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A) What makes you (if this is the case) preferring life path generation to other character generation methods?
I like them as optional generators, maybe with points you can use to influence them to get outcomes you want, but view them primarily as substitutes for crafting a reasonable backstory with the referee. I really like to use them in a totally random fashion, then exercise my brain to fit all the pieces together into a coherent back story.
I like to get a personal contact to my characters life and allowing skills that look much more natural than point buy or leveling.
I think you are asking rules to do what you can do yourself or asking for rules to stop players from doing something you don't like. Point buy is total freedom, you are free to make a unnatural character as you are a natural one. I don't get the comment on leveling. Leveling, as I take it, gives little choice and has the natural aspect baked in.
In any case you can influence things to "natural" skill sets by giving cost reductions for certain synergistic skill sets (the "natural" ones), or by having prerequisites, that is basically link mechanically the skills you want to appear together. If you get too much into this you should just consider classes with skill packages. I do it by rewarding certain constellations (groups) of skills, you get them all at a certain level and you rank up and get benefits/perks. You can buy any skill you want at no penalty, but the benefits require at least a core of "natural" skills.
It should give you a personal history with social integration, not just an adiabate migrating fighter/cleric/wizard/rouge called Bob.
Agree, loved the flavor in how Pendragon and Bushido did it. Again, really just well though out tables for your setting.
B) What are your problems/do you feel missing with/in existing life path generation systems (and do you have ideas for solution)?
Nothing is missing. I've seen several that work great in all flavors. I'd find a pre-existing one you like and follow the format. There really is little to reinvent here from what I see. I like when you can spend build points to craft background or better yet your skill build impacts background, contacts, etc.
The kind of life the character is nominally living at some check time often has no relation to the resulting random events.
(mauled by a bear in an urban cloister school?)
I actually love that kind of thing. You have to work to think of a chain of events, although perhaps improbable, are none the less interesting and likely formative.
The number of events are much to low. With 30 you probably have had every illness in the realm and lost 3 personal fathers and 5 mothers and met at least one random god in person ... .
Only if you write the tables that way. If that is from some real game I'd just call it bad design by that person, many other people have got it the way you want it.
There results often give effects that different characters should have had very different chances to handle.
They do? There exist ones where you can use your current skill to affect the random rolls. You can always easily bolt such a system on. Sounds like you are talking a life path system more akin to Traveller here.
The results often do not fit with the way the character would act or doesn´t consider general behaviour (risk taking vs. risk avoiding, law abiding or ignoring ...) or social standing.
I think this is just a lack of your sample size. Many do and in fact many such systems let you choose if you are going to take that risk; i.e. let you choose which table to roll on.
Different characters from the same (sometimes rather small) area are experiencing some very different meta events (war or no war, famine, plaque, gold rush ...)
Now that is just a result of turning your brain off as a referee. If your tables are going to proclaim on such large meta-events (that is also serve as world generators) then you just have to ensure consistency. Or get very creative like saying sure there was a "war" but this guy got "no war" cause his daddy got him a safe position in the national guard. No random table with major meta events is immune from a referee turning off their common sense.
Family and social bindings take a too small role in my opinion.
Again depends on the tables you been looking at. In some settings this would be important, maybe everything, in others it may mean nothing.
Education and cultural value conditioning should make a difference - even if you rebel against it (which should probably also have its roots from somewhere in the life path).
That's all in the tables and bias. I'd never have a table tell me I rebelled. Rather, a players "rebellion" could just be rolling on the improper table, not one good farmers use. Rebellion is often simply seeking something the rules of society say you can't have. Sometimes it's just teenagers seeking kicks, other times it's a people seeking food and freedom.
C) What unsolved problems do you see generally?
None really. I've seen all these problems solved in one system or another. These things are mostly flavor, so the devil is in the details of the flavor text and if the flavor matches your setting concept. Never expect them to match your concept unless you write them yourselves, but you can copy the mechanistic approach used.
If the life path is rather detailed and following the place of living it sometimes is problematic to get the char to the start point of the game "naturally".
Again that word, naturally. What do you mean, that it falls out of the tables? Getting to the start point should never be an issue. State it simply as thus to your players. We are all here to play this game right? You want these kinds of adventures / experiences. Work together to think of a reason why you have met and are working together so we can start this game. Don't be asses about it and keep it loose. Otherwise I'll just come up with some potentially cliché beginning and we'll get going. We are here to play this game. If we can't get past this simple hurdle maybe we should just paly a board game.
I would like to include/start with the family of the character into the life path too, but then I get the problem of having to go with the flow of time to make sense, but don´t know where to start from, especially in a dynamic and thus more interesting environment with lots of migration or social change happening.
At some point you always have to get off the life path wheel and just play the game. This life path is really just back story. The more you have the players be able to interact and influence it the more it becomes a mini-game in its own right. You can keep it simple for family, small, medium, large, intact or not. Small, medium, large, would be defined by the status/background/region/ time period. Same for chances intact or not. Deaths / sickness in the family? None, few, some, many. Numerically what does that mean? Well that would also be defined by status/background/region/ time period. Also like, never moved, moved some, migrated, refugee, etc. Simply use relative terms in the generation with numerical and specifics tied to status/background/region/ time period, etc. all those things you want to matter.
In the beginning, you are born to a family of status x, of region y, of size z. Over time you lived in (i) and now you family is intact/not with (i) numbers of deaths/illnesses. You grew up supposed to learn a, b and c, and you stayed true (gaining allies in a, b or c) or you rebelled seeking to know e, f and g (making some new friends in e, f or g). Add skill generation/buy in between event risk/choices/table choices. Add tables of different risk; but beware, do you wish to have characters die in character creation? Are your players mature enough to accept the bad consequences without whining?