They try the magic victory on higher difficulties if they get far enough, I've never seen them try the Master Quest or diplomatic victory even though some are saying they go after the Master Quest. In any event they need LOTS of time before they do it.

Yep, a number of times -- usually very early game by having an unlucky encounter with a massive monster or monster army deciding to smash my only city.

In other cases, I'm pretty sure I would've lost in some late-ish game situations, but I tend to quit and not see it through -- starting over from an old save or from the beginning with a new strategy.  On high difficulties, it's not rare to see a rival faction form a frightening army with a seemingly-endless source of units, trying to slowly take each of my cities one by one.  But if it becomes very apparent that I have little means to survive (not being able to generate troops quickly enough, not having researched proper tech etc), I don't have the patience to slowly watch my nation crumble. 

Part of the reason I don't see it through is because rivals are simply too slow while taking you out (whether they're too formidable or I just simply get bored late-game) when compared to most other 4x strategy games.  I've only seen AI always take one city, rest awhile, and repeat.  I'd love it if armies (depending on their faction) would be more wreckless/aggressive and attempt to take one city immediately after the other; either with one massive army charging through, or strategically attacking numerous cities at once from all sides.  I've never witnessed either of these scenarios.  But this would make the process of being at war more challenging, less agonizingly slow, and far more interesting and thrilling.

I'd REALLY like seeing this addressed in the future at some point.

Never once saw a rival faction attempting to win by diplomatic, master quest, or spell of making victory.

There should really be flavors to AI instead of one size fits all "challenging" or whatever.

Warlord Verga should be more crazy aggressive than Queen Porcupine.  The characters don't feel like they exist as characters.   Maybe this will be in the later diplomacy patch I've heard something about

they have different personalities that change the perceived value of trades, their aggressiveness and what their research focus is (you can check it in the foreign relations tab), but like smeagolheart said it will be fleshed out in the 1.5 update that will mainly deal with the entire diplomacy system.

I find the phase of Early Game during which I make first contact with my opponents the most challenging, but once the early part of Mid Game is done, I don't seem to ever be in danger of losing.

Don't pretty much all of of this style of game do that? Civilization certainly does, which is the closest comparison. I believe the Civ AI cheats with fog of war, too.

I was pushing hard for better AI in LH, but by that I mainly meant "less brain-dead" AI. Brain-dead AI is just annoying, it takes away any sense of achievement you get from beating it. To a large extent I think 1.3 fixed this though, the AI is at least fairly competent now. I don't really expect it to beat a human in a fair fight, there are just too many variables.

I've beaten Ridiculous three times in a row now playing different standard factions. Magnar was fairly easy, Pariden and Kraxis I had to reload a couple of times in each game after I lost my best stack from underestimating how strong the AI was. I had to reload the Kraxis game after the AI immobilized my best stack with strategic spells. Call this cheating if you will, but I don't have enough spare time to spend twenty hours playing a game and then have to restart from scratch because of a stupid mistake. The AI might have beaten me in those games, not sure, or I might have been able to recover, but either way it was going to be an additional twenty hours of hard work.

I've not tried Insane yet. I don't believe in switching off Spell of Making. I believe Fallenchar prefers the good guys to the Fallen, but give me Summon Skeleton Horde and Sacrifice any day. Sacrifice basically means you can farm a city or two for mana, and mana will win you the game. I may give Insane a go with one of the stronger factions; Magnar or Kulan or Ceresa probably suit my play style best, I think I'd have a chance on Insane if I played one of those factions. But I can certainly imagine losing to a Spell of Making victory, or just getting crushed by an AI with armies which are too strong for me. Stopping a full AI stack on a high difficulty level can be touch and go.

I guess my answer to the original post would therefore be, if you don't feel the AI is providing a challenge, up the difficulty.

Sure all games cheat at higher difficulty levels but some are more blatant than others. Civilization for example, even on the highest difficulty levels the various units still have the same stats as mine. I haven't played LH on the top difficulty levels but in earlier iterations the AI troops would have ridiculous stats and numbers of perks which were just plain not possible for human armies to have (perhaps this has changed in LH? although I see a bit of it even at Expert difficulty so I suspect not).

I guess it is the difference between the AI clearly playing by different rules and having/doing things that are impossible for the player vs the AI potentially still cheating significantly but at least having a veneer of playing by the same rules.

I've just finished my very first LH games yesterday. I played with the defaults easy level.

I was never ever challenged by the AI. When I first encountered my two AI opponents I was at 50 and they were at 20.

I did get wiped in the late game by a rogue wizard. He use a spell I never seen before and killed 5 of my stacks. Had to bring my main armies to get the b@stard.

I assume I had it to easy. So I started a new game with challenging level. Hopefully this will be better.

Despair that was a cool spell.

I tried to counterspell it but it was resisted.

I wish the AI was as hard as that magician.

Will be playing again tonight