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Then, the tutor should have big martial points/education.
If for some reason the tutor is you, the child will even have some martial lifestyle points already unlocked.
This works for every type of education(stewardship,learning,martial,intrigue,diplomacy)
There is still RNG involved, events, and the existence of a university (and a boatload of gold) also help direct education - as does some cultural traditions, learning skilltree choices, and dynasty legacies.
So, priority is given to generally "good" people, family first, and then consideration for what their education is and/or whether or not they are a genius. I prefer this method, supplemented by the 2nd level of the Kin legacy, and it doesn't hurt to have the 1st level of Erudition for better guest attraction. You can always visit a university and increase the level of your trait with some work. Overall, I would much rather have lower skill levels than bad traits. There is a cascade of potential problems that are always on the horizon, and bad traits are a large component of these problems. And, have a good court tutor. I don't think the personality traits matter at all here, so whoever is most qualified for the job usually gets it.
The Kin legacy, btw, is ridiculously strong if you want to take it the whole way, especially if you want a strong martially inclined character. The capstone "perk" eliminates the loss of prowess from old age (in addition to other goodies), meaning your king (or queen) will kick major ass until the day they die. I have some pretty bad luck with my wives dying in childbirth, so I usually go down this tree early. You throw in some other things like Whole of Body, and Herculean, and it's pretty insane how far you can take a god emperor.
If you don't have access to a Guardian with Genius or Intelligent then select a Guardian that has the highest Martial attribute and if you don't have access to a good Martial attribute then go with highest Learning attribute. What matters here is the Guardians attribute totals not their education focus, someone with 20 Martial will always be a better choice than a Brilliant Strategist with 12 martial.
Plus, you can give them a 4th trait. If, by 13yo, your heir does not have one of your 'good' traits, you can attempt to give it to them. The AI wont.
+1 to this, but it can be expanded to include the Learning stat. A guardian with 18 Martial & 18 Learn will be better than one with 25 Martial & a 10 Learn for a Martial student, all other things being equal.
Attribute totals, 18+18=36...25+10=35. Dont discount the Learning trait of an educator. The higher the better, like your Court Tutor.
At the end of the day...
Have you seen how the CK3 AI plays? Do you really want that educating your heir? Yeah, no, not even the Spare.
GL out there.
For Personality Traits, the ones the Guardian has matter in the way that the Childhood Events that give the Child personality traits the Guardian also has have an increased chance to happen. So, if the child has a guardian with the Paranoid trait, then events that give the child the Paranoid trait are twice as likely to happen.
For the actual Education, it doesn't matter if the Guardian has a 5 Star education or a 1 Star one. What matters is the raw stats.
The game takes the Guardian's stat relevant to the child's education focus (Diplomacy for Diplomacy Education) and also half of their Learning stat. There's an additional significant bonus if the Child and/or the Guardian have a positive intelligence-related trait such as Genius or Shrewd. Another large bonus is granted if the chosen education matches the Child's Childhood Trait, for example a Charming child would get a large bonus to Diplomacy and Intrigue educations and a large penalty to Stewardship education. Certain Cultural Traditions such as Storytellers or Noble Adoption also give a bonus if the Guardian is from a culture with that tradition.
Now, for how the previous bonuses work... the Child has an Education Score that starts at 0 (in normal circumstances), with 4 Star education needing a score of 18 or more. Each year on their birthday from when they become 6 years old, the child has a chance to gain +2 to their Education Score. This chance depends on the factors mentioned previously. So, there's still RNG involved.
Now, there's another type of bonus that just directly gives the Child a flat bonus to their Education Score. Some examples of things that give this type of bonus are the Studious Youth legacy perk from the Kin track, sending the Child to a University (gives +12 to Education score), any event that "Furthers the Education of your Child" and having a Spouse focused on Patronage gives a chance for every Child at your court to gain a bonus to their Education Score. There's also the Court Tutor court position, but that one only applies their bonus if the Child reaches adulthood with them active. So, if the Court Tutor is fired a few days before the Child reaches adulthood, they don't gain any bonus from them. On the other hand, if you only get a Court Tutor a few days before the Child becomes an adult, then they get the full bonus from Court Tutor.