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Quite often, the knight's stronghold has an archer dwelling (where they are given for free).
By day 131, a fairly significant number of these archers usually gather.
Let's try to roughly estimate the number of troops the knight has in the third week (some of the troops may have been recruited not on day 131, but brought in later using a "chain" strategy).
Upgraded archers (taking into account the "stash") - 40+.
Upgraded spearmen - up to 19.
Upgraded swordsmen - up to 16.
Paladins (with a good outcome, crusaders) - up to 10, or champions - up to 13 (presumably only one of these units, or if a very good outcome occurs).
Computer-controlled troops (except for witches and, in some cases, liches) prioritize attacking archers, and so do the castle towers. The units that are eliminated/destroyed can be brought back into line by attacking with upgraded swordsmen (retaliation is disabled), upgraded spearmen, and paladins. The fact is that the defense of even a non-upgraded tier 3 unit (spearmen) is 9 (this is like a bone dragon!!), which allows for quite acceptable losses in battles. It should also be taken into account that by the time the castle is stormed, the knight hero will almost certainly have a defense of around 5, morale +3, and expert ballistics, which significantly reduces losses.
However, if we are facing a powerful mage, things become more complicated...