Morien
09-05-2013, 07:53 PM
Hi all,
As some of you may know, I like looking at probabilities. Well, like might be a bit strong a word, but I like to know what it means when a child survival is what it is, and so forth, as given in the Book of the Estate. I was especially curious to see what the possibilities were for heiresses and childless knights (manor reverting to the lord), and also the demographics of the ages of surviving children.
So I ran a simple test, coding a loop that started with a 21-year old knight and following him with 60 years. The assumptions were that he would be an Ordinary Knight and would be married each year with a chance of childbirth (up to the age of 55; figured that by then the wife would be out of it by then).
Each year:
1. Check for childbirth using the probabilities in the 5.0 Rulebook. (Child born on 1d20 >= 12.)
- Ignored the wife age and even wife dying for simplicity; just assumed that the knight would remarry by next winter phase. I think that sorta balances the cases of an old goat past 55 marrying a young wife.
- Check if the child is a boy or a girl.
- Check if the child survives to adulthood (just one roll from the combined probability in BoE to reach 21: this comes down to about 1/3rd probability, ouch).
2. Check if the knight croaks using the probabilities in BoE.
- Just roll the probability each year.
Here are the results of a peacetime (no warfare modifiers) test (the random numbers seem to be in sub-percent level when using 100000 knights):
Test run with 100000 knights
Peacetime
Probability of a knight surviving over 81: 0.016
Probability of a knight surviving over 55: 0.56686
Probability of a knight surviving over 35: 0.82686
Probability of a heiress: 0.04305
Probability of co-heiresses: 0.05942
Probability of a childless knight: 0.06647
Average number of sons: 2.14316
Average number of daughters: 2.14266
Average number of children: 4.28582
As you can see, there is about 10% chance that the vassal knight will leave only a daughter (or daughters) behind. I'd assume most of these are the young knights who died before 35, so a long wardship is in the offing. Same applies to the about 7% of knights who die childless. Of course, they might have eligible brothers (or brothers-in-law) who might inherit (from the number of sons, we might guess that this is at least often the case). So by and large, you'd expect like 1/6th of the vassal manors to be up for grabs in a generation or so. That is an interesting number for me as a GM.
What happens if it is a wartime, with raids back and forth? Rather than try to model it each year, I just assumed a constant low-scale Raiding modifier and handwaved that the lulls in the fighting would be compensated by the more aggressive fights.
Test run with 100000 knights
Wartime (Raid +1):
Probability of a knight surviving over 81: 0.00209
Probability of a knight surviving over 55: 0.31864
Probability of a knight surviving over 35: 0.68578
Probability of a heiress: 0.12986
Probability of co-heiresses: 0.07641
Probability of a childless knight: 0.27038
Average number of sons: 0.82796
Average number of daughters: 0.83039
Average number of children: 1.65835
The Raid+1 modifier is murder (literally!) for the children, as it makes their chances of survival to adulthood about half of the peacetime one, around 1/6th. Of course, it does kill off more knights, too. These result in higher numbers for heiresses (20%) and childless knights (27%). Since in these cases we could assume many of the vassal knights themselves are the only surviving children (or leave a sister who might still be a heiress now), this means many of the manors would revert to the liege lord for him to grant to deserving people. Hence, during the turbulent times of King Uther's reign and especially Anarchy, you'd expect to see about one half of the vassal manors changing dynasties in a generation, or about 3 times the number of the peacetime transfers. Again, an interesting number for me to play with.
As some of you may know, I like looking at probabilities. Well, like might be a bit strong a word, but I like to know what it means when a child survival is what it is, and so forth, as given in the Book of the Estate. I was especially curious to see what the possibilities were for heiresses and childless knights (manor reverting to the lord), and also the demographics of the ages of surviving children.
So I ran a simple test, coding a loop that started with a 21-year old knight and following him with 60 years. The assumptions were that he would be an Ordinary Knight and would be married each year with a chance of childbirth (up to the age of 55; figured that by then the wife would be out of it by then).
Each year:
1. Check for childbirth using the probabilities in the 5.0 Rulebook. (Child born on 1d20 >= 12.)
- Ignored the wife age and even wife dying for simplicity; just assumed that the knight would remarry by next winter phase. I think that sorta balances the cases of an old goat past 55 marrying a young wife.
- Check if the child is a boy or a girl.
- Check if the child survives to adulthood (just one roll from the combined probability in BoE to reach 21: this comes down to about 1/3rd probability, ouch).
2. Check if the knight croaks using the probabilities in BoE.
- Just roll the probability each year.
Here are the results of a peacetime (no warfare modifiers) test (the random numbers seem to be in sub-percent level when using 100000 knights):
Test run with 100000 knights
Peacetime
Probability of a knight surviving over 81: 0.016
Probability of a knight surviving over 55: 0.56686
Probability of a knight surviving over 35: 0.82686
Probability of a heiress: 0.04305
Probability of co-heiresses: 0.05942
Probability of a childless knight: 0.06647
Average number of sons: 2.14316
Average number of daughters: 2.14266
Average number of children: 4.28582
As you can see, there is about 10% chance that the vassal knight will leave only a daughter (or daughters) behind. I'd assume most of these are the young knights who died before 35, so a long wardship is in the offing. Same applies to the about 7% of knights who die childless. Of course, they might have eligible brothers (or brothers-in-law) who might inherit (from the number of sons, we might guess that this is at least often the case). So by and large, you'd expect like 1/6th of the vassal manors to be up for grabs in a generation or so. That is an interesting number for me as a GM.
What happens if it is a wartime, with raids back and forth? Rather than try to model it each year, I just assumed a constant low-scale Raiding modifier and handwaved that the lulls in the fighting would be compensated by the more aggressive fights.
Test run with 100000 knights
Wartime (Raid +1):
Probability of a knight surviving over 81: 0.00209
Probability of a knight surviving over 55: 0.31864
Probability of a knight surviving over 35: 0.68578
Probability of a heiress: 0.12986
Probability of co-heiresses: 0.07641
Probability of a childless knight: 0.27038
Average number of sons: 0.82796
Average number of daughters: 0.83039
Average number of children: 1.65835
The Raid+1 modifier is murder (literally!) for the children, as it makes their chances of survival to adulthood about half of the peacetime one, around 1/6th. Of course, it does kill off more knights, too. These result in higher numbers for heiresses (20%) and childless knights (27%). Since in these cases we could assume many of the vassal knights themselves are the only surviving children (or leave a sister who might still be a heiress now), this means many of the manors would revert to the liege lord for him to grant to deserving people. Hence, during the turbulent times of King Uther's reign and especially Anarchy, you'd expect to see about one half of the vassal manors changing dynasties in a generation, or about 3 times the number of the peacetime transfers. Again, an interesting number for me to play with.