It is possible to
ensure almost 100% controlled progression without a mentor.
1. Perks.
As a basis, you can use the "Mole" scheme:

(3 basic perks + 3 level 3 perks)
With this configuration, the player can guarantee to level up absolutely any perk or combination (while any basic perk is leveled up in 1-2 picks). Of course, for this, he must have the rest of the skills closed (closed = a skill whose level is equal to the number of perks taken, so new perks cannot be offered in it). But closing skills is not a problem for an experienced player, and it can always be done with a guarantee.
However, this scheme has 3 significant drawbacks:
1) it is monotonous
2) few perks (only 6), no level 2 perks
3) few combinations (only 4)
All these problems can be solved by adding
level 2 perks with mandatory external links from the racial perk. Thus, the player can have 2 scenarios:
1) with a probability of 67% for each attempt, he can take a basic perk in the 1st pick, also levels up a guaranteed racial perk, and after it - a guaranteed level 2 perk
2) otherwise, he can repeat the attempt at the next level up, or take a basic perk in the 2nd pick, in which case he will have a 50% chance of taking the desired level 2 perk per attempt
At the same time, due to external links, level 2 perks will not interfere with guaranteeing the leveling up of level 1 and 3 perks, if the player does not make a mistake by leveling up racial perks too early.
In total, a skilled player, taking into account many attempts, will have
very high (almost 100%) chances of leveling up level 2 perks, and 100% chance of leveling up any level 1 and 3 perks.
2. Skills.
If a hero
starts with 2 different skills + a racial skill, and there is no mentor, then this actually means that when leveling up to level 15, he will only need to take 1 new school.
If the chances of popular schools are 12%, for the racial skill - 10%, and for rare skills - 3%, then
with a probability of about 90%, the player will be able to get any popular skill by level 9-11, and this means that 80% of matches will occur with successfully implemented leveling up of both players without whining about bad luck and a mentor. In addition, there is a
33% chance of getting the desired rare skill and surprising the opponent.
The downside of this system is that the player has less freedom to implement a specific hero, since in addition to the racial skill, 2 more skills are set at the start + he only gets 1 new skill in the leveling up (or tries to play with 2 new ones, but this is already a risk).
On the other hand, if the player knows which hero the opponent is leveling up, then he has enough information about the general direction of his leveling up to build his strategy on this and play more like chess than poker.
The above drawback is easily fixed if the player is given a choice of several heroes, so he can choose the hero that is predisposed to the desired leveling up.
3. How is this approach to stabilizing randomness better than its complete elimination in Heroes 6 or 7?
- It will not be possible to spam the same leveling up if the heroes are different
- Although the probability of the final leveling up is almost 100%, this leveling up requires some skill (and not just choosing any perk)
- In addition, the order of taking perks may vary (randomly), which will affect the build (and in the end, even the same scheme will play out more diversely)
- Knowing which hero the opponent is playing gives much more information
- At the same time, there is still an opportunity to surprise the opponent (during the game, change the strategy if an interesting rare skill is offered).