Link: http://www.wwpd.net/2015/10/star-wars-armada-stats-101-expected.html

Now that I've completed my consciousness transfer from The Mathemagician into the R1H4 Battle Computer, it's time to delve into my favorite topic again: MATH.

Star Wars: Armada's unique dice arrangement - both in facing and in color - makes calculating "Expected Results" extremely difficult or super fun(!) depending on how you look at it. Defensive abilities that modify those dice directly (rather than simply modifying the final result) add a layer of complexity that makes Armada a highly variable (and super fun!) game to play.

Today, we are going to talk strictly about Expected Outcomes from each set of dice in the quantities we see from Capital Ships - specifically in terms of damage output. We will also look at these outcomes through the lens of a basic Pareto analysis; that is to say, which outcomes are greater than 80% reliable. We all know there's a chance we can roll 4 blanks on 4 black dice, but how common is it? Should the rare chance of that occurring impact how we make decisions? Using this "80% Rule" allows us to make decisions based on reasonable outcomes when chance/risk is involved.

Link: http://www.wwpd.net/2015/10/star-wars-armada-stats-101-expected.html

So many words and numbers.

... My God... Its... Its Full of MATH....

You do the math, I play the game.

I would advise you to use binomial(ahem, trinomial with red dice) distributions to obtain correct numbers, yours are off (courtesy of doing Monte Carlo simulations).

The numbers for 2 red dice are as follows:

0 damage 14.06%
1 damage 37.50%
2 damage 34.38%
3 damage 12.50%
4 damage 1.56%

You can check the 4 damage, which is 1/64 = 0.015625 and 0 damage, which is (3/8) * (3/8) = 0.140625.

The math for Criticals is simple: there's a 25% chance for a crit on each type of die, so the change of getting at least one crit is 1 - (3/4)^n, where n is the number of dice.

1 die 25%

2 dice 43.75%

3 dice 57.85%

4 dice 68.35%

5 dice 76.27%

I will shamelessly plug my Math article from July and I will shamefully admit that I haven't produced further content.

Also, on a more game-y note: I disagree with using pareto here, since the distribution isn't close to that. 20% of the dice will NOT generate 80% of your damage. Depending on only 80% certainty dice results will also have you playing too safe for my taste. I would see doing this in X-wing, where some of the moments are PASS/FAIL, and if you fail you lose (Flying Soontir Fel for instance, you don't want to fly him where there's a 50% chance of him dying each round).

I'd queue the lazy music if I wasn't being lazy, but rather than read through it again (I do believe I read it and commended you for it previously) were the numbers statistically-significantly different with your proposed adjustment? Wait, not statistically-significant - I don't want this to turn into one of those semantics street fights you math types love to engage in - but table top significant?

I guess my point is that while I understand there is a certain purity and beauty in refining measurements, for my purposes anything outside of a couple percentage points is not table top significant. As an aside I don't necessarily disagree with your response to a Pareto focus.

I'd also like to see these numbers used to determine what the maximized damage per turn ship/squadron build is. I realize several other considerations should be included in list building but some sort of proof showing that a certain list has the highest likely damage potential would be interesting if not entirely useful on the table.

I'd queue the lazy music if I wasn't being lazy, but rather than read through it again (I do believe I read it and commended you for it previously) were the numbers statistically-significantly different with your proposed adjustment? Wait, not statistically-significant - I don't want this to turn into one of those semantics street fights you math types love to engage in - but table top significant?

I guess my point is that while I understand there is a certain purity and beauty in refining measurements, for my purposes anything outside of a couple percentage points is not table top significant. As an aside I don't necessarily disagree with your response to a Pareto focus.

I'd also like to see these numbers used to determine what the maximized damage per turn ship/squadron build is. I realize several other considerations should be included in list building but some sort of proof showing that a certain list has the highest likely damage potential would be interesting if not entirely useful on the table.

I could argue that anything less than tens of percentage points isn't relevant. How you fly and how you position brings in WAY more damage than knowing on which of two attacks on the same ship to use the Concentrate Fire command. I could say that's one of the reasons I was discouraged from continuing my own analysis, micro-decisions mattered very little.

But he said he liked math, so I pointed him in the right direction.

The moment where it matters is exactly the one you pointed out: When you want to see the limits of a list or of a ship and have a direct comparison with something else.

This type of stuff really pisses off the Dice Gods.

Percentages dont rule my dice results. Pft....sss...tsk. My faith and will is all I need.

"What number do I need to roll?" I ask my opponent while shaking my dice in two hands.

In the example above, my hands are cupped prayerlike. I ask the question to confirm what I need to 'will' out of the dice.

All my dice rolls break the bellcurve, because the Dice Gods are fickly jokesters.

/ducks

Yes, yes Versch.

The real admiral put his trust in his gut instincts ... and sacrifies a lamp or two to whatever gods he belives in ... just to be sure.

So, do whatever you must do to belive in your own rolls. Use the force, if you want so.

Math is just a try to excuse another lost tournament ... otherwise the galaxy would be ruled by mathematicians. But we all know this is not the case ;D

Very interesting. Any chance of a copy of your spreadsheet?

Imperial Officer: "Lord Vader, your mathhammer has failed again to find the Rebel base..." *choaking, claws at throat* Vader: "Do not underestimate the power of math"

Seriously though, I love this stuff. This is why I am a board game nerd!

There is a reason I didn't become an electrical engineer and just became an electrical technician.

This is the evil version of my fun.

Good work.

I'm trying to, when I have the time, also work on a simulator. I think displaying damage histograms in the same arrangement as a ship's arc (replacing their dice) would be a fun infographic to do.

After I paint my x-wings though. And neb-b's. And tie's. And get those microscopic red squadron decals finished.

Very interesting. I appreciate the food for thought!

I agree with one of the commenters on your site, I'm quite interested in the effect that selective rerolls from cards like Darth Vader and Ordnance Experts will have on these probabilities. You know... if you have time and interest.