Ok, I might have got my maths wrong here but I work it out as follows:
assumptions:
.83 chance of passing the test
.83 + (.83*.17) = .97 chance of passing the test when allowed to re-roll a one.
So for a unit of 6 the chance of getting no BMs with no re-rolls:
.83^6 = .33
with one re-roll:
(.83^6) + (.83^5 * .83 * .17 * 6) = .66
re-rolling all ones:
.97^6 = .83
and for a unit of 8:
.83^8 = .23
.83^8 + (.83^7 * .83 * .17 * 8 ) = .53
.97^8 = .78
Sorry if the maths is wrong - I'm never 100% sure that I get this kind of stuff right once it gets past something fairly simple. But basically, allowing one re-roll more than doubles the chance of getting no BMs leaving it pretty much 50/50 (once every other game) when drones are included and about 2 in 9 (once every 4.5 games, down from 1 in 6) without.
[Edit] I should add that this doesn't seem too awful although it is still a risk. Again forgive me if my maths is off, but doesn't that mean for a unit of 8 they have a 53% chance of activating 83% of the time and a 47% chance of activating 66% of the time so:
(.53*.83) + (.47*.66) = .75
so 75% chance of activating on the turn they come in as opposed to:
(.83 * .23) + (.66 * .77) = .70
chance with no re-rolls, but I guess the possibility of getting the BM may be more relevant?
Feel free to ignore all of this if my Maths is way off...
[Edit - my maths was in fact a bit off, but not by much!! Cheers Kyrt
updated the figures...