AngleWyrm:
> I've added a section so that it is quite clear why, called
> Double-Implementation
> http://home.comcast.net/~anglewyrm/dimini****ng_returns.htm
Hello, AngleWyrm.
I don't think your argumentation is correct. What you have
called the top (repeating) implementation is indeed used to
create this rare/common disbalance, to make outstanding things
rare. A great example is Battle Isle, where units' skill level
grew slower as they became more experienced.
You can come to this conclusion if you assume experience is
pro****tional to the time spent in action and that achieving
each next skill level requires more experience that the
previous one. If you're twice more experienced than I, you're
only one step more skilled (not twice as skilled).
This is kind of a logarithm, Skill = log(Experience).
And know what? This has been sup****ted by the best judge --
the reality: WWII stats show that newbie soldiers who survived
their very first battle had 5-10 times higher chence to
survive in the future than complete newbies. So, the growth of
Skill is fast in the beginning and slows down considerably at
higher levels. Logarithm behaves just like this!
Now, back to the number-of-stats problem. You say increasing
this number does just the same. But using your assumtion about
multiplication of stats (which I don't find correct...) I have
come to an opposite conclusion.
Let's assume the stats grow linearly (without loss of
generality, as long as they're sufficiently correlated and
therefore change at approximately the same rate, as you
assume):
x = 0.1, x^3 = 0.001
x = 0.2, x^3 = 0.008 (+0.007)
x = 0.3, x^3 = 0.027 (+0.019)
...
x = 1, x^3 = 1;
x = 2, x^3 = 8; (+7)
x = 3, x^3 = 27; (+19)
As you see, the derivative only increases, meaning that the
more outstanding characteristics will be even more likely than
modest ones, which is actually disgusting to nature. Is it
possible that your stats improve quicker and quicker with
time, without a limit? This prevents the model from converging
and makes it unstable: initially a little bit more skilled
units will quickly develop so emormously an advantage over
those that initially were just a tiny little bit weakier, that
less and less units will make sence (0.0001 against 10000 is
nothing, right). And will be a self-accelerating process, so
the game will be reduced to race for experience, and the
winner will be known quite early...
As for scaling that you say doesn't effect things, you're
again not right. Number one is "the turning point" for the X^N
function. Plot the same graphs for values from 0 to 50 and see
the difference ;)
... If we stick to the scale [0,1] -- things won't be any
better: Near pont point one the skill gaining speed makes a
leap and significally increases. Why? In reality I don't see
no reason for it, so such a model would be at least
unrealisic, and at most -- not playable.
Anton
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