Increasing Skill Levels From default

Pseudonym · 10-15-2015, 08:38 PM

So, I've been trying to wrap my head around raising skills from defaults, and I'm thinking it sounds a bit to me like a programming problem, like some kinda graph.

So let met think out loud and tell me when I make a mistake or a bad assumption, or if the situation is just too contrived.

You have skills a,b,c,d

For simplicity each skill is average, and all stats are 10.

Each skill has 8 points in it, so relative to the attribute which it is derived from, each skill is +2.

Let's say
a defaults to b-1 and c-2
b defaults to c-1, d-2, and a-3
c defaults to d-1 and a-2
d defaults to a-4 and b-2.

I think I understand the GURPS rules to say that if a defaults from b, b cannot default from a.

I think that, extrapolating that further, if a defaults from b, and b defaults from d, d cannot default from a.

So in essence... I feel like this is some kinda weighted and directional graph problem.

http://imgur.com/NtYU22o

So the vertices show the penalty of defaulting from each skill.

Now, say we want to optimize our dependencies for a.

If a defaults from b, a can b IQ+1 for free. plus with the 8 points already invested in a, a becomes IQ+3.

In the same atomic reshuffling if b can default from c, b can be IQ+3 using the same math as above, but that would mean that now a is ((IQ+3)-1)+2 = IQ+4.

c can do the same making it IQ+3, making b IQ+4, making a IQ+5

d being the end of the line however, can only choose to be based off of IQ, making it IQ+2

So now we have this illustration.

http://imgur.com/XWsPdNI

And now here comes the super fun part. As long as this is atomic, and as long as no skill goes below the original relative level (IQ+2) we are now allowed to rebalance these points.

So if we take away 4 points from a, a is IQ+4.
If we put those 4 points in d, d has 12 points an is IQ+3.
If d is IQ+3, c is now IQ+4, and b is now IQ+5... which makes a IQ+5.

If we take away 4 points from b, b is IQ+4, and a is IQ+4, and if we give that to d, d now has 16 points and an IQ+4.
But since d is now IQ+4, c is now IQ+5, so b and a are also both IQ+5.

So finally we take 4 points out of c, so c,b,and a recursively become IQ+4...
we put those 4 in d to give d 20 altogether to be IQ+5... which makes a, b, and c IQ+5...

If I take the remaining 4 points in a away, a becomes IQ+4 defaulting off of b-1.

But we put the 4 points in d so that d now has 24 points. d is now IQ+6, as are c and b. This makes a an IQ+5 skill with 0 points.

I cannot continue, however, to remove points from c and b because a default cannot default from a default.

So we end up with:

http://imgur.com/XGdQfe6

So coming back... now it seems like it is something like a dynamic algorithm problem.

That is the optimum solution for a is the one that is best between (the best solution for b that does not include a which is derived from (the best solution for c which includes neither a nor b which is derived from (the best solution for d which includes none of a or b or c))) or (the best solution for c which does not include a derived from the best of [...])

And so it turns into a tree where each branch below must exclude paths to nodes above...
http://imgur.com/7gwcDvg

So... the weight of each branch becomes the sum of the relative skill of each skill and the default modifier...
But working backwards seems better so, for example from IQ to d is +2, and from d to c is the -1 default of c to d combined with the relative skill of +2 of c, making it a weight of 1... following that using a dynamic algorithm iq to d will give us 2, d to c will give us 1, c to b gives us 1, b to a gives us 1... which adds up to the 5 we get in the first optimization.

But the second part of the problem... the shuffling of the points is what gives me the biggest problem. Once the optimum path of default learning has been established, what is the smart way to optimize points?

10-15-2015, 08:38 PM	#1
Pseudonym Join Date: Jul 2015 Location: Phoenix, AZ	Increasing Skill Levels From default So, I've been trying to wrap my head around raising skills from defaults, and I'm thinking it sounds a bit to me like a programming problem, like some kinda graph. So let met think out loud and tell me when I make a mistake or a bad assumption, or if the situation is just too contrived. You have skills a,b,c,d For simplicity each skill is average, and all stats are 10. Each skill has 8 points in it, so relative to the attribute which it is derived from, each skill is +2. Let's say a defaults to b-1 and c-2 b defaults to c-1, d-2, and a-3 c defaults to d-1 and a-2 d defaults to a-4 and b-2. I think I understand the GURPS rules to say that if a defaults from b, b cannot default from a. I think that, extrapolating that further, if a defaults from b, and b defaults from d, d cannot default from a. So in essence... I feel like this is some kinda weighted and directional graph problem. http://imgur.com/NtYU22o So the vertices show the penalty of defaulting from each skill. Now, say we want to optimize our dependencies for a. If a defaults from b, a can b IQ+1 for free. plus with the 8 points already invested in a, a becomes IQ+3. In the same atomic reshuffling if b can default from c, b can be IQ+3 using the same math as above, but that would mean that now a is ((IQ+3)-1)+2 = IQ+4. c can do the same making it IQ+3, making b IQ+4, making a IQ+5 d being the end of the line however, can only choose to be based off of IQ, making it IQ+2 So now we have this illustration. http://imgur.com/XWsPdNI And now here comes the super fun part. As long as this is atomic, and as long as no skill goes below the original relative level (IQ+2) we are now allowed to rebalance these points. So if we take away 4 points from a, a is IQ+4. If we put those 4 points in d, d has 12 points an is IQ+3. If d is IQ+3, c is now IQ+4, and b is now IQ+5... which makes a IQ+5. If we take away 4 points from b, b is IQ+4, and a is IQ+4, and if we give that to d, d now has 16 points and an IQ+4. But since d is now IQ+4, c is now IQ+5, so b and a are also both IQ+5. So finally we take 4 points out of c, so c,b,and a recursively become IQ+4... we put those 4 in d to give d 20 altogether to be IQ+5... which makes a, b, and c IQ+5... If I take the remaining 4 points in a away, a becomes IQ+4 defaulting off of b-1. But we put the 4 points in d so that d now has 24 points. d is now IQ+6, as are c and b. This makes a an IQ+5 skill with 0 points. I cannot continue, however, to remove points from c and b because a default cannot default from a default. So we end up with: http://imgur.com/XGdQfe6 So coming back... now it seems like it is something like a dynamic algorithm problem. That is the optimum solution for a is the one that is best between (the best solution for b that does not include a which is derived from (the best solution for c which includes neither a nor b which is derived from (the best solution for d which includes none of a or b or c))) or (the best solution for c which does not include a derived from the best of [...]) And so it turns into a tree where each branch below must exclude paths to nodes above... http://imgur.com/7gwcDvg So... the weight of each branch becomes the sum of the relative skill of each skill and the default modifier... But working backwards seems better so, for example from IQ to d is +2, and from d to c is the -1 default of c to d combined with the relative skill of +2 of c, making it a weight of 1... following that using a dynamic algorithm iq to d will give us 2, d to c will give us 1, c to b gives us 1, b to a gives us 1... which adds up to the 5 we get in the first optimization. But the second part of the problem... the shuffling of the points is what gives me the biggest problem. Once the optimum path of default learning has been established, what is the smart way to optimize points?