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?

Re: Increasing Skill Levels From default
 

And now I have another sudden epiphany... say you are improving a skill from defaults... and you only put one point in the skill even though from default the next level cost more than one point. For the sake of learning skill from the default of another skill, is 1 point that doesn't actually buy a level (because they are defaulting past the first two levels of the skill) allow someone to say that they have that skill?

Re: Increasing Skill Levels From default
 

Yes. This is implicit in the rules, and was explained in detail here.

Re: Increasing Skill Levels From default
 

I'm pretty sure that if a defaults from b, b CAN default from a. That is written into most of the Melee Weapon skills.

Re: Increasing Skill Levels From default
 

You cannot benefit from both defaults at the same time, is what he's talking about. I can't use the fact that I've bought Broadsword at DX +20, getting me Shortsword at DX +16 for free, as an excuse to pay only for upgrading my Broadsword from DX+12 (benefiting from the default from Shortsword.)

Re: Increasing Skill Levels From default
 

Well, now that you've delved in the math of it, you see why buying from default is broken. It's never worth it, and at best, you ought to put 1 CP in the defaulted skill to get defaults from that skill in turn, while piling your points on the main skill. It's also awkward to explain, and often misunderstood, so I see no benefit to keep the rule in future editions, and if it's to be left as is, I would rather have it replaced with something that could be useful more often.

In my games, I use a different rule, making buying from default a hard technique that is unlocked by a unique technique perk of the appropriate kind (combat for combat skills, etc...)

Re: Increasing Skill Levels From default
 

Thanks guys for responding.

Thanks, Johndallman for finding that answer too; it was just a thought I had that was tangentially related, but I guess I shoulda used the search before asking.

Thanks Kuroshima for confirming that the system seems as complicated as I think it is, not that I hold it against GURPS. I enjoy poking around in complicated corners and seeing if I can get something interesting to come out of the mess.

One new thought though: because the direction of defaulting can be changed at will according to the RAW, it seems to me that it wouldn't be wrong to say you can calculate the best value through the entire network of defaults relative to skill A and record that.
Then if you go back to the second diagram, if you don't rebalance the points, you could find the best value for skill B and record that. And this would be fine because a player is allowed to change the direction of defaults at will anytime... and would probably not be too confusing to me as long as I disallow the ability to be allowed to shuffle the points around. That's really the part that bothers me the most.

Re: Increasing Skill Levels From default
 

Remember: when you rearrange a skill default tree, no skill can ever go down. So if you change the tree such that a skill would have a lower value that it did previously, you *MUST* spend points to bring it back up to it's prior level.

As such I suspect that you cannot do your trick of rearranging the default tree to maximize each skill in turn, as you would then need to buy up any non-maximized skill back to its maximized value.

Re: Increasing Skill Levels From default
 

There are occasions when you lose IQ permanently. Surely you don't then have to buy up your skills, or take a new disadvantage to pay off a point deficit!

Re: Increasing Skill Levels From default
 

I do not see how losing a point in an attribute would be considered 'rearranging your skill default tree'

This rule is in the right most column of page B173 (the only non-example paragraph in that column)

Re: Increasing Skill Levels From default
 

Ah dang, looking at it closer again, it appears to me you are right.

As an aside, even though it isn't RAW, I feel like it would be a good simulation of the realistic idea of certain skills giving each other a certain synergy. EG, in the real world, If someone were an expert level in all of Chemical Engineering, Materials Engineering, Bio-Engineering, Mechanical Engineering, Bio-Mechanical Engineering, Electrical Engineering, Electro-Mechanical Engineering, and Computer Engineering, I think that each skill would have at the least a teeny synergistic effect with the others, some a little less than others. But for example, just because someone uses their insights from Electrical Engineering to be better at Computer Engineering, doesn't mean they can't use their insights from computer engineering to simultaneously be better at electrical engineering.

BUT, that all being said! It's not how GURPS works RAW.

Re: Increasing Skill Levels From default
 

From what I understand, you can't double default with chains anyway. So you can't have skills A, B, C, with A being the main skill, and then default B from A, and then default C from B. C would ALSO have to default from A. This is true for any given set of defaults.

This prevents default "trees" since one skill bought up from default cannot be used to buy another skill up from default. Programming it is fairly simple IMHO, since you systematically have to test each skill in the set as the primary skill. (You might even test having multiple primaries, but since the default groupings are fairly limited this might be harder than necessary.)

It vastly simplifies the problem- (Capital denotes primary, lowercase denotes defaulting)

Given:
1) All skills are Average

2)
a defaults to B-1 or C-2
b defaults to C-1, D-2, or A-3
c defaults to D-1 or A-2
d defaults to A-4 or B-2

For the given set, the following are possible with one primary:
A, b:A-3, c:A-2, d:A-4
B, a:B-1, c:N/A, d:B-2
C, a:C-2, b:C-1, d:N/A
D, a:N/A, b:D-2, c:D-1

In terms of efficiency, ANY skill that can have ALL other skills default to it, is going to be the most efficient with an arbitrarily large number of points. Total Skills = 4, so any primary skill that has 3 skills defaulting to it, is likely to be the most efficient. In this case, only A has 3 defaulting skills (b,c,d) so it is going to be the optimal skill for total bonuses for an arbitrarily high number of points. B, C and D only have two defaulting skills so they tie. In this case, the total number of penalties is probably going to be a strong indicator of efficiency. B has total penalties of -3, C has total penalties of -3, and D has total penalties of -3. In this instance, for this particular set of skills, A is the most point efficient, with B, C and D tying. A tie-breaker would likely be based on which skill is the LEAST important, so if skill C is the least important, skill B would be second most efficient.

This is true for any set of skills with a single primary skill. If you add multiple primary skills for any given skill set, it changes a little bit, but is still largely the same.

Re: Increasing Skill Levels From default
 

...Raise either your IQ or your DX (or both). Then dump your remaining points into a skill that particularly expresses the character.

Re: Increasing Skill Levels From default
 

Sounds like a GREAT explanation for the TALENT ADVANTAGE.

Re: Increasing Skill Levels From default
 

I think I get what you are saying, and it was another thought I had because I was thinking that maybe the rule about using a skill at double default not being allowed (eg a is b-5; b is c-5; a is NOT c-10) would also extrapolate from this case.

So, we try reversing the relationship and instead think about what skills default to skill A, not what skills A defaults to.

As long as any skill is improved from default of Skill A, skill A may not improve from default of any other skill.

It does make the math easier in a way because we don't need to recursively see if a default of a default is better than a default of a default of a default.

So this doesn't seem like a process best served by automation because it requires a human that understands the context of his campaign to say "a and b to c earns me more value than b and c to a" But maybe some kinda hint that someone could see that would say when looking at skill c that says, "you could get 1 extra level on skill c if you developed from the default to a" or "you can't change skill d to develop from IQ unless you also spend 3 points on skill d"

And yeah David Johnston 2, the obvious obvious solution for really optimizing a character would be investing in talents or base attributes, I get that, but in a hypothetical situation if a character found himself in a place where he already had a bunch of points in skills that default to each other, you are, by the rule of developing from default, allowed to rebalance the points between skills defined as having a dependency relationship....
Now if we want to convolute the original problem even further, I think the social engineering supplement on learning says that if you happen to have a lot of extra points in skills based off of the same attribute, you can take them out of the skills and reinvest them in the base attribute at a slightly inefficient exchange rate... Except the go/no go call on that one is pretty obvious so I don't care to work it out (If I can subtract points from x skills, so that k skills go down a level, it is probably worth it if it makes at least k+1 skills improve by 1.)

Re: Increasing Skill Levels From default
 

Me, I could never understand this rule from the examples in the book. If anything, I understand it even less when I see explanations of the math at play (as in this thread). Personally I had just been hacking the Technique rules, allowing purchase of a Hard technique "I use (X defaulted skill) at reduced penalty" up to the point where the default equals the main skill. Then the Skill Adaptation perk came out and I've never looked back since it was an even cheaper and even easier way to do the same thing.