Even when an interception is impossible, the monster might still try to chase the tofubeast. What, then, is the best ? The ghosted of the escape illustrations in Figure 7 might appear to be the only natural choice, but it's a little misleading: the whole point is that a constant cannot be found, and so the illustrations are only geometrically valid for a certain point in time. The choice of will depend on factors outside the scope of the problem. Some ideas:

- If expects to run straight all the way to a distant
finish line, the best might be defined as the angle that
gets to the finish line with the least amount of lag behind
--which would be
, or a parallel course.
- If expects to reverse direction sometime soon, might
do best to head directly towards the current location of (at any
given point in time):
.
- A good general-purpose would be the angle at which
should travel to intercept if 's velocity were just large
enough to effect an interception at some point in the future (or at
least maintain a distance if behind). For
,
; for
,
. As with any chosen between 0 and
for a non-interception, the problem will change with each
tick: will increase, and point will curve around behind
in pursuit.
- The illustrations above are only valid for a certain point in
time during the chase: the geometry of and the theoretical
point will change, making a straight shot to impossible (and
therefore undefined). But the ghosted and straight
seem to imply a possible solution over time: take a
straight path for a little while by (arbitrarily) picking a time in
the future, calculating the distance will travel assuming
constant velocity and direction, and then heading toward that point
(regardless of ). Of course, once that future time is past, a
new will be needed, and the path of over time, if not
curved, will then be segmented. (Notice this solution and the second
are actually quite similar: this will probably end up being
only a few degrees off 0.)