I need help with combat.

[Clover Creepy Girl™]

I need some help, I am really not understanding combat.
I am sitting here with a 16 combat score as imperialists. The military screen says my opponent has 11. I have armies matching theirs and a city adjacent. I end turn, and they suddenly have a massive amount of power beyond mine. I legit do not understand the mathematics at play in these situations and its making me not enjoy this game.

[third_party]

It's difficult to tell from your description what it is that you don't understand, so forgive me if I cover some obvious stuff.

Combat is resolved on a hex-by-hex basis. Your score on a given hex is equal to the number of armies you have on or adjacent to that hex, times the effectiveness of those armies, plus a few bonuses from technology and (if you're the defender rather than the attacker) cities.

All players take their turns simultaneously, so the predictions you see on the military screen don't take account of the possibility that your opponent might move additional armies next to a contested hex. That's the number one reason why a battle might not go the way you expect.

(The prediction on the military screen also doesn't take into account the possibility that your combat effectiveness and/or your opponent's combat effectiveness might change significantly from one turn to the next, e.g. because you've spending your wealth on something else this turn, or because your opponent had spent their wealth on something else the previous turn but is now going to dump all of it into combat effectiveness.)

[The Secret Games Company]

Hi Stephanie, sorry that it's frustrating you. We can help you so keep the questions coming. My advice is to open up the power overlay and hover on some of the tiles in question and read the tooltips to see what is adding power in that hex.

You need to consider how many units are adjacent to the hex, how much power the empire has, how many power techs they have for the terrain in question and how many cities are nearby (and how big they are). It is important to understand that cities only add power to tiles you are defending, they do not help attacking units.

There are some great guides, which explain the systems. You can also read the How To Play section and the FAQ in-game.
https://steamcommunity.com/sharedfiles/filedetails/?id=2874003001
https://steamcommunity.com/sharedfiles/filedetails/?id=2874454573

[Gilmoy]

Probably what happened was that the AI paid Wealth for a spike in Power.
You can do the same.

+ 11 Power this turn doesn't mean 11 Power forever.
Power (yours and theirs) can swing by +/- 5 every turn, from Wealth alone.

+ Also, that AI may have won a mercenary Opportunity lottery, for a short-term +1 to +3.

You'll notice that the largest AI (= most hexes, largest economy) values having many units.
It will rapidly buy up to 4 units, then later sprawl to 6-8 units if you let it.

The economics of that is to go through boom/bust Wealth spending.
As you know, the 5th - 8th army can cost 120 - 200 Wealth each.
Even a large economy might generate only 200 Wealth per turn.

Deducing the math, the AI's Wealth-to-Power spending must go something like this:
(note: I made up all numbers, but you get the idea)

+ it pays 120 for 4th army, pays 36 for +4 Power -4 Waste, treads water at 8 Power
+ it pays 144 for 5th army, pays 44 for +4 Power -4 Waste, stays at 8 Power
+ it skips a buy, pays 180 for +7 Power -4 Waste = +3 profit, goes to 11 Power
+ it pays 180 for 6th army, pays 32 for +2 Power -6 Waste, drops to 7 Power
+ it skips a buy, pays 168 for +6 Power -3 Waste = +3 profit, goes to 10 Power
+ it pays 224 for 7th army, pays 12 for +1 Power -5 Waste, drops to 6 Power
+ it ceases buying units, pays 268 for +6 Power -3 Waste, adds mercs +2, grows to 11 Power
+ pays 268 for +6 -5 Waste +5 Mercs, grows (over several turns) to 21 Power

Again, you could do this yourself. The math works for you identically.
"All" you need is to own many hexes, for a massive economy.

Over time, a big AI's Power score traces out a sine-like curve, with peaks and troughs.
In your specific case, that AI's 11 Power must have been a trough.
Next turn, it paid for more Power, and hit a new peak.

[charles_d_berger]

Gilmoy - great working out of an example! But I don't think AI's have access to mercs - those come through cards, and only humans get cards. Presumably to make up for our sub-optimal calculating abilities!

I have found some AIs get into a weird pattern of going from say 14 power one turn, to 3 the next, then back to 15, then down to 4 or whatever. It makes them pretty easy to whoop.