A very short illustration of a bit of problem-solving/strategy in Dominions, by way of explanation as to why I enjoy it so much.
Midway through my third solo game, after solidly beating the nation of Agartha's (a nation of cave dwellers described in the manual as "inspired by fantasy RPG's in general, and an Earth Dawn setting of my brother's imagination, ripe with mummified ancestors entombed in ancient cavern halls, in particular. Old ideas of a race of pale, cave-dwelling humanoids from my ideas of the game “Shepherds of Creation” completed the conglomerate. Think of opulent halls adorned with riches of the deeper earth in which reside ancient bloated oracles with pallid skins ruling their kin with increasing desperation; desperation because their proud race is dying. Agartha is perhaps the most tragic of the nations in Dominions. Surviving oracles cling to memories of a glorious past unable to stop the unavoidable disappearance of their ancient race) armies in the field, my siege force was thrown back from their capital by this guy:
He's Agartha's Pretender God; and I had not accounted for his presence because, as the notes say, Dominions dragons are shapechangers who can adopt human form, and so my scouting reports listed him as a human mage (who are a different pretender type that actually exists). The combination of his formidable natural weapons, being able to cast some decent regeneration spells (the 9 next to the tree indicates he's a maximally skilled nature mage), and Agartha's capital defences meant that he won the damage race against my field armies and then was able to strike a large number down as they routed. For two turns after that he'd been rampaging around killing survivors as I attempted to sweep them up (when your army routs, it tends to rout in multiple different directions, this being what does generally happen when people run away). So, I needed a plan. My thought process went like this:
A large army didn't work the first time, and I didn't really have a larger army available without leaving a front unguarded somewhere else, plus they'd take too long to redeploy.
A small force of magical, well-equipped troops would...probably get massacred. Most of the magical buffs actually available to me allow elite troops to destroy armies of mortal infantry; I don't really have anything that'd help armour hold up against the Dragon since its attacks do a lot of damage and have several different types. Plus, his earth magic gives him access to buffs that repel physical weapons quite easily.
Battlemagic? My instant death spell, Soul Slay, has already failed to penetrate his magic resistance. A remote attack spell, Mind Hunt, then did likewise. Mages are squishy things that would need protecting from his physical attacks on the battlefield, too. Direct battle damage is largely done by elemental magic, and I don't have that many elemental magicians available, certainly not nearby - besides, all my good attacks are AoE, so I'll be in danger of killing a lot of my own stuff...
Hmm. What other ways are there to kill an enemy? Aha! Fatigue! He's got a battle wound (my phalanxes weren't completely useless, they just lost the damage race) and some heavy equipment already, so that cancels out his reinvigoration (comes with Earth magic). There's an Astral Spell I've got, Stellar Cascades, that drops 25 fatigue on something with no magic resistance check and perfect accuracy. Not normally that useful, but I have a ton of astral mages and 100 fatigue causes an enemy to fall asleep and stop attacking. And I have a ton of astral mages, it's Arcoscephale's main strength. So...if I can guess where he's going to attack, so I'm on the defence (defender gets the first move), hit him with what's left of my army on this front and all the mages I've got on hand who can cast Stellar Cascades (it turned out to be eight), then he'll just peacefully snooze away while my phalangites stabificate him.
And the result...
I'm sure there were plenty of other ways I could have solved this problem, but that was the one I hit on. It took a fair bit of thinking, and it was quite rewarding when it actually came off - which is pretty much why I love the game in a nutshell. Lots of small tactical-scale challenges and the strategic level challenge of always having a variety of resources to meet each one of them.