Full Version: Karma cost equations
PlatonicPimp
OK, so it has become apparent to me that I've lost over half the math Knowledge I once had from schooling through disuse.

I am trying to render the Karma cost of various improvements in terms of a mathmatical equation. We all know that raising, say, a skill group costs (5 x New rating) for an increase of 1.
How would one render the equations that shows the growth in cost per die over increases of more than 1?
My desire is to write how to figure the Karma cost of any skill, skill group or attribute increase as equations, allowing you to plug in X (the rating you have it at) and Y( the rating you want it at) and find out Z (the Karma cost to increase to that level.)
Jaid
hmmm... well, if i remember right, there's a sigma at the front of it does that help any?
Cold-Dragon
I think you could do it really painfully on an excel sheet with IF functions....but I can't recall where I first used the function in the first place.

Basically, it tallied the cost of the highest point first, then an if statement reduced the rank by one, tallied that result, added it to the 'first', then kept going down till it hit zero or any limit you set on it.

Oh yeah, I learned that programming, lol.

Might still work in excel on a limited scale, but I don't think you can make a basic formula outside of that. Not with the way you judge cost now anyways.
hyzmarca
That's easy

(Σk=(x+1) to y) of mk
where m=karma multiplier, x is your current level, and y is the desired level.

This can be reduced to

m(x+y+1)(y-x)/2

This one equation works for all metahuman stats and skills.
Jack Kain
Just buy it in stages, its not really that hard in fact its easier then trying to write the program.
You could also just use this handy table here

Skill Group
New Skill Group 10 Karma
Rank 2=10 Karma (total 20K)
Rank 3=15 Karma (total 35K)
Rank 4=20 Karma (total 55K)
Rank 5=25 Karma (total 80K)
Rank 6=30 Karma (total 110K)

So it would cost 110 karma to get a skill group from 0 to 6.

PlatonicPimp
 QUOTE (hyzmarca) That's easy(Σk=(x+1) to y) of mk where m=karma multiplier, x is your current level, and y is the desired level.This can be reduced to m(x+1+y)(y-x)/2

So for skill groups, for instance, the reduced equation is

5(x+y+1)(y-x)/2.

If we wanted to go from 3 to 5 we'd get

5(3+5+1)(5-3)/2

or

5(9)(2)/2

or 5x9 or 45

checking this, we get from 3 to 4 is 4x5, or 20, and 4 to 5 is 5x5, or 25, which add to 45.

so they agree.

Looks good, Hyzmarca. Thank you. What operation is Σk? Sum of k, if I recall? I know this is remedial calculus, so I apologize.
hyzmarca
I can't format it correctly on this board; k=x should be below the sigma and y should be above it.

Sigma is the summation symbol and k is the variable that defined the bounds of your summation.

The correct pronunciation of that formula is [The Sum of (k equals (x+1) to y) of mk]

In this case it means that the variable k begins at the integer x+1 and is incremented by 1 until it reaches y and these results are summed together.

However, since this is a purely linear summation this can be expressed by adding together the first and last values of k, multiplying them by the total number of values that k may have, and dividing by 2.

1+100=101
2+99=101
3+98= 101
and so on, so the sum of all integers from one to 100 is going to be 101*50. This is true for any linear summation that has a finite ending.
That's how I got that formula. Your first value (current value +1) plus your last value, times half the total number of values.
Fortune
 QUOTE (hyzmarca) I can't format it correctly on this board ...

Did you try the Code function?
hyzmarca
QUOTE (Fortune @ Nov 14 2006, 02:04 AM)
 QUOTE (hyzmarca @ Nov 14 2006, 05:54 PM) I can't format it correctly on this board ...

Did you try the Code function?

Let me rephrase. I can't format the summation equation correctly using the standard ASCII.
I could do it using some defiantly nonstandard formating options in Word or Open Office, but unless Dumpshock suddenly accepts Open Document Format encoding, getting the summation equation or an integral equation correctly formatted isn't going to happen for me. It isn't exactly a major concern, though.
Fortune
mintcar
hyzmarca's equation is splendid. Another way of doing it would be in the form of a table.

 CODE Example: Improving attribute: Cost=New rating x 3: Horizontal=New rating: Vertical=Current rating [b]       1  2  3  4  5  6   [/b][b]1[/b]  /  6 15 27 42 60    [b]2[/b]  /  /  9 21 36 54 [b]3[/b]  /  /  / 12 27 45[b]4[/b]  /  /  /  / 15 33  [b]5[/b]  /  /  /  /  / 18[b]6[/b]  /  /  /  /  /  /

I made the calculations in my head so they may not be entirely accurate, but you get the idea. You would need to make one for every different multiplier, but once you've done that it would be very simple to figure out costs without any math at all.
PlatonicPimp
Yes, Yes, but both you and Jack Kain have missed the point of the exercise.

That point being not to find the cost, but to find the function that describes said cost.
mintcar
Yes, that's what you said. It was pretty obvious that you got what you needed already. So sorry for tainting your thread with my prefered method, but maybe someone else found it useful .
PlatonicPimp
Sorry, sometimes I forget that this forum and all threads in it don't just exist for my benifit.