It's difficult to explain in words but it's mostly understanding positioning (I'd make a vid clip of such a fight for you if I knew how.) Before every fight, I never make a move before studying the battlefield first. How are our units arranged from the start? Where will my opponent likely move? How many ways can his units reach mine? How can I stop/alter their progress towards me? These are some of the questions you need to ask yourself.
The key on impossible is to use the terrain to your advantage by dividing and conquering. Find ways to splinter your opponents forces or impede them from reaching you (Demon Portals and Traps are great for this because they can't move past one.)
A good analogy to this is a game of chess: It's not about how many pieces you have, it's about how many DEVELOPED pieces you have in useful positions on the board. In AP, my opponent might outnumber me 5 to 1 but if my units create a "chokepoint" such that he can only reach me with 2 of his stacks, then his "advantage" is moot. If I can place my units and spells in such a way that the AI is forced to traverse a set path (not because of shoddy AI but because it's the only way to get to me) then numerical advantage is more or less moot. This is the thing I love about AP more than HOMM or any other so-called "strategy game." Strategy is not about having more units and running him over. It should be about creative use of few resources to overcome impossible odds. And that's exactly what AP on impossible with a mage allows me to do.
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