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Friday 3 July 2015

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?


  1. Looks great!
    I'm curious as to how you set up that script - I'm just learning how to code and some examples would be great.


    1. Well the script is in Python and is not something you would want to look at if you were just learning to code. If you want to learn Python, here is a place to start https://developers.google.com/edu/python/

      The idea is that I'm doing the quick and dirty version with this script, specifically a lot of list comprehensions, map + reduce functions. I let Python do a lot of the work, and not in the optimal way.

      For instance, I just generate all possibilities and assign them probabilities, instead of doing a clean multinomial distribution (for now, hit + crit is different than crit + hit), as I've done before with X-wing calculations. It's incredibly inefficient, but as long as I don't have to wait more than a few seconds, I'm OK with it for now.

  2. Ship placement in the last picture has one cr90 obstructing the other. Unless it's jaina's light, you're going to have to position it differently. Course that probably is a good reason to take that particular title.

    1. You could have Jaina's light, or you could be the first player, take a shot with the first CR90, move, then the Imperial player might activate a different ship (not that specific VSD), then shoot again with the second CR90.

      The image in any case was for illustration purposes, in practice getting double shots with more than one ship is more difficult.

  3. The second cr90 is obstructed by the first in the picture.

  4. Great to see some mathwing for Armada (Math-mada? Armathda?). Keep up the great articles!