Combat Odds...

I put three full health Macemen in my capital, and my enemy Catherine had one Horse Archer and one Archer right next to the city, on a hill.

I charged my first Maceman at the Horse Archer with a 75%ish odd, dead.
I charged my second Maceman at that same Horse Archer with a 90% odd, dead.
I charged my third Maceman at the Archer with a 94.5% odd, dead.

My capital is empty now.

Game over.

Similar things happened not only once. Not complaining, but still...

Why attack under such circumstances? Next time defend. You had more units, fortify them and get some archers / longbows to defend.

In this situation 75% chance attack was too high risk without direct dangers (if I would lose 1st Mace, 2nd and 3rd would defend city - little damaged HA can't do anything against Full strength Mace behind city walls even without Fortity bonus... and archers are bad attackers, still great city and HILL defense)...
And I understand how "painfull" were 90 and 94.5% lost battles...

True that, I just didn't want those guys to pillage my improvements, since there were towns right next to the enemies. I thought the sacrifice of one Maceman would worth it, but who knows I'll lose all three of them

Bad luck that--about a 0.14% chance of that happening.

Bigger questions are:

1) Why are you defending your city with only macemen? Macemen are 70 , longbowmen are 50 and better defenders.

2) How did an AI get units all the way to your capitol in the medieval era (at least for you)? I'd expect at least one ring of cities around, even at high levels. But with you cranking out macemen when Cathy's only able to get ancient/classical units, I suspect you're not playing deity.

Best way to put it for yourself is analogical to poker play. When I had played 10 years and started to know most of the odds from head, I was sure game is treating me unfairly. I was very often sucked out at 90% + winning odds, while the opposite was occurring very rarely. I was sure I was not lucky enough to play poker profitably - what a unfair game it was!

Some years later I understood "post mortem" why I was getting "suckies" much more often that giving ones myself: I was not unlucky, I was just good enough not to put my nose into situations where I was a big underdog.

The same goes for civilization: if you were playing civ as AI does, sometime running countless numbers against seemingly impossible odds, once in few thousand repetitions you would be successful too. As you never attack with propability less than decent, you get the feeling that game is unfair to you.

Oh and else: game is not over with capitol gone. Switch to slavery and whip some more macemen. Expecting you to have a little more luck this time, you would have your capitol back in no time.

I've seen a deity playthrough where the player lost his capital to a barbarian and recaptured next turn. He ended up winning the game with a real high score. Sometimes, this kind of thing causes your capital to move to a better bureau location (meaning you got a free palace) .

IMO, you should have remained defending in your city. +25% fortification and whatever tile bonuses (culture and hill if applicable) get added to that. Just the fortification bonus would give you another 2 strength. They would never have taken your city. Pillaged tiles are easy to fix with workers but rebuilding granary/barracks/library is quite costly.

@Lennier I usually just put a warrior in my capital, but the two maceman arrived (just built by other cities) one turn before Catherine's units came so I let the two stay and upgraded my warrior. Yes, my capital was sort of close to the front line. I was playing at Monarch difficulty.

Whipping longbows would have been preferable and you could've done this while the AI was making its way to the capital (those units only have 1 movement point in enemy territory). 1 longbow would have stopped both AI units and you could upgrade the warrior for piece of mind. Tip: if in a war in the early or mid game, go into slavery. The 1 turn of anarchy can transform a scary situation into one where you are capturing cities.

As I have been moving up the difficulty ladder and remember the monarch level well, I would suggest that you stay away from early wars with 1-move units. Although there are some situations that merit it and they are certainly possible to pull off, mounted wars are usually much more successful and efficient as you only need to whip 1 unit type and they are FAST FAST FAST. If you like siege wars, you'll want to beeline/rush to the techs that unlock those siege. On higher levels, if you don't perform a beeline/rush, your siege can get obsoleted too quickly to capitalize on (ie AI get longbows while you're still pushing catapults). Although this can still work, the war will certainly last longer and be much more costly both in and and can lead to stagnation. I, personally, like the engineering rush (it's something different) and the lib-cannon rush (cannons are only really stopped by infantry and even then pure numbers can still overwhelm).

Of course, on marathon speed, this becomes less of a concern since your units basically get 3x the movement and unit builds only cost 2/3 what they do on normal.

The horse archer and archer had worst odds in attacking your fortified macemen in the city since most cities give a defense bonus to units that fortify there. Seige units are the best units for offense because they cause collateral damage after they die and siege units aren't actual people that somehow were sacrified by foolishness. Offensiveness is good in a way since ai often has better combat odds than the player so stacking up a few units in the offense can often get wins.. Large stacks of mobile units for example such as horse archers can often beat archer fortified cities for example. I've won really poor odds that were often 50% winning chance or less..