Re: Dimini****ng Returns in Game Engineering

"Anton" <anton.txt@[EMAIL PROTECTED]
> wrote in message 
news:Xns9AC3C43B24F7antontxtgmailcom@[EMAIL PROTECTED]
>> I've added a section so that it is quite clear why, called
>> http://home.comcast.net/~anglewyrm/dimini****ng_returns.htm

>  This is kind of a logarithm, Skill = log(Experience).
And what is a logarithm? log_x(x^y) returns y, the number of dimensions. 
Taking the log of something implies that it has multiple 
dimensions/variables.

>  Now, back to the number-of-stats problem.
Which is another way of saying number of dimensions.

>  Let's  assume  the  stats  grow  linearly  (without  loss   of
>  generality, as long as  they're  sufficiently  correlated  and
It is im****tant that they NOT be correlated. First remove all correlation.
If one stat grows at the same time that another stat grows, then they can
be 
reworked so that there is only one growing stat, with two derived stats.

>  therefore change  at  approximately  the  same  rate,  as  you  assume
The assumption I am making is that the center 'diagonal' produces the 
highest number. It could also be called the optimum price/performance
ratio.

>  As you see, the derivative only increases,  meaning  that  the
>  more outstanding characteristics will be even more likely than
>  modest ones ... 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...

Which happens in a lot of games. Most of the 4X space games are an early 
race, the the entire game is decided within the opening moves. Some of
them 
are decided even before the opening moves, by the random layout of the 
terrain.