Taking a majors main city

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You beat the enemy in the field, outmaneuvered all his troops and confined his forces to the last city. But now you do not get any decent odds. What gives? How do you fix that?

The Problems:
There are several reasons why the last enemy city is a veritable fortress. But the big one first:
All Majors start with Ruin Terrain under their city.
Ruins are the single most defensible terrain in the game, only being matched by low Mountains with Forrests and High Mountains.
Infatry and Guns can get a whopping 250 Entrenchment (125 Automatic) in there. And unfortunately we do not know excactly how entrenchment growth works, so there is a serious information gap on how to defeat it.
See Trooptypes for details

The SHQ is close enough to use OHQ skills:
Independant and Militia are usually very far from the SHQ, so they only get the normal SHQ Roll effect. However if they are are that close, they will get the benefit of the SHQ Commanders OHQ Skills.

Too valuable to shell blindly:
There is a lot of population and a lot of usefull infrastructure in there, so just shelling it blindly with weapons that cause Structural damage is not really an option. You would be loosing the things you are trying to capture.

No retreat option
As there is no "avenue for retreat", they never do orderly retreats and double the morale for panic retreat calculations.

The AI is getting their stupidity offset modifiers:
Game AI can not plan ahead. So several rules you have to deal with, the AI does not have to deal with. So the option to "starve them out" is also limited. See 5.18 for a full ist, but the more important ones:
- they do not build danger for having your units that close
- they get some free Logistics Range and Capacity in every city. But the SHQ should need 0 to work with the zone and unit in the hex anyway
- they can get Veteran Sergeant, Leutenant and Captain unit feats for free, based purely on time
- no credit cost for salaries or recruitment
- they do still follow normal recruitment and food/ammo rules.

It is worse if you somehow end up with a minor above ruins, as they get even more bonuses.

Casualty Tollerance
Especially if the attacker plans on actually using infantry, the casualties will be massive. Long and Shorterm casualty tollerances can make that utterly prohobitive.

The Caliber Modfier
This is a easily underestimaed factor and it primarily works for the attacker - as he can bring way more material to the fight.
5.12.3.4 deals with it in detail. But the important factor is, that bullet firing weapons only count as 20mm equivalent, while combat armor counts as 40mm for a -50% to attack. And 100mm is easily doable for the attacker, for a -80% vs Bullets.
It will not win you the battle, but keep your casualties tollerable allowing you to attrition them down.

Trooptypes:
Not every trooptype fights equally well in ruins and the performance often varries on offense and defense.

Infantry
On the defense, those are a big reason you have such a hard time. 250 Entrenchmentment and they fight twice as good on defense as on offense.

On the offense, this is one of the two unit types not suffering penalties. But throwing them in will cause you suffering mass casualties. So unless you got a serious Calliber Advantage for their armors (battledress vs bullets), do not throw them in heedlessly.

Guns
Another thing the defender has for his side.
On the defense, they get full entrenchment and no combat penalties. Particulary the MG's will be the main factor for losses among infantry, with their incredible soft damage

For attackers the can be usefull - as long as you do not actually use them in the attack! On the offense they suffere -50% penalty, on top of their already defense heavy damage profile. But if the enemy does choose to try a breakout, having some of them entrenched all around the city makes sure they will regret it. Artillery used only for ranged attacks can be effective, if you do not mind the Structural havok you will cause (or are even counting on it).

Motorized:
Except for maybe capturing the terrain around the city to block or enable the defender to pull back, these units have no redeeming qualities for either side. Better downgrade them to infantry and give those drivers some guns (recuirt additional infantry units), that way they will at least be somewhat usefull.

Tanks:
Defender: Vehicles can not entrench and suffer a -25% defense penalty. Furthermore their profiles tend to be offensive focussed - it should be better for the defener to use guns instead.

Attacker: This is the biggest hope for the low tech attacker, despite the 50% penalty. Being a hard target with serious armor will negate the bulk of the enemy firepower. And your vehicles anti-soft weapons do not deal too much structural damage. Furthermore the attacker will have his entire industrial base (and propably the enemies captured industrial base) to throw at this.

A light tank with a Howitzer will do very little Structural damage and has a pretty decent soft attack even after the -50% (indeed, that only makes it equal to it's soft defense value). And the 100 mm armor they can bring, will reduce the losses to almost nothing.

APC's are too weak on the offense, even if they can also bring 100mm armor.
Buggies perform like APC's, but with less fuel cost. And since you surrounded them, recon should not be an issue.

Heavier tanks can bring heavier guns (do mind the structural damage however) and heavier armor. Just keep in mind the Calliber modifier caps out oat -90% (200 mm armor vs bullets). And that if you make them too heavy, they may not be able to move this side of strategic movement.

Walkers
Marrying a vehicles durability and firepower with a infanterists ability to deal with hard terrain.
Defender: On the first glance, entrechnment is halved compared to soldiers. But that is the wrong way to look at it: Instead what you get is a Vehicle plus half the infantry entrenchment and no negative modifiers.
Walkers are pretty good at killing vehicles, bringing armor and firepower even Battledress Infantry can only dream off. Still, AT Guns are way chapear and may still be viable in a purely defensive role.

Attacker: They are your best option: The advantages of Tanks (see there), with no attack penalties. This is (propably literally) what they are made for!

Strategy
- The first thing you have to accept, is that you will not be winning this in one attack. You will need to attrition enemy numbers, morale, readiness and especially entrenchment down over multiple attacks, nevermind multiple turns. Even if the attack has poor success chances (chances of a total enemy rout), as long as you deal more (effective) damage to the enemy then to yourself, you will eventually win.
- Encirclement is the biggest factor for a bonus. The +200% for all 6 hexes will almost offset the +250% entrenchment.
- having multiple Formations that not all attack at the same time can help. You should have 1 formation that does nothing but block the enemy counterattacks. Also attacking with alternating formations every turn can help make sure the enemy is not given any time to recover while your attackers are given that time.
- a intentional weakpoint can be a very tempting target for breakout. If there is only 1 Unit in a hex, the AI will usually attack in hope of breaking the encirclement. And usually blody itself at very little cost to you.
- mind the 6th hex. There are 6 hexes around cities, but only 5 frontline units in each formation. You need to cover that 6th hex in some way. If there are some ruins outside you may be able to use your OHQ Units, but do be mindfull not to loose them. Attached Independant units are usually the best bet.
- mind your casualty tollerances as well as your recruitment when sending in infantry.
- Kill hits are of course still the best hits. It is one enemy you no longer have to deal with this turn and all further ones. Also on hit closer to a enemy panic retreat.
- Retreat hits only cost readiness and some Morale. They do not loose Entrenchment. Note that reducing the number of enemy units that way, may cause the ovestacking penalties to build and your chances of getting a full retreat are low. So they might not be as beneficial
- Pinned hits are the 2nd best ones, as they cost 50% Entrechmenent on top of similar damage to a retreat hit. They do however keep the enemy unit in combat, wich can be a mixed blessing
- feats and skills that directly attack entrenchment (like the Autoritarians Bunker Buster and the Demolitions skill) are really helpfull. Retreat causers are a mixed blessing, unless you manage a full enemy retreat. Instant Kills are of course still the best.