So having a lot of Screed experience with black dice rerolls plus the back-up Screed to go fishing for hit+crits, I was curious if one could use an ISD-II equipped with Leading Shots, Captain Needa, and Turbolaser Reroute Circuits to achieve a similar end result with red dice, fishing for as many 2-hits as possible. Vader is generally superior to Screed when it comes to red dice, so this seemed like an area he could shine in. Here's what I came up with:

The odds of a 2-hit coming up are 1/8 - 12.5%.

The first reroll adds (7/8 chance of needing to reroll * 1/8 chance of getting desired result in first reroll =) 10.9%, total of 23.4% chance of a dice getting the 2-hit result.

The second reroll adds (76.6% chance of not yet having the desired end result*12.5% chance of getting it =)9.6%, total of 33% chance per dice of coming out a 2-hit result per dice.

Which, with 4 red dice (and presumed 3 blue dice from using Leading Shots) gives us the following odds:

zero 2-hits: 20% of the time; (average damage = 4.53)

one 2-hit: 39.7% of the time (average damage = 2 + 3.96 = 5.96)

two 2-hits: 29.3% of the time (average damage = 4+ 3.39 = 7.39)

three 2-hits: 9.6% of the time (average damage = 6 + 2.82 = 8.82)

four 2-hits: 1.2% of the time (average damage = 8 + 2.25 = 10.25)

(non-2 hit red dice average 0.57 damage each, blue dice average 0.75)

With Needa+Turbolaser Reroute Circuits involved, you can up the number of two-hits once more (except when you get all four naturally) by flipping another dice (usually red, I would assume). Preferably you'll want to give up a blank dice for this effect (which is a net +2 damage) but sometimes you'll need to flip a single hit or an accuracy. It's difficult to map out exactly how many accuracies you would want to keep in the pool (versus spending blue ones for Leading Shots or red ones for TRCs if there are no blanks), so the assumption is that giving up a non-blank red dice is the average result of the non-blank sides, which is 0.8 (2 hits, 2 crits, 1 accuracy), resulting in a net gain of 1.2 damage. Thus the benefit of flipping is an average of (blank chance*2) + (non-blank chance*1.2).

So we need to look at the chances of a blank showing up in all of the non-quadruple 2-hits results above:

0: 68.4% chance of one or more blanks, meaning Needa+TRC flipping a 2-hit buys us an average of ((68.4%*2)+ (31.6%*1.2)) 1.37+0.38 = +1.75 damage to the 0 2-hits results

1: 57.2% chance of 1+ blanks. So ((57.2%*2)+(42.8%*1.2)) = 1.14+ 0.51 = 1.65

2: 43.7% chance of 1+ blanks. So ((43.7%*2)+(56.3%*1.2)) = 0.87 + 0.68 = 1.55

3: 25% chance of 1 blank. So ((25%*2)+(75%*1.2)) = 0.5+ 0.9 = 1.4

4: all the dice are miraculously 2-hits, so no need to use TRCs.

Okay so this gives us an end result of:

20% chance of (4.53+1.75=) 6.28 damage = +1.26 average

39.7% chance of (5.96+1.65=) 7.61 damage = +3.02 average

29.3% chance of (7.39+1.55=) 8.94 damage = +2.62 average

9.6% chance of (8.82+1.4=) 10.22 damage = +0.98 average

1.2% chance of 10.25 damage = +0.12 average

So the total average damage from an ISD-II front arc at medium range should be 8 damage using this method.

The normal average damage of an ISD-II's front arc is (8*0.75=) 6. So this is a net gain of 33.3% damage.

Whether it's worth the hassle. I leave that to you . I can't say I recommend the second reroll rerolling everything but double-hits unless you've got the TRC backup available, but that requires some more probability math I'd rather leave alone for the time being. If you see any errors I made or have any comments or questions, please let me know.

Edit: Fixed an incorrect assessment of non-2-hit red dice damage. Caught an addition error as well. Average damage actually IMPROVED from my initial assessment from about a 25% gain to a 33.3% gain. That's substantial.

So having a lot of Screed experience with black dice rerolls plus the back-up Screed to go fishing for hit+crits, I was curious if one could use an ISD-II equipped with Leading Shots, Captain Needa, and Turbolaser Reroute Circuits to achieve a similar end result with red dice, fishing for as many 2-hits as possible. Vader is generally superior to Screed when it comes to red dice, so this seemed like an area he could shine in. Here's what I came up with:

The odds of a 2-hit coming up are 1/8 - 12.5%.

The first reroll adds (7/8 chance of needing to reroll * 1/8 chance of getting desired result in first reroll =) 10.9%, total of 23.4% chance of a dice getting the 2-hit result.

The second reroll adds (76.6% chance of not yet having the desired end result*12.5% chance of getting it =)9.6%, total of 33% chance per dice of coming out a 2-hit result per dice.

Which, with 4 red dice (and presumed 3 blue dice from using Leading Shots) gives us the following odds:

0 2-hits: 20% of the time (average damage = 5.25)

1 2-hit: 39.7% of the time (average damage = 2 + 4.5 = 6.5)

2 2-hits: 29.3% of the time (average damage = 4+ 3.75 = 7.75)

3 2-hits: 9.6% of the time (average damage = 6 + 3 = 9)

4 2-hits: 1.2% of the time (average damage = 8 + 2.25 = 10.25)

With Needa+Turbolaser Reroute Circuits involved, you can up the number of two-hits once more (except when you get all four naturally) by flipping another dice (usually red, I would assume). Preferably you'll want to give up a blank dice for this effect (which is a net +2 damage) but sometimes you'll need to flip a single hit or an accuracy. It's difficult to map out exactly how many accuracies you would want to keep in the pool (versus spending blue ones for Leading Shots or red ones for TRCs if there are no blanks), so the assumption is that giving up a non-blank red dice is the average result of the non-blank sides, which is 0.8 (2 hits, 2 crits, 1 accuracy), resulting in a net gain of 1.2 damage. Thus the benefit of flipping is an average of (blank chance*2) + (non-blank chance*1.2).

So we need to look at the chances of a blank showing up in all of the non-quadruple 2-hits results above:

0: 68.4% chance of one or more blanks, meaning Needa+TRC flipping a 2-hit buys us an average of ((68.4%*2)+ (31.6%*1.2)) 1.37+0.38 = +1.75 damage to the 0 2-hits results

1: 57.2% chance of 1+ blanks. So ((57.2%*2)+(42.8%*1.2)) = 1.14+ 0.51 = 1.65

2: 43.7% chance of 1+ blanks. So ((43.7%*2)+(56.3%*1.2)) = 0.87 + 0.68 = 1.55

3: 25% chance of 1 blank. So ((25%*2)+(75%*1.2)) = 0.5+ 0.9 = 1.4

4: all the dice are miraculously 2-hits, so no need to use TRCs.

Okay so this gives us an end result of:

20% chance of (5.25+1.75=) 7 damage = +1.4

39.7% chance of (6.5+1.65=) 8.15 damage = +3.24

29.3% chance of (7.75+1.55=) 9.3 damage = +2.72

9.6% chance of (9+1.4=) 10.4 damage = +1

1.2% chance of 10.25 damage = +0.12

So the total average damage from an ISD-II front arc at medium range should be (1.4+3.24+2.72+1+0.12=)7.48 damage using this method.

The normal average damage of an ISD-II's front arc is (8*0.75=) 6. So this is a net gain of 24.7% damage.

Whether it's worth the hassle. I leave that to you . I can't say I recommend the second reroll rerolling everything but double-hits unless you've got the TRC backup available, but that requires some more probability math I'd rather leave alone for the time being. If you see any errors I made or have any comments or questions, please let me know.

Since I'm bad at math... how would this compare to say, SW7, with or without Screed?

First of all, thanks for all the work you put into this! I know some don't like it, but I'm a big fan of having math behind my game choices.

I haven't gone through the whole thing yet, but it does look like you have an error here:

Which, with 4 red dice (and presumed 3 blue dice from using Leading Shots) gives us the following odds:

0 2-hits: 20% of the time (average damage = 5.25)
1 2-hit: 39.7% of the time (average damage = 2 + 4.5 = 6.5)
2 2-hits: 29.3% of the time (average damage = 4+ 3.75 = 7.75)
3 2-hits: 9.6% of the time (average damage = 6 + 3 = 9)
4 2-hits: 1.2% of the time (average damage = 8 + 2.25 = 10.25)

It looks like you've used an average value of .75 for the reds in here, which would normally be correct. The problem is, the .75 average value includes the possibility of a 2, which you're accounting for separately by defining how many of them are in each roll.

I haven't done the math yet, but I Monte Carlo'd it and your value for the reds exclusive of 2's should be closer to .57/each (my intuition suggests it's probably .575, since that's .75-.125, though I don't have any math to back that up) .

First of all, thanks for all the work you put into this! I know some don't like it, but I'm a big fan of having math behind my game choices.

I haven't gone through the whole thing yet, but it does look like you have an error here:

Which, with 4 red dice (and presumed 3 blue dice from using Leading Shots) gives us the following odds:

0 2-hits: 20% of the time (average damage = 5.25)

1 2-hit: 39.7% of the time (average damage = 2 + 4.5 = 6.5)

2 2-hits: 29.3% of the time (average damage = 4+ 3.75 = 7.75)

3 2-hits: 9.6% of the time (average damage = 6 + 3 = 9)

4 2-hits: 1.2% of the time (average damage = 8 + 2.25 = 10.25)

It looks like you've used an average value of .75 for the reds in here, which would normally be correct. The problem is, the .75 average value includes the possibility of a 2, which you're accounting for separately by defining how many of them are in each roll.

I haven't done the math yet, but I Monte Carlo'd it and your value for the reds exclusive of 2's should be closer to .57/each (my intuition suggests it's probably .575, since that's .75-.125, though I don't have any math to back that up) .

You are absolutely correct and I should amend my math immediately when it comes to the red dice that aren't 2-hits. The blue dice will still average 0.75.

Since I'm bad at math... how would this compare to say, SW7, with or without Screed?

Just so I'm clear, you're looking for average damage from an ISD-II's front arc at medium range with SW7s, both with and without Screed potentially adding a red crit by using his ability?

Also, I just updated the information per Ardaedhel's excellent catch that I was using the incorrect value for red dice average damage once you factored out the 2-hits. It has been amended. I caught another error which means the end average damage increases to 8. The average ISD-II without any help with dice does 6.

Since I'm bad at math... how would this compare to say, SW7, with or without Screed?

Just so I'm clear, you're looking for average damage from an ISD-II's front arc at medium range with SW7s, both with and without Screed potentially adding a red crit by using his ability?

Tell you what, I'm feeling mathy so let's assume that my assumption is correct .

Same circumstances only the commander doesn't affect dice rolls and the ISD-II has SW7s:

Assuming you're using your blue dice for damage alone: 4 damage from blue dice. Easy.

Red dice should produce (4*.75=) 3 damage.

So without anything else affecting the outcome, you'll do 7 damage but that decreases if you spend a blue accuracy to lock down a defense token. You've got a 41.4% chance of 1+ red dice accuracy results, though, which isn't bad but neither is it reliable.

Adding in Screed, he will only be useful in two circumstances:

1) You wish to keep red accuracy results and get 2+ blank red dice

2) You don't care about red accuracy results and just want raw damage - any combination of 2 blanks + accuracies will thus improve your overall damage.

In scenario 1, your odds of getting 2+ blank red dice are (21.1% + 4.7% + 0.4% =) 26.2%. Therefore Screed will add an average of (26.2%*1=) 0.26 damage. So your average would improve to 7.26. Not great.

In scenario 2, your odds of getting 2+ blank or accuracy red dice are (32.9% + 13.2% + 1.9% =)48%, which means Screed will add an average of (48%*1=) 0.48 damage. So your average would improve to 7.48. Still not great.

In my opinion, Screed is king of black dice and black dice crit upgrades. His effect is fairly minimal with red dice and generally subpar with blue dice unless you absolutely need to ensure a crit.

Might it be better to just use Vader and Intel officer with Devastator instead, Chuck away two tokens, gets you two more blues giving you 1.5 more damage... Intel officer/Devastator 17 points, needa/trc/ls 13 points... but then again there is no need for Intel officer

For comparison's sake, Vader by himself if you're fishing ONLY for damage (rerolling all non-hits/non-crits) is...

Red dice = 5/8 chance of damage of some kind. This is split between:

2 hit sides, 2 crit sides, 1 double-hit side. So of those 5 sides, they do an average of (6/5=)1.2 damage.

The remaining 3/8 of the time you would net an accuracy or blank, and thus need to reroll. A rerolled dice will do average red dice damage, which is 0.75.
So by adding them together, you get
(62.5%*1.2=)0.75 damage
(37.5%*0.75=)0.28 damage

For an average of 1.03 damage per red dice

For blues, you only get a non-damage side 2/8 of the time and can't do more than 1 per die, so the math is easier:

(75%*1=)0.75 damage

(25%*0.75=)0.19 damage

For an average of 0.94 per blue dice

So an ISD-II front arc fishing only for damage would do on average ((4*1.03)+(4*0.94))=4.12 + 3.76 = 7.88 damage. Very close to the end result from fishing for double-hits but without all the upgrades required.

It may actually be superior to use a single Vader reroll, rerolling only the accuracies and blanks rather than fishing for two-hits or using Leading Shots (which costs you a blue dice). This also frees up your officer slot for an Intel Officer, who can make that Brace very sad.

So here, let's try it with that mindset (only one Vader reroll, keeping only hits and crits from the original roll) with Needa+TRCs to see if it makes a meaningful difference...
Once everything is rerolled, each red dice has an ((5/8)+(3/8*6/8)) 90.6% chance of being a hit, crit, or accuracy result (assuming that we'd consider keeping an accuracy around after the reroll). 9.4% of your dice will be blanks still. This means of 4 red dice, you've got a 32.7% chance of having a blank still. Making the same assumptions that a flipped blank is a raw +2 to the damage total but a "giving up something that's not a two-hit" is a +1.2.
So you get (32.7%*2=)0.65 + (67.3%*1.2=)0.81 = +1.46 damage

So the average end damage should be (7.88+1.46=) 9.34 with a single Vader reroll rerolling all blanks and accuracies and then using Needa+TRC afterwards.

For the original example, if you're rerolling accuracy blue dice the average damage increases by around 0.6, to around 8.6. Both of these methods make accuracy results less reliable but the damage output is pretty high. It would probably be best to use the Avenger title with this kind of setup to threaten a really powerful haymaker that cannot be Braced.

Also it would appear that the blue die lost to Leading Shots does more total harm to the outcome of the damage than any benefit gained from questing for those fickle double-hit red dice.

Great work and thanks for taking the time to do this.

I think the way to get the ultimate amount of damage from an ISD would be with an ISD1

ISD1

Devastator

Vader

Needa,

Leading Shots

Ordinance Experts

TRC's

You reroll everything that isnt a double hit or hit/crit with Vader, then reroll all black dice that arent hit/crit with ordinance experts, if needed use leading shots to reroll any remaining blanks, then if needed TRC into a double hit. I added Devastator in just or fun but since this is a glass cannon you are counting on killing your opponents main ship quickly and getting out of there anyway and any extra blue dice will help. My highest roll was 16 using just Vader, Devastator, Intel Officer, Leading Shots, and XI7's averaging more around 10-11 damage. With the above building you could get 3 red double hits, 2 blue damage, 3 black hit/crits + any blue and black die you add from Devastator and a concentrate fire command.

Great work and thanks for taking the time to do this.

I think the way to get the ultimate amount of damage from an ISD would be with an ISD1

ISD1

Devastator

Vader

Needa,

Leading Shots

Ordinance Experts

TRC's

You reroll everything that isnt a double hit or hit/crit with Vader, then reroll all black dice that arent hit/crit with ordinance experts, if needed use leading shots to reroll any remaining blanks, then if needed TRC into a double hit. I added Devastator in just or fun but since this is a glass cannon you are counting on killing your opponents main ship quickly and getting out of there anyway and any extra blue dice will help. My highest roll was 16 using just Vader, Devastator, Intel Officer, Leading Shots, and XI7's averaging more around 10-11 damage. With the above building you could get 3 red double hits, 2 blue damage, 3 black hit/crits + any blue and black die you add from Devastator and a concentrate fire command.

I should clarify that the intent here wasn't really to go for "how much total damage can I do with a crazy combo?" so much as "can this relatively inexpensive combination produce a sufficient damage bump similar to how Ordnance Experts + Screed does?"

And the answer to that was "a decent damage increase, yes, but it turns out Leading Shots + Vader is basically overkill." I'll happily do more math if anyone's curious about one combination versus another, though. The tricky part of the math is you can't really account for how good an accuracy result is so it's tempting to just go for raw damage because that's an objective value. As a general rule I'd like 1 accuracy in most results, sometimes 2. But it's very situational.

I'm very skeptical of Devestator overall. It's expensive and the decrease in survivability doesn't seem to be made up in the improvement in offense.

I'm very skeptical of Devestator overall. It's expensive and the decrease in survivability doesn't seem to be made up in the improvement in offense.

Devastator needs to be treated like an expendable ISD sized Raider to get the most from it, but the amount of damage it can push out is crazy plus, it can fire those blues at Red range. (Yeah, it gets hurt easily, but the best defense...) Just remember, that just two attacks can let you burn 3 of your tokens. (+Intel/Vader for #4 if you want, I do like keeping a single one around for Vader rerolls)

I was thinking of making a similar post about leading shots on isd1...

So long range and side arcs nothing, nada...

Medium range...

Red dice do .75 damage average... with a reroll they jump to 1.03..

5 sides with damage, 6 total damage, that's 1.2 damage per damage dealing side

3 non damage dealing sides out of 8 is 37.5 percent of the die

Chance of starting with non damage facing and ending with non damage facing after one reroll is .375x.375=.14 or 86 percent chance of getting a damage facing after one reroll...

.86x1.2= 1.03. For a damage increase of.28dmg from .75dmg per red die rerolled

But we're losing a blue die to do that, and a blue die is worth .75dmg

So we have to reroll all 3 red dice to start to profit at medium range off our 4 points into LS... rerolling 2 reds and a blue is barely break even... chances if all 3 reds coming up non damage in initial roll? A whopping 5.27 percent!

So close range, ISD1... you get .28dmg extra on reds, .1875dmg extra on blues, and .25 on the blacks, giving you 1.7775 but we lose a blue, so 1.0275 extra damage...

Same situation, Ordnance experts gives you .75 extra damage.... plus it affects the side arcs, which is important!

Thoughts? Corrections on maths??

I'm very skeptical of Devestator overall. It's expensive and the decrease in survivability doesn't seem to be made up in the improvement in offense.

Devastator needs to be treated like an expendable ISD sized Raider to get the most from it, but the amount of damage it can push out is crazy plus, it can fire those blues at Red range. (Yeah, it gets hurt easily, but the best defense...) Just remember, that just two attacks can let you burn 3 of your tokens. (+Intel/Vader for #4 if you want, I do like keeping a single one around for Vader rerolls)

I saw you playing on vassal with it and liked how you were playing that way... decided to put together a list and play it your way... went down in a blaze of glory, but took out a raider and flagship ISD easily netting 60 points... Might have had another raider as well if I had gambled... ugh, it was at red range and I had Devastator 4... I think I would have popped it... but focused on isd instead.. :/ anyways, Devastator is a blast!

"a decent damage increase, yes, but it turns out Leading Shots + Vader is basically overkill."

I haven't played enough games to say that I have a decent enough data set, but I have found that just Vader re-rolling 4 red 4 blue from the ISD-II forward battery is enough to kill most things quickly without adding in many upgrade cards.

I don't want to derail the thread to be about devastator but I've found with Vader all you need on it is Intel officer and X17s so 133 points total. Treat like Demo in that you want to move it in towards the end of the round to close range to activate first next round and you will have likely have 2 additional blues for your main shot with a CF command.

I'm very skeptical of Devestator overall. It's expensive and the decrease in survivability doesn't seem to be made up in the improvement in offense.

I have found the Relentless title so valuable that I need to have a very good reason to use a different one. (read: I would almost need to be using 2 ISDs.) The ISD's big gun is powerful enough that it doesn't need much help, especially when that help carries a large setup cost.

I heartily agree with you on this point.

I have found the Relentless title so valuable that I need to have a very good reason to use a different one. (read: I would almost need to be using 2 ISDs.) The ISD's big gun is powerful enough that it doesn't need much help, especially when that help carries a large setup cost.

I heartily agree with you on this point.

I want to make it clear that I think Relentless is a fine title. It tends to become less useful the more experienced you become (as you can set your dials better) but it will always be useful because not even great commanders can foresee every possibility 2 turns away.

The Avenger in the right fleet gives it a run for its money. Even the presence of Avenger can substantially alter an opponent's defense token spending. Knowing you might be on the receiving end of an ISD that disallows you spending an already-spent token makes you rethink how badly you really need to be spending defense tokens against an attack right now. Effectively, the Avenger becomes a "free" half of an Intel Officer on all of its friends' attack rolls provided the Avenger is a legitimate threat against the enemy those friendlies are attacking. It likes to go last (or close to it), though, and needs some friends to help it out so it doesn't work as well if it's just thrown into a fleet willy-nilly.

This is a thread about math/probability, however, so any requests for more math-hammering would be welcome. I may be doing some number-crunching on Vader's benefit to ISD-Is in a bit. Maybe even Ordnance Experts there too.

This is a thread about math/probability, however, so any requests for more math-hammering would be welcome. I may be doing some number-crunching on Vader's benefit to ISD-Is in a bit. Maybe even Ordnance Experts there too.

I would be very interested in this should you put it together.

Thanks for the math Snip.

I to agree with the Avenger thing. I have been using relentless simply because I can't afford the 2 more points for avenger, but you are correct that an experienced player behind avenger that knows how to use threat and focused fire makes the title hilarious fun. I especially like it with bomber swarms. nothing like being in front arc of avenger and 4 firesprays are plinking you and you realize that once the squadron command is done everything you use against the bombers will be effectively the same as discarding it!

I have been working on a 2 ISD list with Devastator and Avenger and a maxed out demolisher in it with Ozzel. Basically an ozzel pounce buzz-saw fleet.

I agree devastator is a lot over-priced but I'm working on the theory that with Needa and TRCs + Leading shots you will have a late-contact, uh, devastating ship. The idea is to delay contact till the last 2 or 3 rounds if possible and burst damage to send ships down in flame while you burn away the TRC at the right time for an extra blue die to use with leading shots (plus any you might get from burning a redirect early), with Devastator pulling fire and dishing it out Demo can run around being demo and Avenger sits at long/medium range punishing anything that dares use a token.

Not my favourite play style but it could lend itself quite well to some objectives like contested outpost and advanced gunnery.

I have found the Relentless title so valuable that I need to have a very good reason to use a different one. (read: I would almost need to be using 2 ISDs.) The ISD's big gun is powerful enough that it doesn't need much help, especially when that help carries a large setup cost.

I heartily agree with you on this point.

I want to make it clear that I think Relentless is a fine title. It tends to become less useful the more experienced you become (as you can set your dials better) but it will always be useful because not even great commanders can foresee every possibility 2 turns away.

The Avenger in the right fleet gives it a run for its money. Even the presence of Avenger can substantially alter an opponent's defense token spending. Knowing you might be on the receiving end of an ISD that disallows you spending an already-spent token makes you rethink how badly you really need to be spending defense tokens against an attack right now. Effectively, the Avenger becomes a "free" half of an Intel Officer on all of its friends' attack rolls provided the Avenger is a legitimate threat against the enemy those friendlies are attacking. It likes to go last (or close to it), though, and needs some friends to help it out so it doesn't work as well if it's just thrown into a fleet willy-nilly.

This is a thread about math/probability, however, so any requests for more math-hammering would be welcome. I may be doing some number-crunching on Vader's benefit to ISD-Is in a bit. Maybe even Ordnance Experts there too.

I pair my Avenger with a raider equipped with overloads pulse just to give them something else to think about.

Okay let's go with Vader and ISD-Is. It has been my fervent belief for some time that Vader can make these things shine so let's see if these two red-headed stepchildren can get together and have some lovely babies.

An ISD-I at close range is throwing its full front arc, which consists of...

3 black dice (average damage 3*1) = 3 damage

2 blue dice (average damage 2*0.75) = 1.5 damage

3 red dice (average damage 3*0.75=) 2.25

For an average of 6.75 damage, 0.75 more than the ISD-II's front arc (but at a shorter range and less chance of an accuracy result).

Past experiments have shown (see above) that if you reroll all the blank and accuracy results your average damage per dice changes. This would result in...

3 rerollable black dice (1.25*3) = 3.75 damage

2 rerollable blue dice (0.94*2) = 1.88 damage

3 rerollable red dice (1.03*3) = 3.09 damage

To compare to later, what are the odds of getting 1 or more accuracy results anyways, even though we're trying to avoid them?

2 rerolled for damage blue dice with a 6.25% chance of generating an accuracy apiece (25% chance of needing a reroll, 25% chance it comes up accuracy anyways =)12.11% chance of 1+ accuracies

3 rerolled for damage red dice with a 4.69% chance of generating an accuracy apiece (3/8 of dice need rerolls, 1/8 of those become accuracies anyways =)13.42% chance of 1+ accuracy from the red dice.

So assuming your red dice fail you here (86.58% of the time they do, but blue dice will save your bacon 12.11% of those times) you get a 13.42% chance of red dice succeeding + a 10.48% chance of blue dice rescuing you during red dice failures = 23.9% chance of 1+ accuracies.

For a total of 8.72 damage, about a 30% increase, if you're rolling only for damage, and you have a 23.9% chance of 1+ accuracy results. You could further improve this with the Needa+TRC combination I mentioned above but I'm not altogether confident it's as good a vehicle for it due to less red dice. It would seem you'd be better off using XI7 Turbolasers to make the most of the fat damage you can get from rerollable black dice.

If you're rolling a raw damage upgrade (like Heavy Turbolaser Turrets) or an Intel Officer, raw damage may be the way to go. But what I'm most interested in is trying to get exactly one accuracy result from the front arc to lock down the Brace while trying to turn everything else into raw damage. Given that rerollable red dice have a higher damage output than rerollable blue dice, the blue dice seem to be the proper vehicle for getting us just one Accuracy. So let's assume we're relying on super-aggro "rerolling for maximum damage" approach with black and red dice (rerolling all blanks and accuracies) which will net us 6.84 average damage. Now it's time to play with blue dice:

In your initial roll of 2 blue dice, you will have the following odds of rolling an accuracy:

zero accuracies: 56.25% of the time

one accuracy: 37.5% of the time

two accuracies: 6.25% of the time

Okay, let's slot away the one accuracy outcome. That's exactly what we wanted. 37.5% locked in, no rerolls there.

Zero accuracies means a reroll of both dice. They then have the same outcome spread as the initial 2 dice roll. So of the three possible slots, that nets us...

56.25%*56.25% = 31.64% still no accuracy

56.25%*37.5% = +21.09% one accuracy

56.25%*6.25% = +3.52% two accuracies

Two accuracies means we need to reroll just one blue dice. These odds are pretty easy to configure as it's a single dice roll. So the spread becomes:

6.25%*75% = +4.69% one accuracy (as this outcome added a hit or crit)

6.25%*25% = +1.56% two accuracies (as this outcome added a second accuracy)

So that leaves our final blue dice outcomes as:

31.64% no accuracy (+2 damage) = +0.63 average damage

63.28% one accuracy (+1 damage) = +0.63 average damage

5.08% two accuracies (+0 damage)= +0 average damage

Total of +1.26 average damage from blue dice using this method with a 68.36% chance of (usually) one or (rarely) more accuracies.

I'd like to factor in the possibility of lucking into a rerolled red accuracy as well. From our original dice pool of 3 red dice, we will be rerolling all blanks and accuracies. So You have a 37.5% of rerolling each red dice and then a 12.5% chance it becomes an accuracy during the reroll, which is a 4.69% chance per dice. So with three red dice the odds of one or more accuracies popping up despite the fact that they're not welcome here is:

zero accuracies: 86.6% chance

one accuracy: 12.78% chance

two accuracies: 0.63% chance

three(!) accuracies: 0.01% chance

I primarily want to consider the possibility of an errant red accuracy saving your no blue accuracies roll to generate AT LEAST ONE accuracy rather than a more specific breakdown of cross-possibilities between red and blue accuracies, so the math there is:

31.64% chance of no blue accuracies * 13.42% chance of 1+ red accuracies saving your bacon = +4.25% chance of 1+ red accuracies saving the day, for a grand total chance of "at least 1 accuracy in the pool" of 72.61% during this attack.

For a grand total of 8.1 average damage when rerolling blacks and reds for maximum damage and prioritizing blues for exactly one accuracy result and a 72.61% chance of at least one accuracy in the pool. This is 0.62 average damage less than rerolling blues for straight damage but the trade-off seems worth it to me.

I pair my Avenger with a raider equipped with overloads pulse just to give them something else to think about.

In my experience this is a gimmicky combo that is easy to see coming. It relies on a lot of precise attack and activation combinations and can be easily "broken" by disabling one of the moving parts (often the Raider, which can be either destroyed or the defender stays out of range). Because the defender gets an activation inbetween the alley-oop Raider and the "beat down" ISD, he can usually run away to a side arc or long range of the Avenger even if you do pull off the first part of the combo.

I much prefer simply combining the Avenger with other bruiser ships or bombers that don't suffer from not being part of a combo but are happy to help the Avenger do its job if they're in the neighborhood.

Okay some more math regarding Vader...

The benefit of Vader rerolls on the ISD-I side arcs :

Normal ISD-I side arc damage = 3.5

2 red dice (2*0.75) = 1.5

2 black dice (2*1) = 2

Rerollable ISD-I side arc damage (assuming you're rerolling all non-hits) = 4.56

2 aggro rerolled red dice (2*1.03) = 2.06

2 rerolled black dice (2*1.25) = 2.5

So it's a 30% improvement in damage. Not too shabby.

Let's take a look at Ordnance Experts by themselves on both the ISD-I front arc and side arcs

Front arc

Normal ISD-I front arc damage (seen above) is 6.75

Rerollable black dice improve their average damage by 0.25 apiece, so 3 rerollable black dice improves that number by 0.75 to 7.5. This is an 11% improvement at close range.

Side arc

Normal ISD-I side arc damage (see above) is 3.5

The 2 rerollable black dice improve that by 0.5 to 4. That's a 14% damage improvement at close range.

Combining Vader with Ordnance Experts

From math I did quite some time ago (in an old Screed vs Vader math thread) I can tell you that the superior choice for double-rerolls on black dice is to go crit-fishing with your first reroll. Reroll everything that's not a hit+crit. After that the math works out the same for continuing to crit-fish with your second reroll or only rerolling blanks.

So to just run through the math for everyone's benefit:

Original roll: 25% chance of 2 damage, 75% chance for everything else. We'll keep the hit+crit and reroll the everything else.

Reroll:

(75% reroll needed*25% hit+crit =) +18.75% chance of hit+crit (we're keeping these)

(75% reroll needed*50% hit =) 37.5% chance of hit

(75% reroll needed*25% blank =) 18.75% chance of still blank

Second reroll, rerolling all non-crit+hits ("crit fishing method"):

(56.25% chance of second reroll needed*25% hit+crit=) +14.06% chance of hit+crit

(56.25% chance of second reroll needed*50% hit =) +28.13% chance of hit

(56.25% chance of second reroll needed *25% blank =) 14.06% chance of blank

So we end up with:

57.81% chance of hit+crit = +1.16 average damage

28.13% chance of hit = + 0.28 average damage

14.06 chance of blank = +0 average damage

Average damage = 1.44, 57.81% chance per dice to crit+hit

Second reroll, rerolling all blanks only ("safer more scared of dice method"):

(18.75% chance of second reroll needed*25% hit+crit=) +4.69% chance of hit+crit

(18.75% chance of second reroll needed*50% hit =) +9.38% chance of hit

(18.75% chance of second reroll needed *25% blank =) +4.69% chance of blank

So we end up with:

48.44% chance of hit+crit = +0.97 average damage

46.88% chance of hit = +0.47 average damage

4.69% chance of blank = +0 average damage

Average damage = 1.44, 48.44% chance per die to crit+hit

I told you they'd wind up in the same place . Conclusion: if you really need that crit for some reason (on an ordnance upgrade ship, your other dice come up with no crit), you lose nothing by aggressively fishing for crits. You generate more probability of crits by double-rerolling for crits and lose no average damage.

Okay so what does this mean for average damage?

The difference between a once-rerolled black dice (1.25) and a twice-rerolled(1.44) is +0.19 damage per twice-rerolled dice. This produces the following changes to Vader rerolled averages:

ISD-I front arc, aggro rerolls on everything = 8.72 + 0.57 = 9.29, a 6.5% improvement.

ISD-I front arc, trying for one blue accuracy (see above) = 8.1 + 0.57 = 8.67, a 7% improvement

ISD-I side arc, aggro rerolls on everything = 4 + 0.38 = 4.38, a 9.5% improvement

Conclusion: maybe worth it when it comes to taking Ordnance Experts on an ISD-I overall and more questionable when combined with Vader. Given the Ordnance Experts are 3.6% of an ISD's cost, improving damage by more than that amount is worth considering. The main downsides are they only work on short ranged attacks (so... once or twice per game, usually) and there are diminishing returns when Vader is involved, as you get the most benefit from the first reroll.

I love it when you nerd out math style

I pair my Avenger with a raider equipped with overloads pulse just to give them something else to think about.

In my experience this is a gimmicky combo that is easy to see coming. It relies on a lot of precise attack and activation combinations and can be easily "broken" by disabling one of the moving parts (often the Raider, which can be either destroyed or the defender stays out of range). Because the defender gets an activation inbetween the alley-oop Raider and the "beat down" ISD, he can usually run away to a side arc or long range of the Avenger even if you do pull off the first part of the combo.

I much prefer simply combining the Avenger with other bruiser ships or bombers that don't suffer from not being part of a combo but are happy to help the Avenger do its job if they're in the neighborhood.

Absolutely correct. This works one time per person, the only way this works reliably is having a couple of raiders performing that role and now you have a fully kitted demolisher worth of points committed to a gimmick that may or may go off once in a game. If I have an avenger and my choice is a couple of raiders with OP OR another Gladiator kitted with all the pretties or a straight up demo I think I know what i'm bringing!

Altho having said that. Having both for a 4 activation fleet with a healthy fighter cover might be fun to play