This is where I put my $40k a year education to work. Muahahaha.
Anyways, it's all very simple. Any time you want to say "and," you multiply. Every time you want to say "or," you add. So if I want to say "the Dire Avenger needs to hit AND he needs to wound AND the space marine needs to fail is armor save," then you take the probability to hit (2/3) and multiply by the probability to wound (1/2) and then multiply by the probability to fail the armor save (1/3).
Re-rolling is an or statement. So if I'm dooming a unit, I'm going to change the way that I wound the model. Either I roll a 4 up and wound him OR I roll and three down AND THEN roll a four up. Which comes out to 1/2+(1/2*1/2), or 3/4.
Anyways, to get an "expected number" of unsaved wounds, do the math, then multiply by the number of shots. Dire Avengers have 30 shots because they're awesome. Guided and Doomed, they get 5/6*3/4*1/3, or about .208. Multiply by the number of shots, and you're estimating 6.25 dead marines a turn.
Now just because the expected is 6.25 doesn't mean you're going to get it every time. This is an average. Getting the distribution (which is to say, how close you'll be to 6 kills every time you shoot) of the dice is much more complicated.
Use this to allocate your forces against an enemy's forces. If you don't need more than 2 units to wipe out that tac squad, then don't send four. That's inefficient and dumb.
Go Eldar.
