Armada Dice part II: Squadron to Ship

With wave 5 on the horizon, I want to put into context the stats for the squadron we already have. As everyone has seen, wave 3 has made a very powerful impact on the squadron game in Armada, because of the cheap activations, cheap squadron pushers and Bomber Command Center.

With the aid of a script I made, I can accurately calculate the damage based on clever ability usage. What does clever ability usage mean? It means not choosing the best order in which to resolve abilities, based on the initial roll

The aim of this blog post is two-fold: to show that there are clever paths to be taken when rerolling with simple rules of thumb that can be followed; to rank bombers based on their effectiveness taking into account the effect of Bomber Command Center and their cost.

X-wings

X-wings are the lowest efficiency bombers currently in the game, with only one red dice. Bomber Command Center in their case helps bring them in line with Y-wing in terms of expected damage. An X-wing with 2 Bomber Command Centers will do an average of 1.15 average damage, as opposed to a naked Y-wing which does 1. Of course, the efficiency is nowhere near, since the X-wing is 30% more expensive.

What about rerolls? With an X-wing and one BCC, you're only expected to reroll Accuracies and Blanks to get the best average result. In the diagram below, the center is the starting point, with the 5 possibilities of the red dice roll. On the next level, the red line represents the best choice, which is rerolling only in the case of the blank or accuracy.

What if we have 2 BCCs? Then the correct answer becomes rerolling all non-doubles on the first reroll, followed by blanks on the second roll. All in all, easy to remember!

To remember: While the X-wings have the lowest damage overall of all bombers, they benefit from having Bomber Command Center the most! 2BCCs increase their anti-ship damage by 50%!

Y-wings/TIE Bombers

Y-wings are the Rebel's cheap, no-fuss bomber option. 1 average damage with 1BCC, up to 1.25 and 1.44 with 2 BCCs! 44% damage increase is still very good! The TIE Bomber has of course the same damage output, but with fewer fleet points, so with greater overall efficiency in terms of anti-ship combat.

What about rerolls? Turns out this is more complicated. The average being 1, if you have a single reroll and you rolled a Hit, you have 2 options:

• You are at average, be content with the result
• Try your luck and go for the Hit/Crit

Both have the same average result, but the second option plays with variance a bit more, while the first option is safe!

If you have 2 rerolls, you can safely reroll Hits on the first reroll, followed by only-blank rerolls on the second reroll for safest and best average result!

Rule of thumb: No matter how many black dice rerolls you have, you can safely reroll hits on any reroll but the last! The last reroll is the one where you make the choice between safe and trying your luck! (but still with the same average result)

Firesprays

Almost not worth mentioning, since the rerolls are extremely intuitive. Anything that isn't a damage you can reroll. Overall they gain 30% damage from having 2BCCs.

B-wings 

With B-wings things get interesting. In terms of damage, they have the highest totals of any unnamed squadron and overall incredible efficiency.

As to rerolls, the priority seems to be the black dice. First make sure you have at least a Hit on that, then reroll the accuracy if you have rolled one. In the image below, all non-optimal choices and their respective consequences have been eliminated, so a red edge represents a correct choice. If there are two red edges, that means that both choices carry exactly the same weight, meaning they come out with the same average damage, no matter what.

Keyan is a special example (and now Ten Numb), because they're the only ones with 2 black dice and Keyan has a reroll capability built in!  Keyan benefits little, only 13% for a single BCC and 22.40% for 2 BCCs, but it takes him to an incredible 3 average damage!

His reroll rule of thumb is similar to Y-wings: Reroll Hits as long as you have rerolls left, otherwise reroll only blanks if you want to keep it safe!

Efficiency

So where does this take us? I have arranged the following table, where red columns are average damage, blue columns are benefits comparing to the vanilla scenario and white columns are efficiency, which I have defined as average damage per 10 points of squadron of that type. In this first table you can see how the X-wing gets to 1.15 average damage, trumping the vanilla Y-wing and TIE Bomber at 1 damage.

	Default		1BCC			2BCC
	Avg	Avg/10p	Avg	Benefit	Avg/10p	Avg	Benefit	Avg/10p
1red (X-wing)	0.75	0.58	1.03	37.33%	0.79	1.15	53.33%	0.88
1black (Y-wing/TIE Bomber)	1	1.00/1.11	1.25	25.00%	1.25/1.39	1.44	44.00%	1.44/1.60
2blue	1.5	0.83	1.83	22.00%	1.02	1.95	30.00%	1.08
1blue-black(B-wing)	1.75	1.25	2.14	22.29%	1.53	2.37	35.43%	1.69
1blue-black + Toryn	1.94	1.39	2.22	14.43%	1.59	2.41	24.23%	1.72
2black(w/o Keyan)	2	1	2.44	22.00%	1.22	2.72	36.00%	1.36
2black(Keyan)	2.5	1.25	2.84	13.60%	1.42	3.06	22.40%	1.53

The second table has efficiency calculated and sorted in descending order. The B-wing tops the list when taken with 2BCCs and is generally more efficient in all conditions.

	Efficiency
B-wing + Toryn + 2BCC	1.72
B-wing + 2BCC	1.69
TIE Bomber + 2BCC	1.6
B-wing + Toryn + BCC	1.59
B-wing + BCC	1.53
Keyan + 2BCC	1.53
Y-wing + 2BCC	1.44
Keyan + BCC	1.42
TIE Bomber + BCC	1.39
	...

For B-wings, both 1BCC and 2BCC bring enough damage to be taken into consideration, although the first BCC brings the bigger boost in efficiency. I also considered B-wings with Toryn Farr nearby. As expected, Toryn Farr is weaker than a Bomber Command Center for an anti-ship of 1blue 1black. Of surprise is that the efficiency of an X-wing with 2 Bomber Command Centers is higher than that of a Vanilla Firespray!

To remember: Bomber Command Center transforms your mediocre bombers into decent bombers and good bombers into great bombers!

Cost of Flotillas 

But let's not get ahead of ourselves! Flotillas cost too, right? So you could argue that efficiency of squadrons has to take into account the cost of those flotillas with Bomber Command Center, 26 pts minimum for the Rebels and 31 pts for the Empire.

In the following table I have filled 134 points with a single squadron type and calculated the damage. Unrealistic, I know, but the point I'm going to make after this remains unchanged..

Squadrons	Points	Avg	Efficiency
Fleet of 13 Y-wings	130	13	1
13 Y-wings + BCC	156	16.25	1.04
13 Y-wings + 2 BCC	182	18.72	1.03
Fleet of 9 B-wings	126	15.75	1.25
Fleet of 9 B-wings + BCC	152	19.26	1.27
Fleet of 9 B-wings + 2 BCC	178	21.33	1.2
Fleet of 10 X-wings	130	7.5	0.58
Fleet of 10 X-wings + BCC	156	10.3	0.66
Fleet of 10 X-wings + 2 BCC	182	11.5	0.63
Fleet of 14 TIE Bombers	126	14	1.11
Fleet of 14 TIE Bombers + BCC	157	17.5	1.11
Fleet of 14 TIE Bombers + 2 BCC	188	20.16	1.07
Fleet of 7 Firesprays	126	10.5	0.83
Fleet of 7 Firesprays + BCC	157	12.81	0.82
Fleet of 7 Firesprays + 2 BCC	188	13.65	0.73

  

It seems that the efficiency is unchanged when taking this into account! So we end up paying the same per point of average damage as before! So what have we gained?

• Activations, a flotilla is an extra activation on the battlefield
• Points for squadrons beyond the 134 point mark, because flottillas can "carry their weight" by directly enhancing squadron damage
• Decreasing variance of squadron rolls considerably: Even if the B-wings + flotillas generate the same average damage, the risk of blanks is removed
• Extra anti-squadron fire
• By having more damage per squadron, we concentrate firepower.

There's certainly things to lose:

• Flotillas might be a liability since only one accuracy can ruin their day
• More damage per squadron also means that you lose a lot of firepower for the same amount of HP lost. Individual squadrons are more important, because if you've only flotillas left, you can't do any damage with them. 

Conclusions 

This went a bit beyond a simple math article, since there are some lessons to be learned from this. Namely, that taking flotillas with BCC further increases your investment in bomber squadrons without increasing their efficiency, but eliminating variance. I admit I thought of flotillas with BCC as a damage multiplier, but it's more akin to a damage focusing element. You get more damage in per squadron activation and with less variation, this is incredibly valuable.

Correction: The second paragraph was a mess and I put 8 points for all my TIE Bomber calculations. Shows how much I play Empire, right?

Focus vs. Target Lock: A fresh look with R3 in mind

Introduction

Because of the blog post on poorgreypilot and the recent Mynock Squadron episode covering the R3 astromech, I felt that there were additional points that needed to be made. Namely the fact that R3 astromech shifts the balance between Target Lock and focus.
 
The debate on Target Lock vs. Focus is as old as the old core set. Which is better? Target Lock is purely offensive, can set up torpedo shots, carries over to the next round. Focus is temporary, but can be used for either attack or defense, as needed. I will talk about the established consensus (feel free to disagree on this or other aspects in the comments section), then I will try to explain why R3 shifts the balance between the two actions.

Math and Context

Let's start with the basic math: A single red die has 8 faces: 1 critical hit, 3 hits, 2 focus symbols and 2 blank faces. So the success rate for a single die is 4/8= 0.5 (50%). It is also rather easy to see that with a focus token you have 6/8=0.75 (75%) chances of a success. What about TL? Well, it's a bit more complicated, but you can break it down like this: You have your initial dice roll which gives you 50% chances of a success. In the other 50%, you get to reroll the die, which nets you another 50%. So the TL is 50% plus another 50% of the times you get to reroll, which means 75%, identical with focus!

To summarize:

• An unmodified die gives you 50% with 1/8 chance of a critical hit
• A focused die is 75% with 1/8 chance of a critical hit
• A TL-ed die is 75% with 3/16 chance of a critical hit (the reroll grants us that)

So math-wise, for attack, there doesn't seem to be much a difference! The true difference comes from context:

For Target Lock:

• If the ship you target locked dies, you lose the target lock
• You cannot change targets if you target lock
• You may keep the target lock for next round if you don't use it 

whereas for Focus:

• You can spend it for attack or defense. If your Pilot skill is lower than your opponent, you may prioritize defense over attack on some of your ships (if 3 Academy Pilots have focus tokens and there's only one attacker, 2 can spend focus for attack while 1 can spend focus on defense if needed)
• You can choose your target when you activate

Chance to spend 

The biggest difference, however, and one that I've never seen in written form anywhere, is the chance to spend. If you're the first to shoot, what is the chance you'll spend your token?

The main assumption is that you're spending the TL if you have less than the maximum number of hits/crits. If you're shooting at a low agility target and you're confident you're shooting the same target the following round, you can get away with keeping the TL at 2 out of 3 hits for example for a 6% boost in damage over 2 rounds (considering you focus the next one). This is a conversation in of itself.

With that assumption in mind, for a 3-dice shot you have:

• chance to spend focus: 58%
• chance to spend TL: 88%

In other words, with TL you have a 12% chance  of keeping your TL for the next round, with focus you have 40% chance of it being used defensively, not needing it for offense.

What is the source of this? Hidden information. Focus gives you complete information of how many extra results you're getting if you spend the token, with TL it's literally a dice roll. Reasons that people don't use Target Lock can also be psychological: how many times have you picked up the dice, spent the TL, rerolled, then got nothing? Even if, on average, the results are the same as with focus, the disappointment felt is real.

Where does R3 come into play?

Where am I going with this? The fact is that when you're using TL, you are discarding a lot of unused results. You're very likely ignoring whether they're blanks or focus symbols but the reality is that 50% of symbols that aren't hits or crits after rerolling are focus symbols. 

How many times are you going to roll perfect 3/3 with a single TL? How many times 4/4? My point is when you're using TL, the are many unused focus tokens. Otherwise said, there's a niche for R3 astromech usage where the impact on damage output is 0. 

What are those odds you say? For any red dice, there's a 7/8 chance that after rerolling you don't get a focus symbol (initial focus symbols are rerolled). So a 3-dice attack has 1 - (7/8)^3 = 33% chance of getting at least 1 focus it's not using. For a 4-dice attack it's 41%.

Assume you're playing with TLs instead of focus: you don't get any added defense, you have a slightly higher damage output (via keeping the token 12.5% of the time), and now you get 33% chance of an evade for 2 points.

Contrast this with Autothrusters, an extremely cost-efficient card, which is also at 2pts (but on a more precious slot, at least for a T70). If you're attacked only once, and it triggers, you get 61% of it generating an extra evade.

Or compare this to Shield Upgrade. This is half the points, and it needs to trigger only once before you get shot to make up its cost.

To summarize:

• It is half as efficient as Autothrusters when you have one attacker at lower PS, but you have no range/arc restrictions, with better stats at range 1
• It is much more efficient than a Shield upgrade if you get shot at least once after getting a token
• It is a low-cost astromech that can be used with Integrated Astromech
• Coupled with Comm Relay, it's a 5pt Shield upgrade that regenerates 33% of the time. 
• It can be comboed with Autothrusters for extra tankiness.
• Coupled with Juke, it's 33% chance of triggering Juke, while also retaining your offensive action

 Uses

All in all, I think there's a place for the R3 astromech. I'm not advocating its use, but it's not as bad as people say. I would use it on a high-PS T-70 that can't use R5-P9 or R2-D2 effectively. It's also best on a ship that is taking off-fire and isn't the centre of attention. Ello seems the best target, for now, the only high-PS T-70 that isn't Poe (until further HotR spoilers). He also can't use R2-D2 effectively (he wants to T-Roll) and R5-P9 reduces his damage output (actually, with the statistic that 40% of focus tokens aren't used..). Juke is the cherry on top and makes him quite dangerous.

Armada Dice part I: Ship to Ship

I'm going to do an article or two on Armada, since I've been playing this just as much as X-wing in the last weeks.

One of the things that felt unfamiliar when starting Armada where the dice. Just like any new game, I did not have a "feel" for the dice. I did not know what to expect from them, if one roll was good or one wasn't. You might say that it's better not to know so you can't blame the dice when you lose! This is partly true, because you may want to gauge your performance realistically, to know how to play it better next time!

Armada dice and probabilities

This has been covered by many people, but we need this for this article as well. The basics of Armada dice are as follows: there are three types of attack dice, each representing a certain weapon type, having a maximum range and hit characteristics. Red dice are turbolasers, blue dice are ion weapons, black dice are missiles.

Red dice are the long-range weapons, that have a rather high variance of damage: there's 3/8 chance that you don't add a hit, but you also have 1/8 chance of a double hit. The average damage is 0.75 per die.

Blue dice are medium range dice. Though they have the same average damage (0.75) as red dice, the damage is more spread out, so you have lower variance among rolls. You also have 2 accuracy symbols, which help a lot in combat.

Black dice are brute force, 1 average damage per die, with a 25% probability of a hit+crit. While they can also come out blank, you are more likely to get good damage out of them. They also have no accuracy symbols, so they're better if mixed with other dice types.

Thoughts on combat 

 

While Armada does not have defense dice like X-wing, it does give ships and elite squadrons some defense tokens. In the rest of the article I will talk about damage dealt to a ship. Talking strictly on the current defense tokens:

• Redirect does not affect damage dealt. It's still damage on the ship. The VSD has 10 shields, but shooting it over the course of the game you won't be able to fire on the same hull zone. Most of the times you'll start from one side and by the time you kill it you'll be on the other side shooting at it. At its weakest the VSD would look like 9HP (8 Hull 1 Shield), if you deplete all shields it will be 18HP. The actual situation will be closer to 18HP, even more if the Imperial player stacks combo Repair commands (+token).
• Evade gets rid of 1 or 2 damage, so it affects damage dealt. 
• Brace cuts the damage in half and is the most important defense medium ships (VSD, AFMkII) have. This token reduces damage on an attack by 2-4 damage, which is a lot in the context of a single round. Of course this will be much smaller if the attacker rolls very few dice, and might not be relevant at all against swarms of small ships (Corvette swarms firing 1-2 dice). 

If  our goal is to reduce damage taken throughout the course  of the game, each round we must guess which attack will have the highest resulting damage and keep the Brace token for that attack. Spending a brace twice is of course a reasonable action in some situations, but that is a topic for another time. Suppose we have the highest attack first, then we use Brace on that. Assuming we're piloting a VSD, we use Redirect more liberally afterwards (also subject for discussion for some other time).

Script for calculating damage dealt

What I'm getting at is the core of my calculation for damage dealt to a ship, specifically to a VSD. This is more interesting since it is relevant in all games, from 180pt to 400pts: How much damage will you deal to the VSD this round? I will make the following assumptions:

• Attacks will be directed at the front, so there will be plenty of room for redirects
• The first attack will carry most dice or at least have the most likely highest hit result. I will always brace on the first attack if it saves me a damage. Unused defense tokens carry over to the next attack
• Redirects are from a "shared" pool, in this case 6HP worth of shields
• The attacker will limit the use of Brace, Redirect and Evade, in that order (with accuracy symbols). If the tokens are used he will not limit them (also a good point of discussion for strategy)

I explore the tree of possibilities (tokens used, damage taken, shields available for redirect etc.). I sum probabilities on scenarios that share common criteria (in this case I aggregate according to total damage dealt in the end, including redirected shields). In this fashion I was able to calculate some average damage and draw some conclusions.

Single CR90

 

Let's take a look at the damage dealt by a single Corvette, firing from its front hull zone at medium range. That's 2 red dice and 1 blue, for a maximum of 5 damage (not possible given that the VSD has Brace).  You can do maximum 4 damage to the VSD if you have 2 double hits and an accuracy to forbid Brace. What you can also notice is that 0 damage is very unlikely, in stark contrast with X-wing. Here, there is no "barrier of entry", you don't have to exceed green dice. When shooting at a Star Destroyer, you're going to do at least 1 damage if you have at least 1 hit/crit symbol in your roll (because it doesn't have Evade). This becomes especially important in squad vs. ship scenarios.

 If you are on the offensive you will probably have a Concentrate Fire command ready on the Corvette. Perhaps you will try adding a third red die first. But red dice have blanks and only one accuracy, so you're not getting rid of that Brace too easily. There is a net increase in damage, but you'll find more average damage with an extra blue die.

 As can be seen in the next graph, just adding a blue instead of a red boosts average damage from 2.23 to 2.31. You can see the difference clearly in the upper and lower limits. 3 Red dice and 1 Blue have 1.32% chance of doing 0 damage, while 2Red 2Blue have only 0.88%.

Conclusion nr 1: Add blue dice over red dice if possible!

 

Double arcs with the CR90

 With a Corvette it's not so hard to get a target in two arcs (front and one side). You might think that the side is too weak, only two dice. It turns out that shooting one more time is significantly better than just adding one die (naturally, since there's two), and it's almost twice as good as the first frontal attack! This may be a bit surprising, until you consider that Brace won't be used for two attacks (especially not 2-3 damage attacks), so the second attack actually has a higher expected damage than what it would normally be, since it will not be Braced for (unless Brace was not used in the first attack)!

 

Conclusion 2: Getting double arcs on a target is more important than commands

Ok, clearly we're starting to be confident in our little corvette. Let's put Concentrate Fire on it while it has this brilliant double arc. We should probably add a blue die, but to which attack? Do we want a large attack and a small one, or two balanced ones? Again, because of the Brace token, we need to split hits between attacks, such that one Brace use cancels as few hits as possible. If we boost the already-large front dice pool, we have 2-2-0 (2 Red 2 Blue) and 1-1-0 on the sides, which amounts to 3.54 average damage. But if we enhance the weaker side (2-1-0 and 1-2-0), we get 3.60 average damage. It's not much, but every bit counts!

Conclusion 3: Even out dice pools if possible!

Bring on the Assault Frigate

We reached 3.60 damage in a round, but we want to bring down that Star Destroyer. We need bigger guns! Let's take a state of the art Assault Frigate mkII with Paragon title, Enhanced Armaments. Enhancement Armaments add a Red die to the side, while Paragon adds 1 Black die to the second attack made on the same ship (which we will get if we have a double arc). This is much harder to do with an Assault Frigate than with Corvettes, but has the advantage of possibly setting this up on the approach and while running away (the rear hull zone is as good as the front). What may surprise you is that Concentrate Fire may add 1 Black die to the second attack!

What we have learned so far is that we want to add the strongest die. Currently this is the Black die, at 1 average damage. We could add this to the stronger attack (2-1-0 from the front and 4-1-2 from the side), or we could balance out the attacks (4-1-0 and 2-1-2). The latter comes out as more efficient, as our newly bred intuition told us, with a 6.45 average damage (vs. 6.34). First this seems great, and feels great too! Dishing out 10 damage to a Star Destroyer definitely seems the best choice. But then again, this isn't much more than double what a single aligned CR90s would do (with no Concentrate Fire!).

Back to CR90(s)

 

Clearly this is a much riskier scenario, and one of the Corvettes might die this round, but let's see how much damage we can muster just by aligning arcs, no Concentrate Fire! These are 10 dice just like the Paragon attacks, but without any black dice and spread across 4 attacks. No attack is obstructed because you attack with the first one, move, survive the VSDs assault, then fire with the second CR90.

... about the same damage. With the same distribution. The brace on the bigger attack cancels out with the black dice on the second, so you get about the same average as with reds and blues.

Conclusion 4: You can achieve the same result with 1 big ship with quality dice or with several smaller with average dice

There are a few things to take from this: Pre-planning is ok, getting that Concentrate Fire when you need it is great, but getting good arcs is substantially better. The more dice you throw at your opponent, the better! This sounds simple, and it was also true in X-wing, but here the expected damage increases linearly, even with the use of defense tokens. It's also important to make the good small decisions, which add up: should I add a blue die or a red die to my pool? Should I add an extra die to this attack or to this one?