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Lately, I've been playing full-random games on the Tower of Destiny map. The most challenging castles are the Dungeon and the Necropolis.
For the Dungeon (with a random starting hero), the criterion for playability is the respawn rate:
1) A good, easily accessible lair (cats, police, or, at worst, eyes; everything else is garbage) that allows you to form a strong army.
2) Enough money/resources in the immediate vicinity to build and buy these cats/police from the dwelling, lair, and portal.
As you can see, only 10-20% of the setups meet the playability criteria.
For the Necropolis, it's even worse – you need to quickly acquire sulfur, stone, and money for the liches; otherwise, the battles will be barely successful. Fighting is even more difficult than with the Dungeon.
However, unlike the Dungeon, the Necropolis has an advantage in the long run – skeletons in the Stronghold and vampire lords in the Tower of Destiny. So, if you successfully survive the nightmare of the first week, things usually go well afterward.
The Dungeon, on the other hand, if you can't achieve a normal development pace in the first few days, there will be no breakthroughs later on.
In the Tower of Destiny, both of these castles are usually restarted when playing full-random.