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Now I'm ready to answer all your questions without any videos.
And now everyone will be able to perfectly replicate this battle in the conservatory.
I finally understood what the problem was.
The problem is that many online players use a modified resource file for Heroes 3 in battles, which controls the delays during battle animations. They place this file in the Data folder of Heroes 3, and it's called Cranim.txt. Driven by my passion for idealization, I once decided to edit this file, minimizing the delays during animations as much as possible. However, the attack speed, response time, and turning speed of creatures, when using this file, somehow didn't change significantly. But I wanted more. In general, in the Cranim.txt file, which online (and offline) players use solely to save real time during battles, I replaced 1s with 0s. And it turns out that this caused the battle map for many battles (or maybe all of them? needs testing) to become fixed. By the way, the issue of controlling the outcome of morale and luck can now, perhaps, be resolved by everyone using this file – the map of any battle will always be the same for everyone. And everyone will be able to replicate any battle based on its description. Now, instead of "generating" morale or luck, you will only need to choose the ideal move along the decision tree on the battle map.
So, here is the link to the Cranim.txt file in the form that most online (and offline) players use, from the Heroes of Might and Magic III file repository on heroesportal: Cranim.txt
And here is the file that is in the Data folder on my computer:
Cranim_vbn.rar
Here are the steps to replicate the battle in the conservatory:
1) Download and unzip the Cranim_vbn.rar file.
2) Go to the Data folder of Heroes 3 on your computer, and if you already have a Cranim.txt file there, make a backup of it.
3) Rename the extracted Cranim_vbn.txt file to Cranim.txt, load the save, and make sure that the unicorns are blinding and the battle map is fixed.