no,knights can get all.they have better chance to get water or air from normal level up,than earth or fire though,so looking for magic universities is always useful

You can check the probability of each skill on this page:
http://heroes.thelazy.net/wiki/Knight

Check the table on the right. The higher the number, the more likely to get this secondary skill on level up.

What? Do you have some kind of source for any of that, because almost all of it sounds flat out wrong.

Yes, might heroes as a whole generally get more attack/defense, while magic heroes get more spell power/knowledge, but the chances for each stat depends on the particular hero class, and after around level 10 or so the chances for each stat evens out heavily in nearly every class. Per ZFR's link above, an alchemist has a 30/30/20/20 percent chance for getting a/d/s/k, while a barbarian is sitting at 55/35/5/5.

Likewise, chances of different skills being offered at level up depends on the hero's particular class. Looks like an Alchemist or a Death Knight have as much chance of being offered Wisdom as a Battle Mage.

Map locations offer skills, but that is outside the leveling system.

The rest of it just sounds wrong.

The first paragraph is correct though, if I'm not mistaken. When leveling up, you get a choice of 1 new secondary and 1 upgrade secondary skill. Unless it's not possible (all secondary skills upgraded - you get 2 new; all slots used up - you get 2 upgrades).

Everything else is new to me though.

-edit-
I may be wrong, reinstalling the game to check it out myself to be sure.

-edit2-
*This post contains semi correct information, for more accurate info, check out my next post*

It's a tidbit I saw somewhere on some forums or something. I tested it out myself and it actually works. You can test it out if you don't believe me. Simply create a map with a whole bunch of Pandora's box, tweak them so they give kabillion experience points, open them with a whole bunch of heroes of both types, always upgrade your existing skills so every level you are given a new skill, and you will see every six levels you are given the opportunity to pick up basic Wisdom if you don't already have it, and every four levels (-edit2- somewhat, see next post) you'll be given the opportunity to upgrade your existing school of magic or pick up a new one you don't currently have.

It's also a tidbit of info I heard about and got confirmation countless times in both Chris67132's and Mekick's (AKA TheKnownWorld) Let's Plays of HoMM3 on Youtube. Although I don't recall the exact minute and second where that info is said, I do recall early in Mekick's Siege Survival Challenge, he levels up both Jeddite and Alamar, trying to get one of them to learn the Earth school of Magic and he relies on the fact the game offers heroes a chance to pick a school of magic every four levels to get it (-edit2- somewhat, see next post).

Thanks.

I almost always pick Wisdom when available. And if I'm not mistaken there have been times when my hero was of high level before he was offered it on levelling up.

Alright, I reinstalled the game, tested my bullcrap, proven myself semi right, semi wrong, then went on the internet to read snippets from a PDF file on the subject matter.

The PDF in question:
https://www.cs.virginia.edu/diochnos/research/other/heroes/internals/on_skills.pdf

For the TL;DR:

The both of you are right in that it is statistics driven. However, there are two exceptions to those statistics:

The Wisdom exception: "A hero can not wait for more than 6 levels so that Wisdom is offered to him; either as a brand new skill or as an upgrade."

In a nutshell, you will be offered Basic Wisdom every six levels, the only way to not get it is to go out of your way to avoid it until your entire skill set is full.

The Magic exception : "A hero can not wait for more than 4 levels so that a Magic School is offered to him; either as a brand new skill or as an upgrade of an existing one."

So in a nutshell, you are at least given a Magic School by level 4 (if you didn't get a bunch of opportunities for Magic Schools before) and if you pick one and max it out as soon as possible, you will be given another school four levels later, and if you max this new one out as soon as possible then four levels later you will be offered another one.

If you are extremely picky which Magic School you want ("Earth Magic or bust!" for example), you can avoid picking one and every four levels the game will offer you a Magic School until your skill set is full, giving you at least four opportunities to pick it up.

It seems like Magic heroes have an easier time acquiring all four Magic School because in addition to the Magic Exception rule, they are offered schools on level up more often than Might heroes statistically speaking. That being said, and granted you are not picky with what Magic School you get, every Might hero can expect to pick up at least two Magic Schools in addition to basic Wisdom by the time his skill slots are full, picking a third school in addition to basic Wisdom for a Might hero is also very common.

So basically, like the both of you said, it's all statistics and probabilities which secondary skills you get, but like I was led to believe, both thanks to that one forum post I first read ages ago, and then confirmed several times through my own playthroughs and from watching Let's Plays of HoMM3, Wisdom and the Magic Schools have special rules that overwrite the statistics and probabilities associated to all heroes classes and make them almost guaranteed you will be able to pick up Wisdom and at least two Magic Schools, even with the least statistically probable of Might candidate.

-edit-
As a quick but unscientifically accurate test just to check out if both exceptions were true, I hired 20 or so heroes (of both types but I put extra focus on Might heroes as those heroes I thought would have the hardest time picking Wisdom and Magic Schools) and I had them run into a bunch of Pandora's boxes with experience points inside. All I did was:

Priority #1: If Basic Magic School shows up, pick it up,
Priority #2: If Basic Wisdom shows up, pick it up,
Priority #3: Otherwise, always upgrade an older skill,
Priority #4: If I can't upgrade or can't pick a new Magic School or Wisdom, pick a skill at random.

That's all I did, once I had exhausted all the Pandora's boxes I put on the test map:

All 20 heroes or so had acquired Expert Wisdom and at least three of the four Magic School.
Not all, but most of the Magic heroes had all four Magic school and Wisdom, those who didn't I think had some sort of skill restriction.
I got one Knight that was lucky enough to get all four Magic Schools and Wisdom.
All heroes who didn't start out with basic Wisdom were offered basic Wisdom by level 6 without fail.
After every three levels up without a Magic School upgrade or offer, on the next level up I was offered one without fail.

Thanks for your time, this is interesting and potentially very potent information. ; )

Is this behaviour cchanged in Heroes Chronicles?

As per my previous post, I remember I had trouble sometimes getting Wisdom for my heroes. The last HoMM3 game I played was Chronicles.

So I just checked that game. Using the XP cheat, I levelled up barbarian heroes. They can get to level 12 without Wisdom, or any magic skill, being offered.

I can't check my HoMM3 complete game because I don't have the DVD with me here.

EDIT:
Just rechecked.
In the 2nd chapter of Heroes Chronicles, Wisdom and Magic secondary skills are offered just like you described.
So it looks like Wisdom and Magic skills were removed from Chapter 1 so it fits the story.
Also, when I reload my save from the last level of that chapter, Tarnum and one of the other heroes do have Wisdom. So either that restriction is for early levels only, or I got it from a witch hut.

Yes, I recall having the same problem, my Battle Mages had Wisdom and Magic Schools and Tarnum was that weak sauce pure Might hero that couldn't cast spells to save his life, which made the very last scenario much harder than it should have been. Considering they overwrote Crag Hack with Tarnum, and considering Yog was turned into a special hero and couldn't be recruited from taverns for story reasons, considering all the non-Stronghold and non-Tower heroes were absent from the campaign (I think? It's been a while since I played that campaign), it is safe to say they most likely also made it impossible for Barbarian to learn Wisdom when they edited the heroes file, again for story reasons.

The chronicles games do have special rules for hero skills (and heroes, and other things), so it isn't indicative at all.

On any of SoD maps (not on RoE or AB ones) you can disable any skill you want in map editor, so it won't appear in all instances where it normally would (levelling, universities, random scholars and Witch's Huts).