Well in our group we all take time plotting, admitedly I take the longest, cause they usually outthink my plans (as I mentioned, they've been running circles around me). I only got a minor upperhand because Verena lost her cool (with me rolling dodge after dodge, at least 6 or 7 times in a row!)
I know you clarified this, but I think the odds of rolling 7 dodges in a row are 1:46,656. I'd have lost my cool, too!
Cower changes the odds to 1/5, so if your officer is able to cower every time (very unlikely) then it would be 1:78,125. Without cower it would be 1:279,936.
Craps tables are the way they are for a reason. It's easy enough to drop a die on any face you want that people can do it unconsciously. If you play a game with exploding dice and the players don't intentionally roll properly, you will unfailingly see hugely improbably rolls on a regular basis.
If you're just playing a campaign for fun it can be annoying, but in skirmish at a tournament it's a big problem.
How do you get to a chance of 1/5 for a dodge with cower?
It is 1-x, where x is the chance to not roll a dodge in two rolls. The chance of not rolling a dodge is 5/6 , so x = (5/6)^2=25/36 and therefore to roll at least one dodge with cower is 11/36. You get the same result if you count the 1/6 chance of rolling a dodge on the first roll and then the reroll which gives you a chance of 5/6 * 1/6 . So if you add this up you also get 1/6 + 5/6*1/6 = 11/36.
Therefore to roll 7 dodges in a row with an active Cower but the cower rolls not counting as an extra roll your chance is
(11/36)^7 ~ 0.024 % ~ 1 in 4000 events.