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The skill tree is generated when the map is loaded. That is, you start the game, and a specific skill tree is generated. This means that you can explore the tree on the first day, and it will remain constant throughout the game.
An important point: if a skill is granted in a witch hut, seer's hut, university, or by a scholar, it completely breaks the skill tree and provides a new, permanent one that does not depend on level-ups!
For example, if Valeska receives the choice of Advanced Archery or Basic Mysticism when she reaches level 2, reloading the autosave will not change it; she will always have that choice. If Valeska learns Basic Navigation in a witch hut at level 2, she will receive a different skill on the right at level 3, but it will always be the same one!
This is how the right heroes are chosen when playing offline!
Finally, there is, of course, a percentage chance of obtaining secondary and primary skills at each level for each of the 18 hero classes. Below, I will provide the probabilities for Valeska (and, therefore, for all knights).
For example, the Navigation skill coefficient is 8. This means that the probability of Navigation appearing when leveling up is 8/112 = 0.0714 = 7.14%