Sigoroth, not sure how you're claiming my math is incorrect. Perhaps you'd like to explain?
You can't just add the chances of a single Aboat
A chance is different from an “average resultâ€
For simplicity I'll show it
without BFI first, as BFI makes the math a bit more complicated.
4 Aboats vs. an escort (2turrets) and additional 2 massed turrets are:
1 in 16 cases all 4 make it
4 in 16 cases 1 is shot down
6 in 16 cases 2 are shot down
4 in 16 cases 3 are shot down
1 in 16 cases 4 are shot down.
Marines destroy any escort on 3+ according to the new FAQ
If 4 make it the chance that a least 1 rolls a 3+ is 80/81
If 3 make it the chance that at least 1 rolls a 3+ is 26/27
If 2 make it the chance that at least 1 rolls a 3+ 8/9
If 1 make it the chance that at least 1 rolls a 3+ 2/3
Now multiply the chance of an event with its Frequency and add all together:
(1 x 80/81 + 4 x 26/27 + 6 x 8/9 x 4 x 2/3) / 16 = (1040/81) / 16 ~ 0.802
So unbraced there is an 80% chance to destroy the escort. If braced, the thing gets a bit more complicated as you have to look on ever possible combination.
In this case it is a bit easier to count the results that doesn't end with the destruction of the escort and subtract them from 1 :
no ship makes it: 1/16
1 make it but does not “hitâ€: ¼ x 1/3 = 1/12
1 make it, hits but is saved : ¼ x 2/3 x 1/2 = 1/12
2 make it, none hits: 3/8 x 1/9 = 1/24
2 make it, 1 hit, saved by BFI: 3/8 x 4/9 x 0,5 = 2/24
2 make it, both hit, both saved 3/8 x 4/9 x ¼ = 1/24
3 make it, none hits: ¼ x 1/27 = 1/108
3 make it, 1 hit, saved: ¼ x 2/9 x ½ = 3/108
3 make it 2 hits, all saved ¼ x 4/9 x ¼ = 3/108
3 make it 3 hits, all saved ¼ x 8/27 x 1/8 = 1/108
4 make it, none hits: 1/16 x 1/81 = 1/1296
4 make it, 1 hit, saved: 1/16 x 8/81 x ½ = 4/1296
4 make it 2 hits, all saved: 1/16 x 8/27 x ¼ = 6/1296
4 make it 3 hits, all saved: 1/16 x 32/81 x 1/8 = 4/1296
4 make it 4 hits, all saved: 1/16 x 16/81 x 1/16 = 1/1296
Add all together: 625/1296 ~ 0.482
1 - 625/1296= 671/1296 ~ 0.518
So the chance is ~ 52% to destroy the escort