I have a couple of battles that I remember where the AI surprised me, though in the opposite way.
First was a pretty basic example of AI stupidity: As the Burgundians (XL, late) I took Ile de France with a force much larger than the French one protecting it. They duly retreated, but sallied just the next year. As happens in Ile de France, I had a defensive bridge battle, the ideal setting. I won't go into details, but in short, the AI head on charge with most of their peak cavalry units except their king, got smashed by my Swiss halbardiers, Swiss pikemen and arbalesters. Then they just sent a force of some 600 (I counted ten units at least) of handgunners up the bridge, while their Chivalric Sergeants waited in the background (as they had came as reinfrocements). Well, handgunners ain't much of a problem. I took the opportunity, and started moving my Chiv Knights across the other bridge some distance away. Almost as soon as my knights have crossed, the French king rides onto the bridge were the battle is. I now have all the time in the world to manouver my knights, kill off the CSs from behind, trap the king on the bridge and annihalate the 600 handgunners. Result: about 150 dead for me, and some 1100 killed or captured on the French side, including the king.
Another two occured during my Bohemian campaign (XL Early, now scrapped). The Germans invaded Friesland, which was my weakest province as I had focused on producing ships rather than troops. Anyway, they out numbered me, and as Friesland goes into the plainsinland-maps, I though I was in for a tough defensive battle (I had mainly UMs).
Anyway, so the Germans move up their force, my army is standing close to the map edge with a forest protecting the rear. I move up my two units of Mounter Crossbowmen to flank the enemy. The enemy MCs, two units for them as well, ride up and a short archery duel take place. When three of their MCs are dead, and none of mine, the ride off. I can then move my MCs up to the enemy rear and start pepper their army from behind. To my surprise, they don't move. At all. They just stood there, with their army looking at mine and their MCs off somewhere else while my MCs peppered their best units (two units of FMAAs with armour +1). I thought this was boring and as it was exploiting the AI, I decided that I'd attack them once I had made maximum use of my MCs, ie. firing up all the bolts. Just when I start to move up my army to attack the attacker (which is really stupid, but it was really boring) the time runs out, and I win. 89 casualties on the enemy side, 0 on mine.
The other one took place in Friesland as well. This time I was technically the attacker, as an overwhelming German force had forced me to retreat to the castle.
Anyway, again, the setting is wooded plains. My entire army starts in a forest. I try to get my men up in position, then before I even leave the forest the entire AI cavalry, general and all, charges head on. I get my own cavalry out of the forest, while I move the rest of troops back inside. The cavalry gets into a fight with my Feudal Sergeants and FMAA, while my own cavalry rout the archers, UMs and single unit of spearmen that the AI has left unprotected.
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