DISCUSSIONS on “Rules for online games in HoMM3 and formulas for calculating player rating.”

Can you give a specific example of a group where two players can only agree through a draw and cannot agree through a 1-0 or 0-1 score?

Such situations can easily occur in any team tournament.

Any situation with an equal number of points between teams or players involves additional criteria. But, to avoid resorting to additional criteria, you can always play to a draw instead of playing for a win; there's no need to even discuss your formulation. A draw can be beneficial to both, for example, when two leaders, knowing the number of points of the nearest competitor, see that the competitor can score at most the same number of points they currently have. Therefore, a draw is good for everyone. I repeat, such cases are very likely, and if you followed any sports with group competitions, you wouldn't ask such questions.

If one stands on a cell, and the second comes to this cell during their turn, then two heroes are on the cell. And one of them must destroy the other to keep the cell for themselves.

I completely disagree. Two heroes cannot stand on the same cell! Only the defending hero stands on the cell and guards the adjacent cells or their own! To stand on a cell and have the ability to continue the turn, the aggressor must conquer it!

Firstly, if you attack a Castle, you say it's a key stronghold. Why do you think a barricade behind a landscape feature isn't a stronghold? Of course, there's Moscow, and there's Borodino, but the essence remains the same. You need flying units for a Castle, and with a certain terrain, you need single-hex units. To get into the Castle, you need to break down the walls, and to get to a barricaded unit, you need either a superior single-hex unit or a spell that removes the landscape feature. If your ballista is destroyed, they will also destroy single-hex units to prevent them from reaching.

Please explain why you are not satisfied with a spell that removes part of the terrain and opens the way. Why do you think it is necessary to remove this spell from the list and generally deprive it of meaning? I believe that if you can't pass, you must have a spell (just as flight is needed to overcome mountains, for example); if you don't have it, you retreat just as you would from a Castle. The same question applies to hex size.

Secondly, back to the cells. Red attacks the standing blue, and red cannot stand on the Adventure map after the battle in the place of blue or in the place of the position guarded by him, unless he is killed or blue retreats (because this will only happen after the battle ends). Red has no other options! Blue stood on his position and does not need to pass the turn to him, but he is safe; he has dealt with staying in the same place.
The aggressor's goal is to move the enemy from the position!
The goal of the defense is to defend against the aggressor's attack!
The goal of the defense has been achieved, and the aggressor's goal has not. This is perfectly fair.

As for the gameplay, you can specifically use defensive tactics against an opponent's attack, as Vic clearly demonstrated in the report he linked.