RyaReisender: I don't even think HoMM3 was ever intended to be a professional competitive game so being fully balanced wasn't really the main focus of the game ever. It's not like Warcraft.
A single match would take way too long anyway to be suitable for real competitive matches.
To start I did and still do play H3 for fun and I find it quite enjoyable to play the different factions and try out different ways to win vs different opponents.
That being said there was quite a bit of competitive PvP tournament playing of this game. There was a site called toheroes.com, aka Tournament of Honor, that is fan made and let people keep track of the people the played against and the maps they played on. ToH is still going to this day although it's for the newer Heroes series now but you can still report games played on H3-5 maps for points.
What players mostly did was play something called Random Map Templates, which were guide lines for the Random Map Generator to produce well balanced maps for ppl to play on and took out game breaking things like Dimension Door and Fly so that the game could be more fun. I will admit that H3 games took around 2hours each to play but it was pretty fun.
I am including a link to the Tournament of Honor site where you can download Random Templates and other fan made maps that are well balanced for playing.
http://toheroes.com/h3maps/Random.htm To use Random Templates
1. Choose the template you want to use from the above site and RIGHT CLICK and choose "Save Link As..."
2. Copy that file to your Heroes 3, Data Folder (default path is something like C:\Program Files\GOG.com\Heroes 3 Complete\Data)
3. Rename the File you just moved to "RMG"
4. Launch Heroes 3, New Game, Single or Multi, choose Random and input settings (keeping in mind the template you have chosen).
5. Enjoy
To confirm that it worked ounce your in your game press "i" for Scenario Information. You will see on the right side it says "Map Created by the Random Map Generator, Template was (whichever you chose)"
NOTE - you will see info about version #'s but if you have the gog version, which is Heroes 3 Complete, you don't have to worry at all, you have the most uptodate.