Game Development Reference
In-Depth Information
We are certainly showing decreasing marginal utility in the above table. Also, as
we wanted, the formula will yield a positive marginal utility for any positive num-
ber of soldiers. However, the curve is significantly different from what we achieved
from our original formula. Notice that there is a very large drop-off between the
first and second soldiers. In our original example, the second soldier had a marginal
utility of 90. It was almost as important to us as the first one. Likewise, the third sol-
dier had a marginal utility of 80, whereas in this example, it is 33.
This seems to run counter to what we originally intended… concentrating on
building initial soldiers. What we need is a formula that supports
n
soldiers with-
out giving a negative utility but keeps to the spirit of the original formula—that the
marginal utility should stay high initially and drop off later on once a reasonably
sized force has been built.
Let's change to this (somewhat contrived) formula:
Our results would now be:
Soldier
Utility
1
100
2
86
3
74
4
63
…
…
9
29
10
25
11
21
…
…
15
12
…
…
20
5
…
…
50
0.053
…
…
100
0.00002
