Skoraj
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Of course, the Archmage has access to all schools of magic. The question is not only theoretical. You write that the Archmage is, by definition, stronger than other classes, but how often do you actually level him up? Can you keep this class viable until the end of the game without giving the hero decent defense? Nobility + Scouting is also a cool combination, especially with the Staff of Death, but the usefulness of such a hero in battle fluctuates with an amplitude from 0 to very high values. The class effect is cool, but in practice, you won't encounter it.
I wouldn't say that the Field Marshal is a strong class – it's a class for strengthening the army, but practice shows that by the end of the map, your army consists of only 7 heroes, and almost no one uses creatures anymore because the difference is already so great.