Prepare for wall of text from some of my ideas
Okay so I've been thinking about the ageing of characters and about possible heirs.
Estimate that age of manhood is reached at 15 years, and they live to be on average 50 years old (which I believe was a lot during the timeperiod they are aiming for), then that would mean that the player has about 3000 in game days to develop his character, and this is quite a long time.
So, imagine your character get's a kid within 5 years, then by the time your character is 35-36 (and still have a bit more than 1000 days left to play on) your son is 15 ish and will be able to join your party as a companion and level up like that. This would easen the transition between characters and lower the level gap and not having to start from scratch.
So if you die around 50 with level 40 something, maybe you can start with your heir at level 20-30 or something.
Of course the numbers here are just estimates and speculation, but if the system worked something like that, it would be neat.
If your character happens to die in battle, then everything should default to your heir, and if you don't have one, well... game over I guess. I know quite a few won't like this but it would add a whole new dimension to the game which I find fascinating.
Of course, if you have an heir to inherit things, your lords (if you have them) should, depending on their personality traits, take different actions such as swearing loyalty, or try to claim power for themselves. This would be an incentive to always try to have only (or at least a majority so you can crush rebellions) honorable lords, which of course are harder to get. The easiest lords to get will always be the traitorous scum.
Also, if your heir is too young to fight, you can either play as the companion/lord that you have most trust/friendship points with until you come of age. Or the game basically makes a time-skip, calculating all the changes that could happen and implements them, though I believe this could be very very troublesome for a PC as you then basically have no control over what happens.
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Another thing I thought would be cool is the ageing effects.
Assuming lifespan up to average 50, then middle age can be around 30-35, old 40-45 and venerable 50+.
Also, when you hit venerable, there should be a dice roll to determine how long you live, and anything beyond 70 is just crazy.
Middle age: -1 to physical stats / +1 to mental stats
Old: -2 to physical stats / +2 to mental stats
Venerable: -3 to physical stats / +3 to mental stats
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Also, if a lord is defeated in battle, there should be a % chance that he may die. If the lord has heirs, they would of course automatically assume control of all the armies, towns/villages and everything else, assuming they are of age (not kids). If they are too young, they should have to wait until they are old enough to fight, and the right to control the troops should default to the king, while they are being paid by the lord's coffers.
If the lord has no heir it would mean the end for his bloodline, and a young promising knight should be raised to lordship, similarly to how a player is able to do that.
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Hopefully the companions work somewhat similar to all of the above mentioned. They should be able to get wifes, heirs and stuff, otherwise they should get replacements. What is the point of having your character die when your companions are OP?
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It would be cool to see a civil war, if a king that dies has 2 sons and both consider themselves to be the rightful king. So if if a king has 2 sons, there would be a dice roll, 1/20 or 1/10 or something. Of course, this would mean they are weaker and other factions would be able to eat them up more easily. This should also apply to your own kingdom if you happen to have one.
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Of course, this whole thing with heirs would all be made mute if there is not easy way to marry someone, so instead of having just noble wifes, a PC (as well as companions) should be able to get a "default" kind of wife. Someone that is of low standing (but who cares, because love, right?). Of course, getting a noble woman to marry takes a lot more time, but it would get you a connection with a noble family, which gives you diplomatic bonuses.
So if you pursue a noble woman, but change your mind because your character is growing old, then you can just marry a wench from some time and make a baby so you get an heir and won't get the "game over".