A program for determining luck/morality in Heroes 3!

R does not change when skipping a turn, casting a spell, or during enemy unit turns, unless they attack.

Apparently, this isn't all the information? Because in practice, it IS possible to achieve a morale drop, for example, for archers against neutral units, in the first round with all other actions being the same.

It is impossible to repeat the battle exactly as described (I checked battles without a Hero on the enemy side).

If there is no enemy hero, then I agree. But when there is one, it becomes much more interesting, because there have been cases of almost 100% reproducibility of complex battles, although even there, differences were possible after a few rounds.