Re: PBM design: give away the formulas? (*FORMULAE !)

From: ulim@coli.uni-sb.de (Ulrich Mayring)

Date: Tue, 22 Jun 1993 10:41:26 +0000

rob@ccc.govt.nz (Rob McNeur) writes:

>Let the players *PLAY* Oly II, rather than have to pass a math test to gain
>entry. Having to work through formulae should be left to mathematicians and
>accountants....    :-)

As I said above, for a serious strategy/tactics game you won't go anywhere
if you don't know how a square root behaves or what it means to divide
numbers by other numbers. Now, since I didn't explain it in my earlier post:

Q: Why do you have (amongst other skills) to have a _feel_ for simple
arithmetic when being successful in strategic/tactics games?

A: (IMHO) Because a large part of strategic skill comes from being able to
anticipate the outcome of certain actions and adjusting one's own plans
according to what one believes to be the outcome. This involves COMPARING
options.
How do you compare options? You translate abstract game situations into
arithmetic representations of those. Why do you do that? Because you can
compare numbers quite easily (10>5 is immediately accesible to everyone), but
without a sense of mathematical equivalence you cannot compare e.g. this:

Should I recruit quality, but few, troops, or quantity, but bad, armies?
Without having some way of translating _lots, but bad_ and _few, but good_
into numbers or number-like concepts, you will not be able to compare these
two abstract concepts.

However: Formulas involving more complicated mathematical concepts than is
taught in High School must be simplified as to render the game playable.
Even mathematicians won't want to type formula after formula into their
Reverse-Polish calculator, when playing a game. A good example for a powerful,
but simple formula is this one, which determines how much you get for selling
something on a market site in Gladius et Pilum:

1500 * Value * Demand
              ------------------------------------
              sqrt(Availability+10) + sqrt(Supply)

This is the price you get for each unit of a good that you sell.
Value is the set value of the good, e.g. gold has V=35 and wood has V=3.
Demand is 1-6 and can change by +-2 each round (or remain the same or
change by +-1 only). It represents the daily demand situation.
sqrt is Square Root. Availability is how many units of that good are already
available on the market (=Supply situation) and Supply is how many units you
want to sell now (=adds to the Supply situation).

What this boils down to (and I think after some observation anyone has to
see it, else he won't go anywhere in this game):

-You get lots, if the Value is high and Demand is high
-You get less, if you sell lots at a time.
-You get less, if lots was already sold by someone else before you came.
-The two most important factors that should determine, whether it is
profitable to sell something or not are Demand and Availability, because
all other numbers are (not mathematically, but for practical purposes)
constant.

So there, gotta run now,

Ulrich

References

PBM design: give away the formulas?
skrenta@rt.com (Rich Skrenta)
Sat, 19 Jun 1993 18:12:59 +0000
Re: PBM design: give away the formulas? (*FORMULAE !)
rob@ccc.govt.nz (Rob McNeur)
Mon, 21 Jun 1993 12:00:33 +0000

Referenced By

PBM design: give away the formulas?
skrenta@rt.com (Rich Skrenta)
Sat, 19 Jun 1993 18:12:59 +0000
Re: PBM design: give away the formulas? (*FORMULAE !)
rob@ccc.govt.nz (Rob McNeur)
Mon, 21 Jun 1993 12:00:33 +0000