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Friday, January 22, 2021

Empire Total War advanced tips

Empire Total War predates popularity of let's plays, game wikis and such, so I don't think these tricks are widely known.

I assume you played some Total War games and know basic game mechanics, and get right to the good stuff.

Where these stand on scale of legitimate gameplay to outright exploit is up to everyone to decide on their own.

I'm aware there are some exploits much more powerful than those (notably cycle selling military access and movement detach exploits), but they take hours of your own time to execute and aren't really any fun.

All these apply to vanilla or lightly modded game (I usually play with Additional Units and No Walls mods). If you're playing a bigger mod like Darthmod, most of these techniques still work, but a few might not.

I also wrote followup post with more tips.

How to avoid 0 FPS sieges

If you siege a fortified settlement, and make holes in its walls as God intended, it usually triggers pathfinding issues that drop game to 0 FPS, and make it somewhere between extremely frustrating to completely unplayable.

There are two solutions:

If you insist on playing without mods, the easiest way is to use howitzers. Approach diagonally, as fort guns are only places along cardinal directions. Bombard fort with anti-personnel ammo only. Once they softened sufficiently, send in your infantry. This is super easy, and super effective, but really boring, so I recommend mods.

Ship jumping

This works in a lot of strategy games, so no surprise it works here too.

To get army from point A to point B the faster way is by sea, using multiple ships. Here's the technique:

  • get army on a ship (either in port for 0 action points or just jumping from coastline for 1 action point)
  • move that ship in direction you want to go, but don't use all its movement
  • get another ship to this navy (it doesn't matter if old or new ship does the joining)
  • move original ship that used almost all its movement out of the navy
  • now the army is on new ship which hopefully has more movement points
  • repeat for as long as you want

Creating a chain of ships like that can move people from Sweden to Egypt or Guyana to Quebec in one turn, without risking anything happening to your troops on the way.

If your troops land in port, they'll have full movement points no matter how many ship swaps they made. If not...

Fast naval landing basic technique

When you land an army on shore without port, it's supposed to reset their movement to 0.

What game actually does is figure out which unit in your army has the fewest action points left, and subtract that from all units.

For simple example:

  • land army with mix of cav (20 action points left), inf (18 action points left), art (16 action points left) next to an enemy settlement
  • what game really wants to do is reset it to cav (0 action points), inf (0 action points), art (0 action points)
  • but it actually subtracts 16, so it resets their movement to cav (4 action points), inf (2 action points), art (0 action points)
  • select everyone except art, move them a bit towards enemy settlement
  • now that attack enemy settlement
  • leftover art units will join as reinforcements anyway, so your whole stack participates!

I recommend saving game before it until you get used to it, as you only get tiny bit of movement to work with.

If your inf can't reach the settlement, you can try detaching just cav. That means more awkward reinforcement time, but you still get to fight with everyone.

Fast naval landing advanced technique

You can do a lot more than that. Before embarking on the ship, pick one unit in your army, waste most of their action points (walk away from army, then walk back into army), then embark everyone.

  • land army with mix of cav (20 action points left), inf (18 action points left), art (16 action points left), unit that moved (3 action points left)
  • that resets their move tho (17 action points), inf (15 action points), art (13 action points), unit that moved (0 action points left)
  • select everyone except that one unit, and move almost as much as you could normally

Embarking (outside port) and disembarking takes a bit of movement, so don't try to waste all the points (or save game before that until you learn how to do it).

Direction of reinforcements

This is true in all Total War games, but game never explicitly says so, so many players are unaware. As a general rule, reinforcements show in the battle from same direction as they are on campaign map - relative to direction of attack.

So if your reinforcing army stands behind you, they'll reinforce from behind. If they stand on the left, they'll reinforce from the left. If they stand opposite of the enemy, they will show up behind the enemy.

University spamming

In most games tech progression is pretty very limited, but Empire has no such limits. If you have 2 universities you'll research 2 times faster. If you have 10, you'll research 10 times faster.

There's no reason not to get a lot of them fast - either by conquest or building them. Opportunity cost of a few building slots to get crazy tech advantage is very low.

Universities cause unhappiness. If you're a republic (Netherlands is the only republic major at start of the game; you can flip into republic as someone else too), this is reduced by 80% so you can build them pretty much wherever.

If you want to stay absolute or constitutional monarchy, to completely avoid problems you should really only build 1 university per province, and only in 5 slot provinces (as it has some slots for happiness buildings). Building 2 universities in our home province, or building 1 in 2-slot province without too much religious unrest can lead to minor unrest issues, but it shouldn't be too bad.

You're going to capture some universities, and if they're in location where you don't want them, just tear them down, it doesn't costs much time or money to exchange one building for another.

You must keep university in your home province as that's the only one you can upgrade to tier 4, and you need one of those to unlock final enlightenment technologies.

Technology priorities

Empire lets you race like crazy with technology, but it matters fairly little. Only two technologies are game changing - Canister Shot and Fire By Rank.

You should always get Canister Shot as your first tech no matter what. After that it makes sense to do infantry techs (different Bayonettes, Square Formation), as they provide nice bonuses themselves, and lead you to the ever important Fire By Rank.

Carbines unlock Dragoons which are nice for rebel suppression, but cavalry techs are basically worthless as their fancy formations aren't useful at all.

Artillery techs beyond Canister Shot aren't very useful.

Navy techs are basically worthless.

Farm techs are nice as they speed up your population growth, which gives you more building slots. Farm buildings are always worth upgrading. For wheat farms, level 3 has -1 lower class unrest, but then it disappears at level 4 (level 5 is expensive and pointless). Weirdly wine farms never get rid of unrest, and rice farms never get any unrest. I don't really get the logic.

Industry techs are low priority, as their bonuses are low, and high tier industry buildings have terrible return on investment.

Enlightenment techs give you a lot of unrest from universities. It doesn't apply to provinces without universities, so it's usually no big deal. As exchange you get higher research rate and small some town wealth bonuses. High tier enlightenment techs (Secular Humanism, Abolition of Slavery) offer big unrest reduction for all that trouble.

Building priorities

Low tier buildings have excellent return on investment, high tier buildings are terrible.

For example level 1 weavers gives 600 town wealth for 1000 cost. Level 2 gives 300 more wealth for 2000 cost (4x worse). Level 3 is 300 more wealth for 4000 cost (8x worse) and -1 lower class unhappiness. Level 4 is 300 more for 6000 cost (12x worse) and another -1 lower class unhappiness. (or different number depending on town wealth; but ratio is alwasy the same)

Mines scale even wore than that.

So basically you should always build low tier economic buildings before doing any upgrades.

You can do a lot of micro to optimize your income, but that's not where most of the money is going to be coming from.

Buildings to just destroy

Wrong religion religious buildings should be destroyed immediately. Any universities you don't want (generally those in bad religion 2 slot province; unless you're a republic and don't care) destroy as well.

Any fishing ports need to be destroyed and replaced by trading ports. Game has far too many dockyards, and you're best off replacing half of them by trading ports as well.

Build up rice farms up to the max (no unrest).

Build up wheat farms up to level 4 (level 3 gives unrest, which level 4 removes; level 5 is just too expensive).

Wine farms up to level 2 (level 3 gives unrest).

Level 1-2 roads are worth it as they're cheap and give armies nice movement bonus too. Level 3 might be a bit much.

Destroy any happiness buildings, especially in wealthy slots, once province is fully under control. They're worth keeping for a while in newly conquered lands as they mean fewer turns of babysitting unrest. If you're a monarchy you might want to keep some in university provinces indefinitely.

Religious unrest

This is an aside, but religious unrest in Empire Total War works on complex table of who hates whom how much.

A tl;dr of religious relations table is:

  • everyone else hates Animist (New World Natives) government
  • Muslim peasants absolutely hate everyone else
  • Hindus/Sikhs moderately dislike everyone else (including each other), but to lesser degree than Muslims
  • everyone else mostly gets along

There's a second interesting fact is that speed of religious conversion by missionaries and religious schools is slower in high population provinces.

Taken together these mean that if you play European Christians:

  • converting Muslims - medium population, high unrest - good ROI
  • converting India - high population, medium unrest - medium ROI
  • converting New World - low population, low unrest - medium ROI
  • converting other Europeans - high population, low unrest - very low ROI

If you play Hindu, you should prioritize converting Muslims (and Sikhs) over Christians and Buddhists.

If you play Muslim, you should prioritize converting Hindus (and Sikhs) over Christians and Buddhists.

If you play Animist there are different mechanics for it anyway.

How to get good income

Game gives you 3000 income for free (unless you use mod to play minor power, they get less)

Beyond that you get tax and trade income.

Tax income suffers from administrative costs depending solely on number of provinces you hold. It quickly escalates and at mere 10 provinces you'll already suffer -14% penalty, but then grows more slowly. By the time you conquer the world and its 137 provinces you'll be at nearly -57%. Conquering poor land might very well end up losing you money. (here's the formula)

Trade is a much bigger money maker.

For trade income you need trade goods and at least one trade partner with unblocked access. You get extra money from more partners, or from wealthier trade partners, but it's not actually that much.

To get trade goods you can build plantations, but most of all you can spam cheap trade ships, and put as many of them into all 20 trade nodes as you can. Fancier trade ships Spain and Netherlands can build are not actually worth it, they won't even pay for themselves and aren't even particularly good at fighting.

If you keep your wars low and get rid of pirates, you might be able to leave your trade ships largely undefended. If one of 4 trade areas is too contested, just move your trade ships elsewhere.

Choosing trade partners

Let's say you have massive pile of trade goods coming from your trade ships and your colonies.

Now you need some trade partners.

To maximize money you could trade with everyone you can, however many trade slots are allowed. This is however highly risky - if their ports are blockaded due to their wars, then that proportion of your trade is completely lost, it doesn't get rerouted to your other trade parters!

So Mughals are a terrible trade partner, they'll get their ports blockaded in a few turns pretty much every game.

Best trade partners are actually one province minors you neighbor, or even better your protectorates. If you trade by road, it cannot get blockaded, and they can take all your goods no matter how many you produce.

Other fairly safe partners are Marathas (who have naval superiority in India) and Britain (who has naval superiority around itself).

Destroying Pirates early

Naval combat is a huge hassle, and even as inland power fighting other inland powers you pretty much need trade ships for meaningful income.

Fortunately there's a way. Pirates have only 2 tiny islands you can land on and destroy in first few turns of the game. Trinidad & Tobago is barely defended (2 Pirate Mob garrison). Their capital at Leeward Islands has some defenses (7 Pirate Mob garrison, depending on difficulty I think). Destorying them removes all their fleets.

If you have any presence in New World, you should probably just do it. Otherwise they'll keep harassing your trade ships in all 4 trade areas.

If France gets destroyed in Europe, their Carribean island joins Pirates as well.

Destroying European Colonial Empires the easy way

European powers have very impressive empires, but if they lose their European possessions, all their colonial regions instantly rebel. This applies to:

  • Portugal - 1 home region
  • Nethterlands - 1 home region
  • France - 2 home region
  • Great Britain - 3 home regions
  • Spain - 6 home regions

I'm actually not sure what happens to Persia if you take all their provinces except Afghanistan (which is technically in India theater). Or to non-European powers with wrong-theater holdings.

Army Use

This is true in all Total War games. Armies are stupidly expensive to upkeep, but very cheap to recruit. The ratio is typically about between 3:1 and 4:1.

So having army do nothing for 3-4 turns costs as much as losing the whole army and recruiting it from scratch.

That's why it pays to aggressively use your armies all the time. Massive losses are no big deal at all!

Expansion strategy

A followup to this is that your armies should always be doing something useful, and as much as possible that something should be conquering new territory.

As much as possible, try to face just one enemy at a time. Fighting two enemies is much worse.

But what's even worse than that is fighting one enemy while your second army just guards border with the other and collects upkeep.

For example - if you play Poland, your early enemies will be Prussia, Austria, and Sweden (who will attack one of your allies). One easy strategy is to ignore Sweden as they're too far and likely won't do much damage, ignore Austria as they're too big to rush, and focus all your troops on destroying Prussia as fast as you can. If you do that, you only have Austria as active enemy. Even if you temporarily lose a province or two, eliminating Prussia is absolutely worth it.

Army Composition

Once you get Canister Shot, artillery becomes stupidly good, so best army composition is something like 10 Line Infantry, 6 Artillery, 4 Cavalry.

Pikemen and such melee infantry are trash.

Militia units are trash - initially they're actually worse Line Infantry for a bit less money, but Line Infantry gets upgrade after upgrade and Militia sees none of that.

One Attacker Per Battle

In a land battles it's easy to be on defensive or on attack, but the worst option is for both sides to advance at the same time.

It's usually very easy to predict if AI will attack or not. It mostly checks who has artillery superiority, and ignores artillery that's not ready to shoot.

So if you want AI to leave you alone for now (usually because you want reinforcements to come), just keep all your artillery limbered. The moment you unlimber even one they'll start moving.

Artillery is stupidly good, so you'll generally have artillery superiority and will be able to enjoy the defensive.

If you're advancing (usually because nobody has any artillery), pick best direction, form lines, and advance with whole line in good order.

AI Artillery

AI often keeps its starting fixed artillery for far too long. You can ignore it, deploy a bit back, and they'll just sit there out of range the whole fight.

Even more interesting is that in Empire units can deploy entrechments, but artillery entrechments are ridiculously terrible. They not only stop artillery from moving, they also stop it from rotating. So just walk around and they whole artillery will sit out the whole battle pointing in wrong direction.

AI artillery crews are somehow so frustrated they abandon their guns and run towards your army with kitchen knives. But mostly they just sit there.

Unit Range Logic

Game shows unit ranges, but if even 1 soldier in your unit can see even 1 soldier in their unit, then everyone can see everyone else. This makes range actually a lot bigger than it appears.

Targetting Ground

In addition to targetting units, you can also target ground. This isn't necessary to play the game, but it can greatly improve your artillery skills.

If you target unit, artillery seems to target its side not center, and that's rarely what you want.

You can target between two units to get cannister shot exactly the right place, you can target in front of moving unit to get more accurate shot, you can target place where you know or suspect hidden units are.

However, the most inteteresting kind of targetting is targetting beyond artillery's range. Artilery shots going beyond range cannot kill humans, but they can still damage buildings and enemy artillery pieces.

Shooting out of range against forts would be great, if it wasn't for 0 FPS bug if you actually do that.

Shooting out of range against enemy artillery lets you gain artillery superiority regardless of how few guns you have. In principle if AI has 20 guns and you have 8, they'll just stand there waiting for you to attack. You can stand from outside range, target land next to their guns, max speed, and in suitably long time minutes you destroy enough of their guns with no losses (but none of their crews) that enemy will abandon its lines and attack you.

This takes very long time, but you don't actually need to do anything in that time, you can just leave the game running.

A less extreme version of this is just having your artillery target theirs while AI is running around trying to form line. In 10 minutes its going to take anyway, you'll kill some guns. Otherwise your artillery would stand there doing nothing.

Canniter Shot Line Formation

A super easy way formation is mixing infantry and artillery in a line. There's many combination, like 1-2 artillery units, separated by 1-3 infantry units.

Some examples, they work approximately equally well:

  • IAIAI
  • IAIIAI
  • IIAAII
  • IIAAIIAAII
  • IIAAIIAAIIAA

It's about the strongest defensive formation in game. Anyone who approaches wanting to get into a shootout will die to canister shots from both side.

Before enemy gets in range, you can switch artillery to round shot to obliterate their cavalry or just let them shoot whoever.

If they try to charge you frontally, you might need to counter-charge your line infantry to protect your artillery. If you get charged on the side, use Square Formation - this magically gives units big melee bonus even if they're not actually in formation.

This kind of army should be augmented by a few units of cavalry, mostly to cleanup routed enemy units. That cavalry should generally start the battle behind the line as reserves on both sides. So total would be something like 10 Line Infantry, 6 12-pound Foot Artillery, 1 General, 3 any Cavalry.

This formation is quite flexible. Early game you can use your starting fixed artillery and militia.

It has some weaknesses. Enemy with too much melee infantry will just charge you and ignore your firepower. Your line can stand firm or slowly move forward, but it's bad at quickly changing direction it's facing. If enemy attacks from the side, your other side will have hard time reinforcing (so your cavalry reserves can help).

There's some depth to this formation, especially after battle starts, but it's easy to learn.

For expected peformance (on hard/hard) against equally sized enemy army, you should typically be able to inflict about 5x the casualties you receive.

Having artillery stand separately on a hill behind the lines like the game implies you might want to, is a terrible formation. Canister shot is just stupidly effective, and round shot is just far too weak, expecially from longer distance.

No Artillery Combat

If you have no artillery and you have infantry vs infantry fight, your main objective is to have more of your guys shooting than their guys.

Only soldiers in front row shoot (until you have Fire By Rank tech) so just going wide is perfectly fine. One unit deployed wide will beat one unit deployed narrowly every time. If you can have multiple units shoot at one enemy unit, that's even better.

Your infantry is primarily for shooting, but it's perfectly decent at melee, and if you think you can break enemy unit by attacking from multiple sides, that's much more effective than prolonger shooting. Routing a few enemy units suddenly means your remaining units now outnumber your enemy!

On higher difficulties AI gets modest bonuses to shooting ability, but relatively high bonuses to morale. So breaking enemy morale works great on normal, but on higher difficulties canister shot to just kill them is king.

Cavalry in Empire is weak and will not win in prolonger mele. It gets even weaker on higher difficulties as enemy morale is higher. Cavalry is still amazing at eliminating routing units. They're OK as a reserve to quickly reinforce part of your line that's doing poorly.

To counter enemy cavalry charge, pressing Square Formation is stupidly effective - even if you press it after getting charged, as it works by magic, not by formation.

Empire land battles are reasonable balanced. Getting 5:1 casualties ratio in even battle is doable, but defeating a force twice your size would be a big struggle (unless AI derps).

Naval? Not even close. One Sloop vs full stack of 20 best ships (like 100:1 by cost) is trivial if you have enough patience or are willing to press magic win button.

So here are some basic facts the game won't tell you about:

  • AI never uses anything except regular shot
  • chainshot destroys enemy masts and so immobilizes enemy ships
  • every ship type has dead zones - it can be back or front or both; also diagonals but that's more fiddly
  • if enemy ship is immobile you can approach it quite close from certain angles and damage them with round shot until they surrender; or come even closer and grape shot their crew to death
  • expensive ships are resistant against hull damage (round shot), but not against mast damage (chain shot), or crew damage (grape shot)
  • cheap ships have range 500 guns, expensive ships have range 400 guns, so cheap ships can always outrange expensive ships
  • cheap ships are much faster than big ships
  • ships with even slightly damaged masts massively lose max speed
  • chain shot does drastically more damage if shot at ship sailing directly with wind

So the tactic is to position yourself so that wind goes from them to you, and zigzag away from them while shooting chainshot left then right at whoever's chasing you closest. Whenever you damage ship's masts they'll start falling behind, and another enemy ship will pursue you instead.

Soon enough, all enemy ships will have severely damaged masts - and will be far away from each other. You can stop running away, move into their dead zone, and fire at them with round shot or grape shot to make them rout or surrender.

Expensive big slow ships with 400 range guns are no frontal guns are a joke to your one Sloop navy.

This strategy can be executed by Sloops, Brigs, Sixth Rates, and Fifth Rates Doing it with 2-3 ships, or with ships that have more firepower is reasonable alternative to One Sloop Navy, but it's much harder to zigzag them, so you're not actually saving that much real time - your bigger ships will also have harder time early on while enemy still has light ships with full mobility, but they have easier time later in the battle.

Never get any ships bigger than a Fifth Rate, as you lose range - Fourth Rate and bigger ships are absolutely worthless floating garbage.

Slow low range ships like Indianmen will mostly mess things out for you, so don't include them in the battle.

This strategy has a few risks:

  • this strategy is basically perfect if executed exactly, but you need to be quite patient and quite careful, especially early in the battle
  • enemy fast ships with 500 range guns need some extra caution, especially early on before you damage their masts
  • ships with front facing guns need some extra caution
  • enemy light galleys and galleys are surprisingly hard to deal with, as they have huge front facing guns, you can't mobility kill them as they use oars (you'll still slow them down), and they're small and difficult to hit
  • if you reach edge of the map, you can get trapped and unable to keep your distance, so turn around well before that happens
  • if you touch the red edge of the map, you can also get stuck there by a game bug
  • routing armies rarely recover when pursued, but routing ships will routinely do that as you're not dealing any damage to them when you chase them - this means chasing a ship that's running away has high risk of them recovering, and just turning their guns on you as you got too close
  • if you get too close, even to enemy dead zone, their marines can still fire their muskets in every direction
  • your admiral can sometimes suicide in the battle due to glitch, even with enemy nowhere close to you; or some other stray event can cause morale hit

The opposite end of the spectrum is to have a lot of heavy ships, run as close to enemy, and keep roundshoting them until they sink or die.

This is also extremely tedious, and I found it basically impossible to play this other than on half speed or constantly pausing. Your ships won't even turn to shoot their guns, and there's no easy indicator where they are.

The upside of this build is that you can win by autoresolve. Empire autoresolve is stupidly biased against the player, and will somehow lose you what should be a 5:1 zero loss massacre, so always save before autoresolving. They only fixed it in Rome 2 (and went too far the other way, but it's still far far better than old style autoresolve).

Keyboard Shortcuts

I strongly advise rebinding "cancel order" to TAB to make naval combat a bit more bearable - you'll be doing it all the time, and getting your hand all the way to press backspace or moving your mouse to anchor doubles the tedium.

Battle Timer

At any time you can change your timer settings between 20, 40, 60, and unlimited.

Empire battles are slow, so I normally keep it unlimited. This doesn't mean battles will last over an hour, most battles have long periods of early artillery skirmish or moving into formation phase you'll play at high speed. Actualy fight is usually at reasonable pace.

If timer runs out the battle doesn't end in a draw as you'd expect - instead attacker loses, and somehow loses with massive additional casualties.

This is maybe too cheesy, but absolutely best way to win naval battles is:

  • be defender
  • set time limit to 20 minutes
  • do chainshot zigzag or whatever, just keep your distance and don't lose your ships
  • timer runs out, enemy autoloses and usually it sinks half their ships
  • remember to change it back before your next battle (those settings are in save file not in game settings iirc, so if you reload you might need to change it again)

This can sort of work even with a fleet of Indianmen attacked by a real fleet - you might lose some, but they won't sink them all in 20 minutes so your trade fleet sinks a lot more of their ships instead.

This is really cheesy, but it's a thing.

Technology Stealing Trading

If you know what you're doing, you will have more universities than any AI, so you can always outtech them, but you can supplement this with technology stealing and trading.

Your gentlemen can either help research tech, or steal tech. Stealing tech is random, but it has technically much higher expected value. They can also duel, but that's pointless other than getting an achievement for it.

Technology trading is much more interesting. Early game, before everyone hates you, and before you trade techs too much, you should be able to buy 1 tech for 2 or 3, or for some petty cash.

I'd advise against selling Cannister Shot and any infantry tech. Industry tech unlocking new buildings can be good for AI, as it often has nothing to spend its money on, but that makes them upgrade their buildings faster, and you'll then conquer better lands.

For some reason save game remembers how many times you traded each tech. I suspect that's the primary reason why early game 2-for-1 trades become 6-for-1 trades by mid game. AI just values something less if you sold it a bunch of times already, but I don't know the formula.

Diplomacy

If you ever played Empire you'll see how happy AI is to declare war on you. All your neighbours will attack you. Most of your allies will backstab you. If you have a coastline, Great Britain will declare war and drop a full stack on you too. White peacing out anyone is basically impossible - and conquering one country just means you got new neighbours who will attack you in turn.

Especially if you play on hard or very hard, it gets really frustrating.

If you play vanilla and expand at all, AI will all hate you for it with big diplomatic penalties. You can use a mod to make those penalties more reasonable (I even decoded those diplomatic tables back in the day, trying to fix it), but this has far less impact on AI behavior than we expected.

Fortunately there are ways to help it a bit.

Alliances

AI usually defends its allies against attack, except when that ally is the player.

Call to arms always happen defensively. You can decide to call your allies into an attack - but generally they'll refuse, and I don't think AI uses this function much. Allies cannot be called into preexistent wars, so making allies with someone already at war is fine.

Alliances in Empire do not chain. If Spain is allied with France and Genoa, and you want to fight Spain without also fighting Spain, declaring on Genoa usually works. Of course the downside is bringing in any other of Genoa's allies instead.

Protectorates act like one-sided alliances. Saxony is protectorate of Poland. Attacking Poland will not bring Saxony into it. Attacking Saxony will bring Poland, but none of Polish allies. Protectorates don't normally have any allies, so any country with protectorates (like Poland, France, Spain, Great Britain, Ottomans) is very easy game.

Some countries like Austria are guaranteed to get into tons of wars, so if you start allied with them, just break that, otherwise you'll be in a bunch of extra wars for no value.

Your AI allies will not be very useful, but alliance somewhat discourages them from attacking you.

Bribing AI for White Peace

If you want to have fewer wars, AI will not take white peace unless it's severely beaten. The easy way is to pay AI to go away. And the best payment is tech. You'll be far ahead in tech, so paying someone a few techs to go away after you took some of their land is usually a great idea.

There's little downside to that, other than game counting how many times you traded techs. Try not to trade important military techs this way.

Giving Away Military Access

This is pretty much an AI bug, but for some crazy reason if AI has indefinite military access to your lands, it massively reduces its bloodthirstiness. It's not absolute safety, and you can still be attacked, but the chance is drastically reduced.

So turn one give way military access to every great power and every neighbour except those you want to fight soon. Your whole campaign will be so much easier.

You can even get a bit of cash for it, at least early game, but it's not really worth much.

At any time you can cancel military access and give it again - if you don't like where AI troops went. This bounces any AI army back to the border, and they don't mind one bit.

Population Happiness

Empire has 3 classes (upper, middle, lower), but for each government one is irrelevant.

Lower class is the hardest to please, especially late game once industry seriously develops. This makes Republics (which have big lower class bonuses), and Constitutional Monarchies (which just plain don't have lower class) easier to play.

It's a bit of micro, but you should generally really prioritize getting governent ministers with bonuses to lower class happiness. +1 lower class happiness is usually worth more than some management stars.

Microing happiness is more important to your Empire gameplay than microing economy or army composition.

Stages of Unrest

If either class has below 0 happiness, you'll get unrest.

Unrest has 3 phases:

  • strike - it is just a warning, nothing bad actually happens
  • riot - some building gets seriously damaged
  • rebellion - a snack of about 6 rebel units spawns

Ticking off taxes (at normal rate), gives +4 happiness. If unrest is -1 to -4, you can just tick taxes back and forth every other turn. This will make province pay their taxes half the time, but have zero actual negative effect of unrest - which is strictly better than them paying zero taxes.

The game notifies you which provinces are in which state when turn starts, but there's no way to check it later, so you should write it down if you want to micro it.

Rebels

Taking enemy capital gives -30 unrest from resistance to foreign occupation, gradually reducing by 1 a turn. This means you can get stuck babysitting for very long time.

It's quite rare to get serious unrest in provinces with no resistance to foreign occupation. If you're playing well, all other modifiers rarely stack high enough to make a province go negative.

You can improve happiness by thingl like:

  • repairing government and happiness buildings (they're damaged when you take settlement, and that can be even +8 happiness for enemy capital)
  • destroying infidel religious buildings, and setting up your own to convert population and add happiness (especially outside Europe)
  • getting good ministers
  • optionally destroying universities to remove Clamor for Reform
  • not doing any upgrades which would give unhappiness due to industry until everything is in order
  • stationing troops in city itself (elsewhere in province won't count)
  • disabling taxes
  • defeating rebels

Never disable taxes unless it removes unhappiness. Untaxed -10 or taxed -6 unhappiness has exact same results, except you won't be making any money.

There's pretty much no way around it, and you'll often need to babysit conquered capital for a while.

Having whole 20 unit army there is usually a bad idea - it will cost you ridiculous amount of money. Rebel stacks are usually around 6 units, so a half stack can handle them perfectly fine. You can even autoresolve rebels most of the time.

Some unis like Dragoons have bonus to happiness from garrisoning, and other units like Militia are just much cheaper than your army. If you need to long term garrison some place, use units like that, not real troops.

Defeating rebels gives non stacking +6 happiness, but it deteriorates by one a turn. So -20 resistance and +6 crackdown will tick down together over next six turns to -14 resistance and +0 crackdown. Happiness will not improve at all during that time.

Population unrest will be a limiting factor in your expansion a lot, and there are no big tricks, just a lot of small tricks, so learning how to best deal with it is well worth your time.

If rebels take any province that's not your original capital, they'll either make it join another country, or become independent country, or become rebel-held province.

Government Types

If rebels take your original capital, they can change your government type.

You should absolutely use it to change it intentionally. The only way it can change is absolute monarchy to republic, republic to constitutional monarchy, or constitutional monarchy to absolute monarchy.

I'm not completely sure if republics or constitutional monarchies are better (probably constitutional monarchies, but not by a huge margin), but either is far superior to absolute monarchies, especially late game.

I don't think I ever did constitutional monarchy to absolute monarchy change, as it's pretty much the worst government type.

Changing Government Type

To change government type you need your capital to rebel. To do that, max out taxes in your home theater. You'd probably prefer your other provinces to not rebel, so as soon as they strike disable their taxes for a turn, that generally works.

To have a super easy revolution, move all your armies out of you home region, so rebels can walk in unopposed. You can even keep the rebel stack, but it's often trash, so you might want to disband it other than the general.

This will make most countries massively hate you. This is pretty much a bug, but if you flip republic, all monarchies hate you (so far so good). But if they then flip into republics as well - that does not remove those diplomatic penalties.

Debug Camera

One last trick - Empire has 2 camera modes, but you can enable "debug camera" which can go as high as you want over the battlefield by editing preference file.

The problem with this is that if you change any settings at all, it will go back to regular camera. Even changing music volume does that.

One thing that somehow doesn't break debug camera is changing battle time limit, as that's per-save not per-game setting.

How bad was Empire anyway?

Like most people, I was mostly disappointed by Empire, but after playing some Rome 2, I think we might have all judged Empire a bit too harshly.

Empire had a lot of issues, but it was still the most ambitious Total War game ever, on new engine and that invariably had to suffer from new engine issues. Rome 2 on the other hand, had none of such excuses, could have just followed a well established formula, and somehow still managed to be worse than that.

Saturday, January 16, 2021

Conquering Empire Total War World as United Provinces

I last played Empire total war two years ago (post 1, post 2).

Empire Total War has 3 game breaking issues:

  • fort sieges will go 0 fps if you use artillery to make breaches, and 10 turns into campaign, every province has a fort
  • naval battles are painfully boring beyond belief
  • diplomacy is completely broken, especially on hard+ - everyone will declare war on you and never peace out - including your allies and countries on the other side of the world

I always use my mod to remove forts, so that fixes the first problem. Naval battles can be somewhat minimized depending on playstyle. I was never able to fix the final one, even though I was leading Empire Total War diplomatic data decoding efforts decade ago. We managed to make AI numbers more reasonable, but somehow AI acted pretty much the same anyway.

But it turns out there's a way, which I somehow never heard of before, that just involves piles of cheese with military access. It has 3 parts:

  • AI massively overvalues getting military access to your land, and is willing to pay a lot for it - we'll be using that for sure
  • AI will be much less likely to attack you if it has military access to your lands - this is how we'll fix diplomacy, by toning down AI aggressiveness and backstabbiness to reasonable levels; this doesn't guarantee safety, just tones it down a few notches
  • you can repeatedly cancel military access and sell it again without repercussions, taking all their money - this is way too exploity for me, and I will absolutely not be doing that

I'm going for some of the achievements I don't have yet:

  • conquer Americas
  • conquer Europe
  • research all tech
  • win game at hard

I have one for India from some past game, probably as Marathas.

I never "won" the game, as conditions are to conquer some lands, and then hold them until 1799, which I never bothered with. But I might do just that this time.

Mods for this:

  • my no forts mod
  • Additional Units mod
  • halfway through I added dry weather mod, that massively reduces battle weather effects, it's mostly visual

Starting position

So United Provinces, the only republic major in the game, it starts with 4 provinces in 3 theaters:

  • Curacao and Dutch Guyana in Americas
  • Netherlands in Europe
  • Ceylon in India
Each will be fighting its wars pretty much separately, as sending troops between them takes very long time.

My traditional opening as anyone who can is rushing pirates. Pirates have 2 islands, one with fairly easy 2 Pirate Mobs units, and capital with much harder 7 Pirate Mob units. Destroying them eliminates their 20 or so ships harassing trade ships all over the world.

I started by a naval battle of 1 Sloop vs pirate 2 Brigs and 1 Sloop, which was super easy, just a bit tedious. Even with me trying my best to minimize such battles, there's a lot more where that came from.

1 vs 3 - Super Easy, Barely An Inconvenience!

Then I landed 1 Militia and 1 recruited General on Trinidad & Tobago to deal with the first pirate enclave. It was defended by 2 Pirate Mobs, each better than a Militia even on normal. This was somewhat questionable move on my side, and I should have probably recruited second General.

With that out of the way, I allied Hannover and Westphalia, sold them military access, and broke starting alliance with Austria to avoid getting dragged into their stupid wars.

I declared war on Spanish protectorate New Spain, which brought me into state of war with Spain without including France. I need to get Flanders to have any hope for security.

Then I gave all great powers except Mughals and Spain free military access to my lands, so I might get attacked less.

After that I destroyed weavers' workshop in Ceylon to build my second university there. And that was a good first turn.

French attack

France attacked me turn one anyway. Free military access is supposed to tone down AI aggressiveness a notch, but it's not an exploit. This attacks looks totally reasonable, if I was France I'd have attacked Netherlands for sure.

I wanted to destroy the pirates, but their second province looked awkwardly strong, so I took some French islands instead first.

All that French nonsense caused so many delays. I really planned to start this campaign by recruiting some army in Ceylon and invading the Mughals. That will need to wait.

After inflicting sufficient losses on them on the land and on the sea, France decided to accept white peace.

I was then able to destroy the Pirates, and that was a really hard fight. They had 7 garrison troops, each a bit better than Militia. I gathered all my New World force - 2 Line Infantry, 1 Hessian mercs, 2 Militia, and 2 generals, all depleted from fighting the French. And that was extremely close victory.

So far:

  • in Europe - Netherlands and Flanders
  • in India - still just Ceylon
  • in New World - Dutch Guyana, French Guyana, Curacao, Trinidad & Tobago, Martinique, Antigua.

Invasion of Mughal India

Spain still wouldn't accept a peace deal, so I kept attacking their New World islands. Eventually they got tired of it, and offered peace deal. That didn't include their New Spain holdings, but New Spain got magically annexed by Spain at some point, so that other war was over too.

A much more important thing is that I finally had some breathing space to invade India before Mughals completely collapse.

Landing in Orissa and Bengal and then moving West, I took 6 regions - a band through Central India from Bengal to Gujarat, peaced them out, and I finally had peace with everyone (not counting Barbary States). All without firing a single cannister shot yet, just with trashy starting units and trashy fixed artillery firing just cannister shots.

Second Mughal War

That peace of course lasted just a few minutes. My New World army had nothing better to do, so I attacked some natives. That's always nice, as attacking natives never leads to any naval combat, and their units are different from Europeans, so it's good variety.

For side note, Empire massively nerfs tax income based on number of provinces you have. It's a weird system. Eventually it goes to -80% when you conquer the map of 140 provinces, but it goes aggressively up for mid-sized empires, and you get -20% at mere 10, -30% at 20, -40% at 30 provinces, and -50% at 50 provinces.

So by mid-game it makes sense to rely mostly on trade. And so I've been spamming trade ships like crazy.

In India I needed a few turns to reorganize army and deal with unrest. I sort of wanted to go South to fight Marathas, but they had way too many ships, as well as way too many armies for a fast finish, so it would mean endless naval battles. I attacked Mughals the second time instead.

Cherokee and Mughal capitals were at -30 unrest so they'd both need babysitting for a while.

Just as I was about to strike the final blow and take Kashmir, Spain declared war on me. Only getting declared twice by 1709, I'm pretty sure selling military access makes a big difference.

Also 25 regions taken, 115 to go.


My still mostly trash army advancing on Mughal city

War with Spain

War with Spain was annoying, as I now had my trade ships everywhere, basically unprotected, and Spanish fleet was huge. On the other hand, their fleet was mainly located near Spain, so they didn't actually harass my traders too much.

European powers were all really busy fighting each other, so they'd hopefully leave me alone. Even not counting wars with minors:

  • France vs Austria, Britain
  • Spain vs Austria, Britain
  • Britain vs Spain, France,, Poland
  • Poland vs Austria, Sweden, Britain
  • Austria vs Spain, France, Poland, and Prussia
  • Prussia vs Austria, Poland
  • Sweden vs Poland, Russia
  • Russia vs Ottomans, Sweden
  • Ottomans vs Russia

They rarely got any territory, and then it usually was lost a while later, but they were constantly raiding each other's ports and sinking ships. Every ship sunk is one I don't have to deal with.

The Iroquois declared surprise war on me. I guess I never offered them military access, and I didn't even notice I now had a border with them. I bribed them with some techs to go away, as it really was completely off my way.

I grabbed 3 Spanish colonies - all garbage land, but I'm going for World Conquest here.

Beyond provinces, game also has 20 naval trade nodes, and I got 14 of them before it even became crowded. I grabbed 2 from Spain in this war. France, Marathas, Ottomans, and Persia have remaining ones, and Persia lost their only port to Ottomans so they're just wasting that node. As things progress from this point, I kept losing them whenever anyone tried to attack them with a real fleet, as I have no patience for that, and then I kept gaining them whenever a country got destroyed. So my control level was close to 14/20 for quite a while.

All that plus a big bribe in form of technology transfer convinced the Spanish that they don't need this fight.

Conquest of France

I wanted to peace out Spain as I had something far more important to do - destroy France.


Battle of Paris, which looks a lot smaller than I expected it to be.
French armies go into battle conveniently carrying white flags.

Paris fell in two easy battles as French troops were mostly sitting in Alsace, but then I had a nice big battle between my first full stack, and Alsatian French full stack.

I thought that would be it, standard take two provinces destroy France, but amazingly France took Algiers a while back and moved their capital there. I did not consider that at all.

I took New Orleans, and that somehow got -30 resistance as major settlement. That's baffling. Capitals of majors get -30, minor settlements get -13, but sometimes there's weird exception, and capitals of minors can go either way. Like that used to be capital of Louisiana colonial nation before France annexed it, so it somehow counts as capital of major power? Annoying.

Especially because in France there's like +16 worth of happiness buildings, and New Orleans is just some alligator infested swamp with nothing of value except port to export cotton and tobacco.

Soon after, France mysteriously lost Algiers, which flipped to Barbary States. I'm not sure if Barbary States got it, or it was just their rebels.

That was some peace and quiet again, not counting my inactive wars with Poland, Barbary States, and assorted rebels.

Conquest of Italy and Canada

I had 3 armies, all on rebel duty:

  • New World army which had 2 fake "major" settlements to babysit, so it was stuck for a while
  • Indian army only had two ways to go - Persia which was garbage land, or rich South India currently controlled by Marathas, who were far stronger than them
  • European army, which was babysitting France at first, but that was surprisingly easy due to all the happiness buildings in France

Indian army would need major reinforcements to do anything, so I let them rest for a while. I disbanded trash units, to be replaced by proper troops.

New World army got a new job invading Canada, which turned into rebels when France collapsed, with exception of one province Quebec.

France's -30 unrest was mostly cancelled by all the happiness buildings, so my European army could march on Italian minors with little opposition.

I let rebels take over Lower Louisiana, hoping that would wipe out its damn -30 unrest when I recaptured it. It did not.

Sweden attacked my ally Hannover, and I declined to join their war, as that would be really annoying new front. Also they did not come to my aid back when I was attacked by France so screw them. Prussia attacked my other ally Westphalia, and I declined the same way.

I finally got Fire by Rank in 1715 (definitely did not rush that like I should), and quickly wrecked Genoa, Savoy, Pope, and Malta, getting me four new shitty -30 unrest provinces to babysit. Of them only Rome had enough happiness buildings to have any hope of fast end of this. In either case, al my European troops were stuck there for a while, so switching to other theaters for a few years.

Half of my New World army got "Agvituk, Montagnais" from the Inuit, and that was -30 unrest province. Very heavy polar bear resistance.

The other half sailed up to Great Lakes, sadly they're not connected to the ocean, so it took slow walk to deal with some natives, and another -30 unrest province.

Conquest of South India

At that point my European and new World armies were mostly stuck on rebel duty, so it was time to look back at India.

This was long overdue, as I was 6 provinces away from conquering the whole damn thing and then I'd no longer to maintain any army there. Selling Marathas and Mysore military access did something to stop them from attacking, but that was not guaranteed, so if I had no army there, they'd probably attack me and that would be a huge mess.

Marathas and Mysore together outnumbered my Indian army by 3:1, and somehow managed to recruit real troops not peasant trash. In other words super easy, barely an inconvenience. In opening battle I deployed 1856 against their 2136, and losses were 382 mine vs 1985 theirs, fairly typical for hard/hard.


Battle against Marathas full stack standing on my border.
I had 24 cannons vs their 16. Vereenigde Oostindische Compagnie Cavalry charged their artillery to achieve artillery superiority, taking heavy losses.
Marathas attacked my right flank, and then the whole battle turned into huge chaos.

Mostly Artillery does the damage, Line Infantry holds the line, and Cavalry makes sure nobody runs away to fight another day, but many more interesting situations happen

Some keys to a good fight:

  • I have nice line of infantry and artillery that can win every straight firefight
  • AI usually suicides their cavalry trying to charge my lines or prancing around, so usually I have cavalry superiority regardless of how many units we start with (I think it used to be a lot worse in early patches, did AI get at least somewhat better at some point?)
  • if AI takes forever to engage, I'll just keep shooting them with my artillery, no rush - this is minority of battles, but it definitely happens sometimes
  • my cavalry mainly makes sure broken units running away do not come back, and tries to kill as many as possible
  • in some fights I get my cavalry some risky tasks, like charging at enemy artillery or routing low morale units - this costs me tons of horses, but I can achieve some strategic advantage
  • I research a lot of unit upgrades, so my units are better thanks to tech; AI wastes their research on navy and such nonsense, and generally just doesn't have enough universities
  • in melee just pressing Square Formation makes everyone fight better, even if they're not actually in formation
  • if some enemies are running away but their army is still fighting nearby - it's best to let them go; they usually regroup later, but by that time their friends are out of the fight, so it's usually no big deal; impatiently chasing broken units too early just cost too much loses
  • I totally love any cavalry units who can shoot - in Europe they are high tech Light Dragoons and such, but in New World there are Mounted Natives who can do that - that's amazing harassment force

There are some weaknesses to this. Inf+Art formation can stand its ground or advance forward, but it takes forever to turn around when attacked. So especially if AI changes me from the side, the other side cannot easily support. It's still a good default.

And of course the best way to destroy enemy army is to take their last settlement - then it disappears. Interestingly it doesn't in most other Total War games, where it would turn to rebels.

I took 3 of 6 remaining regions in initial assault and destroyed a third of Indian armies, but I had to run away as more than two full stacks were chasing just one of my stacks.

Western stack took two settlements with little opposition

Eastern stack destroyed one Marathas stack (leftovers in rice farm East of Hyderabad), then took Hyderabad, and ran back to the river to avoid facing those 2 full stacks to the South East.

I fully expected them to take Hyderabad back and just hoped they'd separate, as fighting 2 full stacks at the same time is just too much.

I thought this war would take a while, but after a few quick naval battles peace was offered. 

Hilariously Marathas instead of taking abandoned region back, or chasing my armies just offered me peace if I gave them some techs. Then Mysore paid me money for another peace. I guess than works.

So by 1719 I have 45/140 regions. Game lasts until 1799, so plenty of time to world conquest.

I have 31 of 79 techs I can research, with most other powers being somewhere around 13. Not like such counting matters terribly much - Cannister Shot and Fire By Rank are the only true game changers, everything else is a minor military or economic bonus.

I'll keep playing this campaign over the next few weeks, as it's quite fun, but it's still like 100-200 battles to finish world conquest.

Sunday, January 03, 2021

Overextension is just a number

It's an interesting question how well EU4 matches history. So I loaded EU4 history files, and checked - how much overextension would various countries have.

I'm counting all change of ownership events by their year only, except when province becomes colonized, assuming every overextension event lasts exactly 3 whole years.

As some situations are ambiguous, I did the simplest possible thing and notably did not consider:

  • integrating subjects
  • forming new countries (like Commonwealth or Russia)
  • core reconquest
  • getting free cores through independence
  • administrative efficiency
  • any special treatment of colonial nations, as they're treated as part of parent nation in history files
  • only years where a country had 100% or higher OE are given
This way the list doesn't miss anything, even if it has some entries that probably shouldn't be there.

As you can see, overextension is just a number, and you should never be afraid to go over 100% or 753% for that matter (the record of 839% for Spain is a false positive).

So here's the list, with affected country, total OE, and previous owners:

  • Afghanistan 1747 - 119% - Baluchistan 9%, Mughals 3%, Persia 107%
  • Afghanistan 1748 - 119% - Baluchistan 9%, Mughals 3%, Persia 107%
  • Afghanistan 1749 - 119% - Baluchistan 9%, Mughals 3%, Persia 107%
  • Afghanistan 1752 - 135% - Bukhara 24%, Mughals 91%, Persia 20%
  • Afghanistan 1753 - 115% - Bukhara 24%, Mughals 91%
  • Annam 1802 - 103% - Dai Viet 103%
  • Annam 1803 - 103% - Dai Viet 103%
  • Annam 1804 - 103% - Dai Viet 103%
  • Aq Qoyunlu 1469 - 363% - Baluchistan 10%, Bitlis 19%, Kharabakh 9%, Qara Qoyunlu 295%, Timurids 30%
  • Aq Qoyunlu 1470 - 363% - Baluchistan 10%, Bitlis 19%, Kharabakh 9%, Qara Qoyunlu 295%, Timurids 30%
  • Aq Qoyunlu 1471 - 295% - Baluchistan 10%, Bitlis 19%, Qara Qoyunlu 236%, Timurids 30%
  • Aragon 1503 - 102% - France 91%, Naples 11%
  • Aragon 1504 - 102% - France 91%, Naples 11%
  • Austria 1458 - 104% - Bregenz 5%, Croatia 6%, Styria 93%
  • Austria 1477 - 213% - Brabant 56%, Burgundy 73%, Flanders 42%, Holland 42%
  • Austria 1478 - 213% - Brabant 56%, Burgundy 73%, Flanders 42%, Holland 42%
  • Austria 1479 - 213% - Brabant 56%, Burgundy 73%, Flanders 42%, Holland 42%
  • Austria 1526 - 283% - Bohemia 128%, Croatia 19%, Glogow 10%, Hungary 113%, Opole 13%
  • Austria 1527 - 283% - Bohemia 128%, Croatia 19%, Glogow 10%, Hungary 113%, Opole 13%
  • Austria 1528 - 283% - Bohemia 128%, Croatia 19%, Glogow 10%, Hungary 113%, Opole 13%
  • Austria 1620 - 136% - Bohemia 136%
  • Austria 1621 - 136% - Bohemia 136%
  • Austria 1622 - 136% - Bohemia 136%
  • Austria 1699 - 103% - Ottomans 68%, Transylvania 35%
  • Austria 1700 - 103% - Ottomans 68%, Transylvania 35%
  • Austria 1701 - 103% - Ottomans 68%, Transylvania 35%
  • Austria 1704 - 113% - Bavaria 102%, Passau 11%
  • Austria 1705 - 113% - Bavaria 102%, Passau 11%
  • Austria 1706 - 113% - Bavaria 102%, Passau 11%
  • Austria 1713 - 133% - Netherlands 49%, Spain 84%
  • Austria 1714 - 306% - Netherlands 49%, Sicily 25%, Spain 232%
  • Austria 1715 - 306% - Netherlands 49%, Sicily 25%, Spain 232%
  • Austria 1716 - 173% - Sicily 25%, Spain 148%
  • Austria 1718 - 152% - Naples 55%, Ottomans 51%, Wallachia 46%
  • Austria 1719 - 152% - Naples 55%, Ottomans 51%, Wallachia 46%
  • Austria 1720 - 117% - Naples 55%, Ottomans 16%, Wallachia 46%
  • Austria 1797 - 166% - Commonwealth 56%, Venice 110%
  • Austria 1798 - 110% - Venice 110%
  • Austria 1799 - 110% - Venice 110%
  • Austria 1814 - 315% - Bavaria 57%, France 70%, Italy 188%
  • Austria 1815 - 315% - Bavaria 57%, France 70%, Italy 188%
  • Austria 1816 - 316% - Bavaria 67%, France 61%, Italy 188%
  • Bavaria 1714 - 113% - Austria 113%
  • Bavaria 1715 - 113% - Austria 113%
  • Bavaria 1716 - 113% - Austria 113%
  • Bengal 1526 - 120% - Delhi 100%, Tirhut 20%
  • Bengal 1527 - 100% - Delhi 100%
  • Bengal 1528 - 100% - Delhi 100%
  • Bengal 1540 - 332% - Mughals 332%
  • Bengal 1541 - 332% - Mughals 332%
  • Bengal 1542 - 332% - Mughals 332%
  • Bengal 1543 - 105% - Gujarat 26%, Gwalior 8%, Hadoti 10%, Malwa 53%, Marwar 8%
  • Bengal 1544 - 244% - Dhundhar 13%, Gujarat 35%, Gwalior 8%, Hadoti 15%, Jaisalmer 3%, Jangladesh 6%, Malwa 53%, Marwar 8%, Mewar 10%, Mughals 30%, Sindh 63%
  • Bengal 1545 - 244% - Dhundhar 13%, Gujarat 35%, Gwalior 8%, Hadoti 15%, Jaisalmer 3%, Jangladesh 6%, Malwa 53%, Marwar 8%, Mewar 10%, Mughals 30%, Sindh 63%
  • Bengal 1546 - 139% - Dhundhar 13%, Gujarat 9%, Hadoti 5%, Jaisalmer 3%, Jangladesh 6%, Mewar 10%, Mughals 30%, Sindh 63%
  • Bengal 1707 - 244% - Mughals 244%
  • Bengal 1708 - 244% - Mughals 244%
  • Bengal 1709 - 244% - Mughals 244%
  • Bohemia 1618 - 151% - Austria 151%
  • Bohemia 1619 - 151% - Austria 151%
  • Bohemia 1620 - 151% - Austria 151%
  • Bukhara 1502 - 115% - Timurids 36%, Uzbek 79%
  • Bukhara 1503 - 115% - Timurids 36%, Uzbek 79%
  • Bukhara 1504 - 133% - Timurids 36%, Uzbek 79%, Yarkand 18%
  • Bukhara 1507 - 139% - Khorasan 134%, Sistan 5%
  • Bukhara 1508 - 139% - Khorasan 134%, Sistan 5%
  • Burgundy 1475 - 104% - Friesland 24%, Gelre 29%, Lorraine 32%, Provence 19%
  • Colombia 1810 - 156% - Spain 156%
  • Colombia 1811 - 156% - Spain 156%
  • Colombia 1812 - 156% - Spain 156%
  • Colombia 1819 - 146% - Spain 30%, Venezuela 116%
  • Colombia 1820 - 146% - Spain 30%, Venezuela 116%
  • Colombia 1821 - 146% - Spain 30%, Venezuela 116%
  • Commonwealth 1569 - 506% - Lithuania 204%, Poland 302%
  • Commonwealth 1570 - 506% - Lithuania 204%, Poland 302%
  • Commonwealth 1571 - 506% - Lithuania 204%, Poland 302%
  • Deccan 1724 - 279% - Mughals 279%
  • Deccan 1725 - 279% - Mughals 279%
  • Deccan 1726 - 279% - Mughals 279%
  • Delhi 1451 - 112% - Kashmir 7%, Sirhind 105%
  • Delhi 1452 - 159% - Jaunpur 47%, Kashmir 7%, Sirhind 105%
  • Delhi 1453 - 152% - Jaunpur 47%, Sirhind 105%
  • Delhi 1486 - 152% - Jaunpur 152%
  • Delhi 1487 - 152% - Jaunpur 152%
  • Delhi 1488 - 152% - Jaunpur 152%
  • Delhi 1553 - 146% - Bengal 146%
  • Delhi 1554 - 146% - Bengal 146%
  • Delhi 1555 - 146% - Bengal 146%
  • Dzungar 1740 - 127% - Kazakh 127%
  • Dzungar 1741 - 127% - Kazakh 127%
  • Dzungar 1742 - 127% - Kazakh 127%
  • France 1477 - 103% - Burgundy 103%
  • France 1478 - 103% - Burgundy 103%
  • France 1479 - 103% - Burgundy 103%
  • France 1499 - 112% - Geneva 13%, Genoa 38%, Savoy 53%, Switzerland 8%
  • France 1500 - 112% - Geneva 13%, Genoa 38%, Savoy 53%, Switzerland 8%
  • France 1501 - 112% - Geneva 13%, Genoa 38%, Savoy 53%, Switzerland 8%
  • France 1504 - 177% - Milan 86%, Naples 91%
  • France 1796 - 113% - Austria 50%, Bavaria 51%, Sardinia-Piedmont 12%
  • France 1797 - 314% - Aachen 14%, Austria 139%, Bavaria 43%, Liege 27%, Prussia 14%, Sardinia-Piedmont 22%, Trier 22%, Venice 33%
  • France 1798 - 275% - Aachen 14%, Austria 89%, Bavaria 43%, Liege 27%, Prussia 14%, Sardinia-Piedmont 33%, Trier 22%, Venice 33%
  • France 1799 - 220% - Aachen 14%, Austria 89%, Liege 27%, Prussia 14%, Sardinia-Piedmont 21%, Trier 22%, Venice 33%
  • France 1801 - 163% - Cologne 27%, Mainz 10%, Parma 15%, Spain 34%, Tuscany 77%
  • France 1802 - 173% - Cologne 27%, Great Britain 10%, Mainz 10%, Parma 15%, Spain 34%, Tuscany 77%
  • France 1803 - 129% - Cologne 27%, Great Britain 10%, Parma 15%, Tuscany 77%
  • France 1805 - 106% - Austria 40%, Genoa 38%, Lucca 14%, Prussia 14%
  • France 1806 - 106% - Austria 40%, Genoa 38%, Lucca 14%, Prussia 14%
  • France 1807 - 208% - Austria 40%, Corfu 11%, Etruria 77%, Genoa 38%, Lucca 14%, Prussia 14%, Ragusa 14%
  • France 1808 - 111% - Berg 9%, Corfu 11%, Etruria 77%, Ragusa 14%
  • France 1809 - 166% - Austria 9%, Berg 9%, Corfu 11%, Etruria 77%, Ragusa 14%, The Papal State 46%
  • France 1810 - 383% - Austria 9%, Berg 9%, Denmark 20%, Hamburg 19%, Italy 21%, Lübeck 19%, Netherlands 211%, Oldenburg 7%, The Papal State 46%, Westphalia 22%
  • France 1811 - 390% - Austria 9%, Bremen 16%, Denmark 20%, Hamburg 19%, Italy 21%, Lübeck 19%, Netherlands 211%, Oldenburg 7%, The Papal State 46%, Westphalia 22%
  • France 1812 - 335% - Bremen 16%, Denmark 20%, Hamburg 19%, Italy 21%, Lübeck 19%, Netherlands 211%, Oldenburg 7%, Westphalia 22%
  • Great Britain 1707 - 749% - England 658%, Scotland 91%
  • Great Britain 1708 - 749% - England 658%, Scotland 91%
  • Great Britain 1709 - 749% - England 658%, Scotland 91%
  • Great Britain 1761 - 105% - Bengal 95%, France 10%
  • Great Britain 1762 - 105% - Bengal 95%, France 10%
  • Great Britain 1763 - 292% - Abenaki 6%, Creek 7%, Fox 3%, France 260%, Potawatomi 4%, Spain 12%
  • Great Britain 1764 - 282% - Abenaki 6%, Creek 7%, Fox 3%, France 250%, Potawatomi 4%, Spain 12%
  • Great Britain 1765 - 413% - Abenaki 6%, Assam 6%, Bengal 125%, Creek 7%, Fox 3%, France 250%, Potawatomi 4%, Spain 12%
  • Great Britain 1766 - 182% - Assam 6%, Bengal 125%, Deccan 48%, France 3%
  • Great Britain 1767 - 182% - Assam 6%, Bengal 125%, Deccan 48%, France 3%
  • Great Britain 1801 - 212% - Carnatic 58%, Deccan 24%, Gwalior 9%, Marathas 26%, Mysore 48%, Oudh 47%
  • Great Britain 1802 - 211% - Carnatic 58%, Deccan 24%, Gwalior 9%, Kandy 7%, Marathas 26%, Netherlands 30%, Oudh 47%, Spain 10%
  • Great Britain 1803 - 311% - Carnatic 58%, Gwalior 74%, Kandy 7%, Marathas 27%, Nagpur 58%, Netherlands 30%, Oudh 47%, Spain 10%
  • Great Britain 1804 - 187% - Gwalior 65%, Kandy 7%, Marathas 17%, Nagpur 58%, Netherlands 30%, Spain 10%
  • Great Britain 1805 - 140% - Gwalior 65%, Marathas 17%, Nagpur 58%
  • Great Britain 1818 - 240% - Baroda 31%, Gwalior 23%, Marathas 127%, Nagpur 50%, Nepal 9%
  • Great Britain 1819 - 203% - Baroda 31%, Gwalior 23%, Kutch 3%, Marathas 127%, Nagpur 19%
  • Great Britain 1820 - 194% - Baroda 22%, Gwalior 23%, Kutch 3%, Marathas 127%, Nagpur 19%
  • Italy 1805 - 149% - Austria 86%, The Papal State 63%
  • Italy 1806 - 149% - Austria 86%, The Papal State 63%
  • Italy 1807 - 149% - Austria 86%, The Papal State 63%
  • Jaunpur 1553 - 152% - Bengal 152%
  • Jaunpur 1554 - 152% - Bengal 152%
  • Jaunpur 1555 - 152% - Bengal 152%
  • Kazakh 1755 - 122% - Dzungar 122%
  • Kazakh 1756 - 122% - Dzungar 122%
  • Kazakh 1757 - 122% - Dzungar 122%
  • Khorasan 1449 - 159% - Afghanistan 47%, Timurids 112%
  • Khorasan 1450 - 153% - Afghanistan 47%, Timurids 106%
  • Khorasan 1451 - 172% - Afghanistan 47%, Ajam 19%, Timurids 106%
  • La Plata 1816 - 125% - Spain 125%
  • La Plata 1817 - 125% - Spain 125%
  • La Plata 1818 - 125% - Spain 125%
  • Manchu 1616 - 189% - Donghai 34%, Jianzhou 142%, Udege 13%
  • Manchu 1617 - 189% - Donghai 34%, Jianzhou 142%, Udege 13%
  • Manchu 1618 - 189% - Donghai 34%, Jianzhou 142%, Udege 13%
  • Mexico 1810 - 681% - Lipan 3%, Spain 678%
  • Mexico 1811 - 681% - Lipan 3%, Spain 678%
  • Mexico 1812 - 681% - Lipan 3%, Spain 678%
  • Ming 1648 - 154% - Qing 154%
  • Ming 1649 - 184% - Qing 184%
  • Ming 1650 - 184% - Qing 184%
  • Morocco 1549 - 167% - Fez 56%, Tafilalt 83%, Tlemcen 28%
  • Morocco 1550 - 167% - Fez 56%, Tafilalt 83%, Tlemcen 28%
  • Morocco 1551 - 167% - Fez 56%, Tafilalt 83%, Tlemcen 28%
  • Morocco 1668 - 107% - Tafilalt 107%
  • Morocco 1669 - 107% - Tafilalt 107%
  • Morocco 1670 - 130% - Sus 23%, Tafilalt 107%
  • Mughals 1526 - 369% - Delhi 220%, Timurids 149%
  • Mughals 1527 - 400% - Delhi 220%, Gwalior 8%, Sindh 23%, Timurids 149%
  • Mughals 1528 - 438% - Bengal 38%, Delhi 220%, Gwalior 8%, Sindh 23%, Timurids 149%
  • Mughals 1554 - 119% - Punjab 10%, Sirhind 109%
  • Mughals 1555 - 249% - Delhi 130%, Punjab 10%, Sirhind 109%
  • Mughals 1556 - 249% - Delhi 130%, Punjab 10%, Sirhind 109%
  • Mughals 1557 - 153% - Delhi 130%, Multan 23%
  • Mughals 1558 - 129% - Delhi 16%, Jaunpur 90%, Multan 23%
  • Mughals 1559 - 129% - Delhi 16%, Jaunpur 90%, Multan 23%
  • Mughals 1560 - 106% - Delhi 16%, Jaunpur 90%
  • Mughals 1574 - 121% - Baglana 6%, Gujarat 73%, Navanagar 5%, Porbandar 5%, Sindh 32%
  • Mughals 1575 - 178% - Baglana 6%, Bengal 57%, Gujarat 73%, Navanagar 5%, Porbandar 5%, Sindh 32%
  • Mughals 1576 - 253% - Bengal 213%, Bishnupur 8%, Sindh 32%
  • Mughals 1577 - 221% - Bengal 213%, Bishnupur 8%
  • Mughals 1578 - 164% - Bengal 156%, Bishnupur 8%
  • Mughals 1686 - 120% - Bijapur 120%
  • Mughals 1687 - 254% - Bijapur 120%, Golkonda 134%
  • Mughals 1688 - 254% - Bijapur 120%, Golkonda 134%
  • Mughals 1689 - 134% - Golkonda 134%
  • Muscovy 1478 - 128% - Novgorod 128%
  • Muscovy 1479 - 128% - Novgorod 128%
  • Muscovy 1480 - 128% - Novgorod 128%
  • Naples 1734 - 157% - Austria 157%
  • Naples 1735 - 157% - Austria 157%
  • Naples 1736 - 157% - Austria 157%
  • Netherlands 1549 - 178% - Spain 178%
  • Netherlands 1550 - 178% - Spain 178%
  • Netherlands 1551 - 178% - Spain 178%
  • Netherlands 1813 - 204% - France 204%
  • Netherlands 1814 - 204% - France 204%
  • Netherlands 1815 - 362% - France 345%, Great Britain 17%
  • Netherlands 1816 - 158% - France 141%, Great Britain 17%
  • Netherlands 1817 - 158% - France 141%, Great Britain 17%
  • Ottomans 1516 - 208% - Dulkadir 23%, Fadl 11%, Hisn Kayfa 6%, Mamluks 119%, Persia 49%
  • Ottomans 1517 - 349% - Fadl 11%, Mamluks 324%, Persia 14%
  • Ottomans 1518 - 349% - Fadl 11%, Mamluks 324%, Persia 14%
  • Ottomans 1519 - 205% - Mamluks 205%
  • Ottomans 1536 - 100% - Persia 100%
  • Ottomans 1537 - 100% - Persia 100%
  • Ottomans 1538 - 182% - Mamluks 46%, Mikhlaf 7%, Persia 118%, Yemen 11%
  • Ottomans 1540 - 104% - Dongola 6%, Mamluks 46%, Mikhlaf 7%, Persia 18%, Venice 16%, Yemen 11%
  • Ottomans 1590 - 122% - Persia 122%
  • Ottomans 1591 - 122% - Persia 122%
  • Ottomans 1592 - 122% - Persia 122%
  • Oudh 1724 - 115% - Mughals 115%
  • Oudh 1725 - 115% - Mughals 115%
  • Oudh 1726 - 115% - Mughals 115%
  • Persia 1501 - 103% - Aq Qoyunlu 68%, Ardabil 9%, Shirvan 26%
  • Persia 1502 - 103% - Aq Qoyunlu 68%, Ardabil 9%, Shirvan 26%
  • Persia 1503 - 103% - Aq Qoyunlu 68%, Ardabil 9%, Shirvan 26%
  • Persia 1504 - 193% - Aq Qoyunlu 185%, Mushasha 8%
  • Persia 1505 - 193% - Aq Qoyunlu 185%, Mushasha 8%
  • Persia 1506 - 193% - Aq Qoyunlu 185%, Mushasha 8%
  • Persia 1507 - 155% - Aq Qoyunlu 155%
  • Persia 1508 - 189% - Aq Qoyunlu 155%, Mushasha 34%
  • Persia 1509 - 189% - Aq Qoyunlu 155%, Mushasha 34%
  • Persia 1510 - 137% - Bukhara 103%, Mushasha 34%
  • Persia 1511 - 103% - Bukhara 103%
  • Persia 1512 - 103% - Bukhara 103%
  • Persia 1612 - 116% - Ottomans 116%
  • Persia 1613 - 116% - Ottomans 116%
  • Persia 1614 - 116% - Ottomans 116%
  • Persia 1739 - 100% - Bukhara 24%, Mughals 76%
  • Persia 1741 - 123% - Khiva 9%, Mughals 76%, Oman 38%
  • Poland 1807 - 166% - Austria 56%, Prussia 110%
  • Poland 1808 - 166% - Austria 56%, Prussia 110%
  • Poland 1809 - 166% - Austria 56%, Prussia 110%
  • Prussia 1701 - 188% - Brandenburg 188%
  • Prussia 1702 - 188% - Brandenburg 188%
  • Prussia 1703 - 188% - Brandenburg 188%
  • Prussia 1795 - 111% - Commonwealth 111%
  • Prussia 1813 - 133% - Berg 23%, France 7%, Westphalia 103%
  • Prussia 1814 - 259% - Berg 23%, Danzig 16%, France 51%, Hanover 7%, Poland 59%, Westphalia 103%
  • Prussia 1815 - 380% - Berg 35%, Danzig 16%, Denmark 29%, France 78%, Hanover 16%, Poland 59%, Saxony 44%, Westphalia 103%
  • Prussia 1816 - 247% - Berg 12%, Danzig 16%, Denmark 29%, France 71%, Hanover 16%, Poland 59%, Saxony 44%
  • Prussia 1817 - 121% - Berg 12%, Denmark 29%, France 27%, Hanover 9%, Saxony 44%
  • Qara Qoyunlu 1451 - 150% - Ajam 150%
  • Qara Qoyunlu 1452 - 139% - Ajam 139%
  • Qara Qoyunlu 1453 - 144% - Ajam 139%, Khorasan 5%
  • Qing 1636 - 413% - Manchu 413%
  • Qing 1637 - 413% - Manchu 413%
  • Qing 1638 - 413% - Manchu 413%
  • Qing 1644 - 202% - Ming 20%, Shun 182%
  • Qing 1645 - 613% - Ming 246%, Shun 348%, Xi 19%
  • Qing 1646 - 753% - Ming 365%, Shun 348%, Xi 40%
  • Qing 1647 - 697% - Ming 491%, Shun 166%, Xi 40%
  • Qing 1648 - 286% - Ming 265%, Xi 21%
  • Qing 1649 - 206% - Ming 206%
  • Qing 1650 - 169% - Ming 169%
  • Qing 1651 - 198% - Ming 198%
  • Qing 1652 - 138% - Ming 138%
  • Qing 1659 - 101% - Ming 41%, Xi 60%
  • Qing 1660 - 101% - Ming 41%, Xi 60%
  • Qing 1681 - 250% - Zhou 250%
  • Qing 1682 - 250% - Zhou 250%
  • Qing 1683 - 260% - Ming 10%, Zhou 250%
  • Qing 1697 - 117% - Dzungar 117%
  • Qing 1698 - 117% - Dzungar 117%
  • Russia 1503 - 411% - Lithuania 14%, Muscovy 389%, Ryazan 8%
  • Russia 1504 - 411% - Lithuania 14%, Muscovy 389%, Ryazan 8%
  • Russia 1505 - 437% - Lithuania 14%, Muscovy 389%, Perm 26%, Ryazan 8%
  • Russia 1552 - 138% - Kazan 132%, Nogai 6%
  • Russia 1553 - 138% - Kazan 132%, Nogai 6%
  • Russia 1554 - 138% - Kazan 132%, Nogai 6%
  • Russia 1722 - 106% - Persia 34%, Sweden 72%
  • Russia 1723 - 106% - Persia 34%, Sweden 72%
  • Russia 1795 - 165% - Commonwealth 152%, Kurland 13%
  • Russia 1796 - 103% - Commonwealth 90%, Kurland 13%
  • Russia 1797 - 103% - Commonwealth 90%, Kurland 13%
  • Russia 1814 - 130% - Armenia 6%, Kharabakh 9%, Moldavia 17%, Ottomans 11%, Poland 87%
  • Russia 1815 - 102% - Armenia 6%, Kharabakh 9%, Poland 87%
  • Sardinia-Piedmont 1720 - 105% - Austria 21%, Sicily 84%
  • Sardinia-Piedmont 1721 - 105% - Austria 21%, Sicily 84%
  • Sardinia-Piedmont 1722 - 105% - Austria 21%, Sicily 84%
  • Sardinia-Piedmont 1814 - 147% - France 147%
  • Sardinia-Piedmont 1815 - 147% - France 147%
  • Sardinia-Piedmont 1816 - 147% - France 147%
  • Shun 1644 - 348% - Ming 348%
  • Shun 1645 - 348% - Ming 348%
  • Shun 1646 - 285% - Ming 285%
  • Sirhind 1553 - 109% - Bengal 109%
  • Sirhind 1554 - 109% - Bengal 109%
  • Sirhind 1555 - 109% - Bengal 109%
  • Spain 1516 - 839% - Aragon 323%, Castile 516%
  • Spain 1517 - 839% - Aragon 323%, Castile 516%
  • Spain 1518 - 839% - Aragon 323%, Castile 516%
  • Spain 1519 - 256% - Austria 251%, Aztec 5%
  • Spain 1520 - 283% - Austria 251%, Aztec 5%, Tlaxcala 27%
  • Spain 1521 - 421% - Austria 251%, Aztec 108%, Butuan 6%, Huastec 3%, Otomi 3%, Tarascan 3%, Teotitlan 7%, Tlaxcala 27%, Tripoli 3%, Tzotzil 10%
  • Spain 1522 - 186% - Aztec 103%, Butuan 6%, Huastec 3%, Otomi 3%, Tarascan 3%, Teotitlan 7%, Tlapanec 21%, Tlaxcala 27%, Tripoli 3%, Tzotzil 10%
  • Spain 1523 - 200% - Aztec 103%, Butuan 6%, Colima 27%, Huastec 3%, Otomi 3%, Tarascan 17%, Teotitlan 7%, Tlapanec 21%, Tripoli 3%, Tzotzil 10%
  • Spain 1524 - 118% - Aztec 10%, Chorti 3%, Colima 27%, Kaqchikel 5%, Kiche 21%, Mixtec 12%, Tarascan 14%, Tlapanec 21%, Zapotec 5%
  • Spain 1525 - 110% - Aztec 10%, Chorti 6%, Colima 27%, Kaqchikel 12%, Kiche 21%, Mixtec 12%, Tairona 3%, Tarascan 14%, Zapotec 5%
  • Spain 1532 - 118% - Carib 3%, Guamar 6%, Inca 21%, Siena 20%, Tarascan 45%, Tonala 6%, Xalisco 17%
  • Spain 1533 - 312% - Carib 3%, Guamar 6%, Inca 248%, Montferrat 12%, Siena 20%, Tonala 6%, Xalisco 17%
  • Spain 1534 - 289% - Guamar 6%, Inca 248%, Montferrat 12%, Tonala 6%, Xalisco 17%
  • Spain 1535 - 330% - Charrua 7%, Inca 240%, Milan 71%, Montferrat 12%
  • Spain 1537 - 120% - Can Pech 7%, Charrua 7%, Inca 35%, Milan 71%
  • Taungu 1563 - 157% - Shan 157%
  • Taungu 1564 - 177% - Ayutthaya 20%, Shan 157%
  • Taungu 1565 - 177% - Ayutthaya 20%, Shan 157%
  • Timurids 1448 - 127% - Transoxiana 127%
  • Timurids 1449 - 127% - Transoxiana 127%
  • Timurids 1450 - 127% - Transoxiana 127%
  • Timurids 1458 - 137% - Khorasan 132%, Qara Qoyunlu 5%
  • Timurids 1459 - 137% - Khorasan 132%, Qara Qoyunlu 5%
  • Timurids 1460 - 113% - Khorasan 108%, Qara Qoyunlu 5%
  • Tokugawa 1600 - 201% - Chosokabe 7%, Hosokawa 7%, Ikeda 7%, Mori 48%, Oda 132%
  • Tokugawa 1601 - 201% - Chosokabe 7%, Hosokawa 7%, Ikeda 7%, Mori 48%, Oda 132%
  • Tokugawa 1602 - 207% - Chosokabe 7%, Hosokawa 7%, Ikeda 7%, Mori 48%, Oda 132%, Satake 6%
  • Transoxiana 1409 - 127% - Timurids 127%
  • Transoxiana 1410 - 127% - Timurids 127%
  • Transoxiana 1411 - 127% - Timurids 127%
  • United States 1776 - 282% - Great Britain 282%
  • United States 1777 - 282% - Great Britain 282%
  • United States 1778 - 290% - Great Britain 290%
  • Venezuela 1811 - 116% - Spain 116%
  • Venezuela 1812 - 116% - Spain 116%
  • Venezuela 1813 - 116% - Spain 116%
  • Westphalia 1807 - 256% - Hanover 29%, Hesse 43%, Nassau 9%, Prussia 175%
  • Westphalia 1808 - 256% - Hanover 29%, Hesse 43%, Nassau 9%, Prussia 175%
  • Westphalia 1809 - 256% - Hanover 29%, Hesse 43%, Nassau 9%, Prussia 175%
  • Xi 1644 - 106% - Ming 106%
  • Xi 1645 - 106% - Ming 106%
  • Zhou 1662 - 257% - Ming 46%, Qing 205%, Xi 6%
  • Zhou 1663 - 257% - Ming 46%, Qing 205%, Xi 6%
  • Zhou 1664 - 238% - Ming 46%, Qing 186%, Xi 6%
An obvious followup to this question would be how far Aggressive Expansion went, and how many countries would get coalitioned, but that's a much more complicated calculation, even to approximate.