HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

However, from the point of view of modifying the game, it is quite easy to remove this system time synchronization, and then, provided that the players repeat all actions exactly, the damage, morale, etc., will be the same as in the first battle.

I think that would be the right thing to do. If the battle runs smoothly, there will be no difference, and if a disconnect occurs, it will be easier to restore. Although it didn't catch on in offline mode, they like to generate random maps there :D