The result: if accuracies are eligible for rerolls, 2.40 dmg/attack. If they are retained, 2.28 dmg, with quite a lot of swing. Overall, I think this is comparable to a Swarming TIE Interceptor, but with a bit higher variance.

dmg result : inverse chance, rounded

0: 1/10 (annoyingly frequent)

1: 1/5

2: 1/4

3: 1/4

4: 1/6

5: 1/16

6: 1/98

So, it turns out that you can use 2D convolutions to figure out the distribution of damage for a Z95 Headhunter under the influence of Lt. Blount in a closed form (ie, without resorting to Monte Carlo). The general idea is to write down a matrix with one type of result along one dimension (the probability of a specific amount of damage) and some other result along another dimension (in this case, the probability that I want to reroll that one die).

I convolve one red squadron die's probability matrix with itself twice to get a baseline attack matrix. This includes columns from 0 to 6 damage, and rows from zero to three eligible rerolls.

Policy choice: I re-roll dice one at a time, once for swarm, and once for Horn. So if my first reroll of one die is also a miss, then I can still reroll that die again. I'm newish to the game, so please correct me if that isn't true.

To implement the rerolls, I pick off the section of the matrix that is eligible, convolve that with one red die, and add it to the portion of the matrix that is not reroll eligible. Twice, for the two sequential rolls.

This function is executable in GNU Octave (it might also work in Matlab).

Enjoy!

function [dist, avg] = blount_rolls(keep_accuracy = true)
  % return the chances for each amount of damage, starting from zero, as well as
  % the average damage.

  % 2D probability map, with number of hits along columns, and number of
  % rerolled dice along the rows (0 or 1)
  sred = zeros(2, 3);
  if (keep_accuracy)
	  sred = [1, 2, 1; 4, 0, 0]/8;
  else
	  sred = [0, 2, 1; 5, 0, 0]/8;
  end

  % Two red anti-squadron dice
  sred2 = conv2(sred, sred);

  % Three red anti-squadron dice
  z95_base = conv2(sred2, sred)

  % z95_base with one swarm reroll
  z95_swarm = [z95_base(1,:); zeros(3, 7)] ...
	  + conv2(sred, z95_base(2:end, 1:end-2))

  % z95_swarm with one Lt. Blount reroll.  The reroll is deliberately
  % sequential.
  z95_blount = [z95_swarm(1,:); zeros(3, 7)] ...
	  + conv2(1red, z95_swarm(2:end, 1:end-2))

  % Collapse the result into only the damage columns.
  dist = sum(z95_blount, 1);
  dmg = 0:1:6;
  % And also compute the expected value of the distribution (the average damage output).
  avg = dmg * dist';
end

#mathpron

Much appreciated!

Can I fit 98 in my fleet list?

11 minutes ago, Ginkapo said:

Can I fit 98 in my fleet list?

So long as you're playing a ~2000 pt game, sure!

In all seriousness, their fragility and high demand for squadron commands does rather limit their utility. However, on the fleet builds section I've seen a few posts where the author mentions how they aren't quite sure how the Z-95 will perform. Here is an answer, at least to the offensive portion of the question: They are high-variance cannons. I had a suspicion that they were still just high-variance plinkers, but Swarm and Blount really do help them out. In effect, there are enough blank sides that the second reroll is almost as valuable as the first.

The same cannot be said for the Nebulon-B, which also fires three red dice, and has an opportunity for up to two individual rerolls.

I used the same technique for this and other complex situations, like "What does Sato really do for the Nebulon"? (he adds about 0.5 dmg/attack) What about with dual turbolaser turrets (still 0.5)? What about on the Salvation (still 0.5)? Is it worthwhile to stock a concentrate fire token when I have dual turbolaser turrets (no - two blanks are quite rare)? How about with slaved turrets (yes)? Things like that.

I will confess I haven't tried to fly the Z's yet. Bout when the game first came out I tried a TIE swarm and found that quantity over quality pays a steep price in activations. Point for point TIEs are a really great deal (as are Z-95's). But they take up so many activations to activate very many points worth of TIEs. But then I found out how they were more useful. Activate your others fighters with your ships and leave your TIEs for the fighter activation phase. Sure they won't get to attack, but they can move fast and mess up other fighters attack plans. Sure they end up losing any dog fights they get into, but something in the Imperial Commander of my heart thinks that is okay.

I imagine Z-95's are likely used similarly. Use you ship activations on your x, b, and y-wings. But then give them some help in the after party. For 7 points, not needing to spend orders on them, makes them a real steal.

4 hours ago, Hrathen said:

I will confess I haven't tried to fly the Z's yet. Bout when the game first came out I tried a TIE swarm and found that quantity over quality pays a steep price in activations. Point for point TIEs are a really great deal (as are Z-95's). But they take up so many activations to activate very many points worth of TIEs. But then I found out how they were more useful. Activate your others fighters with your ships and leave your TIEs for the fighter activation phase. Sure they won't get to attack, but they can move fast and mess up other fighters attack plans. Sure they end up losing any dog fights they get into, but something in the Imperial Commander of my heart thinks that is okay.

I imagine Z-95's are likely used similarly. Use you ship activations on your x, b, and y-wings. But then give them some help in the after party. For 7 points, not needing to spend orders on them, makes them a real steal.

I once ran an 800 point game were I had as my fighter wing Shara, Tycho, 4? X-Wings, Jan, Blount, and a mess of Z-95s. . . they went up against a Dengar/Interceptor swarm. I had 3 flotillas to activate my fighters, and man was it glorious. Getting 5 hits on a shuttle from a 7 point squad is awesome. 1-shotting escorts? With Blount, I got 3 hits almost 50% of the time. . . I love Z-95s

My girlfriend says "somebody should give this guy a wedgie... and I say that as someone who enjoys statistics"

I tried out a Z-95 swarm (5 of them) and totally forgot about swarm. I found exactly what the data suggests: Swingy cannons. In my alpha strike my first Z-95 rolled 5 natural damage and none of the others rolled lower than 3. They decimated all the escorts and the intel from the enemy rhymer ball and my opponent thought he was done for and that z-95s were WAY OP for the cost, then the dice turned on me and I don't think those buggers managed more than 1 damage each attack the rest of the game lol. Wish I had remembered the swarm...

I was trying something goofy with 5 Zs, 2 VCX, Bigs and a YT and Jan, a transport, a cr90 and 2 MC30s under mothma. The whole idea was to bank squad tokens on everything and relay commands for an alpha strike. CR90 with squad dial/token, transport with token, mc30s each with a token = 7 activations Bigs and YT there to soak for the fragile Zs

Frankly it worked quite well for the alpha and quite garbage for every turn after haha! it did manage to kill or scatter his rhymerball and I think he got 1 bomber shot off the whole game