Marginal Utility - Behavioral Mathematics for Game AI - page 178

the lower we are on health, the more important the Health Kit is to us—despite the
fact that the value of the Health Kit does not change. If we have 80% health and are
only loosing it at the rate of two points per second, getting a 50% Health Kit isn't a
very high priority. If we have 50% health and are losing it at the same rate, we might
want to keep an eye out for one. If we only have 20% health, it becomes a top pri-
ority. The reason for this is that the last 20 points of health we lose—those between
20 and 0—are far more important than the first 20 points of health we lose —from
100 down to 80. That is, the marginal utility of each health point increases as our
health drops lower.
In that example, we considered that the utility of a single point of health was
static. Fifty percent is fifty percent. However, we may not have been comfortable
letting our health get too low in the interim even if the outcome would have been
better in the end.
This phenomenon is more apparent if we compare the importance of the first
health point (e.g., from 100 to 99) lost to that of the last health point we may lose
(Figure 8.6). Obviously, losing that first point of health is not important. Losing the
last one is… well… fatal. By extension, losing the next -to-last one is pretty darn im-
portant as well. On the other hand, going from 99 to 98 isn't anything to fret about.
The same could be said for going from 98 to 97. Someplace in the middle ranges of
health, however, these two views on the importance of a single point of health are
going to have to meet. Eventually, as we continue to lose health point by point, we
are going to have to be more concerned about bleeding all over the place. Accordingly,
the importance of each health point lost is gradually going to increase. That is, the
marginal utility of each health point increases as we approach zero health.
FIGURE 8.6 As our level of health decreases, marginal utility of the
Health Kit increases. The lower we are on health, the more important
it is to find a Health Kit to replenish our supplies.