
Planning 3 turns ahead:

- first I reduce my +Power buying to ensure ~80 Wealth next turn, and get -2 = 3 Power
- then I pay -56 for 2nd army, and both are weak, with another -1 = 2 Power
- finally, I pay max for +3 = 5 Power, and the 2:1 combined attack wins Gojoseon's city.

Meanwhile, Kuru and Oxus threaten my SW hills, and I grit teeth and let them fall.
Ultimately, I throw Gojoseon off the mainland, eliminate Zhou, and flag most of their tiles.
In the east, I lose 2 desert + 3-4 hills to Kuru and Oxus. It's a winning trade.

Finally, I'm the #1 economy, and I can focus full attention east.
3 armies at Power 14-16 evict Oxus from the hills, and capture 3 of its desert/plains cities.
I send 2 fleets east to capture seas, eating my way toward Gojoseon's last island city.

Most other games end long before this stage.
Huns' slow early start has the delightful benefit of prolonging the tense midgame.

I think I had decent anti-AI Victory Conditions.
I finally won on 30 city pop, 3 city captures, 90 tiles, and 300 Wealth.
More deeply, the AIs happened to partition land so as to not dogpile me.
AIs fought each other non-stop, and largely ignored me for ~30 turns.
Trading the same land back and forth, none of them could attain 30, 90, and 3.
AIs are inefficient at killing each other off.

Huns' strength really is its Militant trait making units 20% cheaper.
That means you can launch your 1st attack 20% earlier, when AIs are even less prepared.
It can be terrifying to be last in economy until then, but trust the attack to win your space.

[sly_squash]

Emergent Gameplay is quite a thing.

It's fascinating reading the stories of other players and how they came to better their understanding of the game through theory crafting and practice. This is like watching the process of someone developing their understanding of math from arithmetic to advanced calculus in just a few hours.

This is why I'm hoping they implement Game Recaps, like little animations that show the map progression of the whole game turn-by-turn from start to finish. Imagine if you uploaded videos of those recaps to youtube so we could watch what you describe happen.