I may well do some deeper thinking and playing of trial games for a piece in the TFL Summer Special, but here's a couple of things that did occur to me. For now, I'm just thinking about the 'deploy from a single point' version of the patrol phase.
First off - the 3 vs 4 patrol markers question. 3 patrol markers limits you to a frontage of at most 24", where as 4 gets you a max of 36", but you move the whole thing slower. The problem with those max widths, though, is that if you have markers in a line that wide you can only move the end ones..
|Movement indicated by red arrow.|
Note that you can't move the middle ones because they are already at the maximum distance apart. It turns out that the optimum setup for a rapidly advancing frontage is more like this (parts of a series of equilateral triangles)....
|Movement again indicated by red arrow.|
The other interesting question is, if you get bonus patrol phases before your opponent, how far can you get? Assuming you move in a straight line...
- 1 bonus moves? 12"
- 2 bonus moves? still only 12" (2 @ 12" from start, rest at start)
- 3 bonus moves? 24" (1 @ 24", 1 @ 12" away, 1 or 2 @ start)
- 4 bonus moves? 24" (1 @ 24", 2 @ 12" away, 0 or 1 @ start)
- 5 bonus moves? still only 24" (2 @ 24", 1 @ 12")
- 6 bonus moves? finally you can get to 36".