Elitist Jerks - View Single Post

• Aldriana · 04/14/08, 6:21 PM

Originally Posted by Troffel

But the same problem remains. The expected value of the number of procs in a long time segment is not the quotient of the the time segment divided by the expected value of the time between procs. But i think the approximation can be used, if the proc chance is high enough. Try it for yourself, generate a large enough sequence $(I_i)_{i=1..n}$ and calculate $\frac{T}{n}\sum^n_{i=1} \frac{1}{I_i}$ as the expected value of the number of procs and $\frac{T}{\frac{1}{n}\sum^n_i I_i}$ . You will find a hugh difference depending of the generation (distibution) of the sequence...

Wrote a little code to do it for me:

max = 10000000
segs = 0
sum = 0
spread = 999

from random import random

while sum < max:
    # Each step, add a random number between 1 and spread, inclusive.
    # Count how many segments it takes to get to max.
    sum = sum + 1 + int(spread * random())
    segs = segs + 1

print "Simulation: "
print segs
print ""
print "Theory: "
print max * 2 / (1+spread)

Output of a few runs:

> python segs.py
Simulation:
19993

Theory:
20000

> python segs.py
Simulation:
19950

Theory:
20000

> python segs.py
Simulation:
20062

Theory:
20000

> python segs.py
Simulation:
20022

Theory:
20000

> python segs.py
Simulation:
20047

Theory:
20000

I don't know about you, but that seems to me to be running pretty close to $\frac{T}{I}$ . And trying it with different parameters doesn't seem to change that:

Spread = 9:
Simulation:
1999124

Theory:
2000000

Spread = 99:
Simulation:
200303

Theory:
200000

Spread = 9999:
Simulation:
2003

Theory:
2000

The question is, what we do practice or want we do theorycrafting. For practice are simple rules of thumb sufficient and often used for raiding. But my understanding is, that this is elitist jerks and the elite are not afraid of infinity sums nor Illidan either. So my target is to discuss how far the model reach and when/what approximations are useful.

Well, I agree that the problems are to some extent interesting in their own right; but I'd also argue that, particularly when writing a quick reference document, something that can be incorporated into a class modeling spreadsheet is more useful than something that can't. If we do come up with an exact solution, I'll happily throw in a mention of it and mark what I have as the easy-to-use approximation. But I think we're an extremely long way from having an exact solution, as we haven't even touched on the notion of attack distribution yet; most of these assume that they're either perfectly periodic or totally random (and sometimes, both in the same derivation) - when, in truth, they're not. So even assuming you're correct about the summation (which I don't think you are), and that you come up with a closed form approximation of it (which I expect to be hard)... it'll *still* just be an approximation. Which doesn't make it useless by any means - it's just not immediately clear to me that it's necessarily more useful than the stated one.