| 1 |
Some more observations, starting from your integral before you set g(X)=1/f(X):
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1 |
Some more observations, starting from your integral before you set g(X)=1/f(X):
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| 2 |
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2 |
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| 3 |
For a fixed (f-independent) choice of g(X), your equations boil down to a simple linear system of equations. That should be easy enough to solve in a few example cases to demonstrate results. I'm too tired right now though (is lack of a solution for that system what you mean with your convergence problems?).
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3 |
For a fixed (f-independent) choice of g(X), your equations boil down to a simple linear system of equations. That should be easy enough to solve in a few example cases to demonstrate results. I'm too tired right now though (is lack of a solution for that system what you mean with your convergence problems?).
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| 4 |
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4 |
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| 5 |
I don't see why you choose g(X)=1/f(X). It seems downright arbitrary. Maybe I'm mistaken, but your resulting "simple" integral also yields weird/contradicting results: If s(X, Y)=0.5 (so s(Y, X)=2), then you conclude f(X)=0.5 and f(Y)=2, so f(Y)/f(X)=4 instead of 2 which the non-integral approach you started with suggests.
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5 |
I don't see why you choose g(X)=1/f(X). It seems downright arbitrary. Maybe I'm mistaken, but your resulting "simple" integral also yields weird/contradicting results: If s(X, Y)=0.5 (so s(Y, X)=2), then you conclude f(X)=0.5 and f(Y)=2, so f(Y)/f(X)=4 instead of 2 which the non-integral approach you started with suggests.
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| 6 |
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6 |
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| 7 |
If
I'm
not
mistaken
with
that
example,
then
there
most
be
a
fallacy
on
the
way
through
your
example
where
you
conclude
f(
X)
~hp_X*dps_X,
because
it
contradicts
that.
I
can't
find
it
right
now
though
(
although
suddenly
integrating
over
hp*dps
instead
of
individual
units
is.
.
.
confusing
me?
What
if
two
units
have
identical
values
for
that?
Then
you
get
a
different
result
than
your
original
integral.
.
.
)
.
|
7 |
If
I'm
not
mistaken
with
that
example,
then
there
consequently
must
be
a
fallacy
on
the
way
through
your
example
where
you
conclude
f(
X)
~hp_X*dps_X,
because
it
contradicts
that.
I
can't
find
it
right
now
though
(
although
suddenly
integrating
over
hp*dps
instead
of
individual
units
is.
.
.
confusing
me?
What
if
two
units
have
identical
values
for
that?
Then
you
get
a
different
result
than
your
original
integral.
.
.
)
.
|
| 8 |
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|
8 |
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|
| 9 |
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|
9 |
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| 10 |
Further, I think there's a dimension error in your first formula, because subtracting HP from DPS doesn't make sense in any case I can come up with.
|
10 |
Further, I think there's a dimension error in your first formula, because subtracting HP from DPS doesn't make sense in any case I can come up with.
|
| 11 |
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|
11 |
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| 12 |
I totally missed the multiset meaning of ψ, despite it being very obvious. Oops!
|
12 |
I totally missed the multiset meaning of ψ, despite it being very obvious. Oops!
|
| 13 |
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|
13 |
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| 14 |
PS: It's "loser", not "looser" :P
|
14 |
PS: It's "loser", not "looser" :P
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How to balance (calculate strength of) units in any strategy game