Heroes of Might and Magic III - Complete Collection + Era2 + VCMI + Utility.

Basically, I spent about half an hour searching around, and eventually, although not immediately, I managed to get it working – as practice shows, if you don't set it in the "only player vs. computer" section (or set it to 0), everything else works normally.
Based on what I've found, it seems like I should try installing FIX3 and, while maintaining the same condition, try creating a random map in the new version of the game.