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

3. In offline auto-battles, including those with the Q button pressed after a certain number of iterations, different random numbers will be generated each time the battle is replayed.

In my opinion, this is obvious. You don't have to look far for examples. You can press A at different times, and the results of the battles will be different, as the outcome depends on the time, including the chance of luck/morale, the damage range, etc. But this was fixed thanks to the LM patch, which removed the dependence of random numbers on the animation of the units, and as a result, no matter how many times you replay, the battle will have the same damage range and morale in the same places. A similar process occurs in Heroes 2. The patch didn't take hold offline, but online it would be a real find in case of a disconnect in some complex final battle; it would be easy to repeat the moves. Leader1 should remember all these subtleties.