Here's an analysis of a simplistic case for your amusement:
We have a destination
directly upwind at distance L.
We have two identical boats which can sail at 45 degrees to the true (westerly) wind
on either tack and the conditions are such that this gives the optimal upwind VMG.
If the wind
speed doesn't change, the boat
speeds don't change and the optimal course (for these boats) is to sail at 45 degrees to the wind on either tack until the destination
is at 90 degrees, and then tack towards the destination. The routing is along the two short sides of an equilateral triangle, with the hypotenuse (L) pointed directly along the wind. The total distance traveled will be L*2^(1/2) and there is no preference for starting out on port or starboard tack.
Now, let's start again and send Boat
1 off to the SW on a starboard tack and Boat 2 off to the NW on a port tack.
But now, just as the destination appears at 90 degrees (off the beam) for each boat (which will happen at the same time in this simple case) the wind suddenly shifts 45 degrees to the SW.
Boat 1 now has a direct head
wind and must tack. Its change in heading is 90 degrees to starboard and it heads directly to the destination on a port-side beam reach. Total distance for Boat 1 is L*2^(1/2).
With the new SW wind, Boat 2 has a 45 degree lift
and can head
up to a westerly course. Thing is, it is off to the NE of the destination which is now directly upwind. So now it must sail to the new lay line directly south a distance of L/2 and then west a distance of L/2 to the destination. The total distance for Boat 2 is L*(2^(1/2)/2 + 1).
Thus, Boat 2 goes about 20% farther than Boat 1. Plus, Boat 2 is close hauled the whole trip whereas Boat 1 enjoys a leisurely beam reach for the second half of the trip.
I just made this up so hoping it's both correct and useful.