| 1 |
This kind of ideal balance you are referring to cannot and should not be true for every pair of units, specifically not if they are of different types as you said correctly. This first equation is only used as a motivation for the following integral equation, which says that this "ideal balance" should be true for a unit only on average. For example a raider will be more effective vs skirmishers and less effective vs riots. The integral calculates an average cost for that.
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1 |
This kind of ideal balance you are referring to cannot and should not be true for every pair of units, specifically not if they are of different types as you said correctly. This first equation is only used as a motivation for the following integral equation, which says that this "ideal balance" should be true for a unit only on average. For example a raider will be more effective vs skirmishers and less effective vs riots. The integral calculates an average cost for that.
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| 2 |
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2 |
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| 3 |
The problem are infinite effectivities as described in my first post. But there are ways to solve that, for example only comparing same unit types or considering unit groups.
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3 |
The problem are infinite effectivities as described in my first post. But there are ways to solve that, for example only comparing same unit types or considering unit groups.
|
| 4 |
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4 |
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| 5 |
chi
and
ψ
are
multisets
which
means
functions
that
assign
a
number
to
every
unit
in
the
game
to
describe
unit
groups.
For
example
a
group
of
2
Glaives
and
1
Rocko
would
be
described
as
ψ(
Glaive)
=2,
ψ(
Rocko)
=1,
ψ(
everything
else)
=0,
where
units
are
unit
stat
vectors.
ϕ
depends
on
those
functions
and
we
integrate
over
those
whole
function
spaces.
[spoiler]I
added
a
description
of
ϕ
as
the
unit
group
generalization
of
the
superiority
function
f.
[/spoiler]
|
5 |
chi
and
ψ
are
multisets
which
means
functions
that
assign
a
number
to
every
unit
in
the
game
to
describe
unit
groups.
For
example
a
group
of
2
Glaives
and
1
Rocko
would
be
described
as
ψ(
Glaive)
=2,
ψ(
Rocko)
=1,
ψ(
everything
else)
=0,
where
units
are
unit
stat
vectors.
ϕ
depends
on
those
functions
and
we
integrate
over
those
whole
function
spaces.
[spoiler]I
added
a
description
of
ϕ
as
the
unit
group
generalization
of
the
superiority
function
s.
[/spoiler]
|
| 6 |
Maybe it's better to remove the terms 1/chi(X) and integral_(Z in Omega\{X})chi(Z)f(Z)delta(Z)dZ in the last formula in "Generalization on unit groups".. Then it would be also much easier to calculate.
|
6 |
Maybe it's better to remove the terms 1/chi(X) and integral_(Z in Omega\{X})chi(Z)f(Z)delta(Z)dZ in the last formula in "Generalization on unit groups".. Then it would be also much easier to calculate.
|
How to balance (calculate strength of) units in any strategy game