Custodes Ka'Tahs, Mathematics, and the complicating of a supposedly "streamlined" edition

 So Games Workshop gave us a preview of Custodes Ka'Tahs yesterday. You can go read more on it by clicking that hyperlink (takes you to Warhammer Community, I swear its not a Rick Roll... but for what's to come you might as well save time and go Rick Roll yourself anyway).

I am not going to dive into the the Ka'tahs they previewed. That is not the point of why I am writing this article. What I wanted to dive into is how Ka'tahs work, why everyone seems to feel like it is unnecessarily complicated, and ultimately why I think it is a bad game design move.

So the part in focus is this

Basically it works like this (I am copying and pasting this from an earlier discussion I had on this topic. For the purposes of this, a Ka'tah is a "Discipline", A is a primary choice, B a secondary and C the tertiary. 1 and 2 are the stances within each of those.

• When the game starts you pick Discipline A, B, C from a list of disciplines (current # unknown, at least 3)
• Turn 1 you have to pick stance 1 or 2 from discipline A. Lets say you pick stance 1.
• Turn 2, you can now pick stance 2 from discipline A OR you can pick stance 1 or 2 from discipline B, but not discipline C. Lets say you pick stance 1 from discipline B.
• Turn 3, you can now pick stance 2 from discipline B OR you can pick stance 1 or 2 from discipline C. You cannot go back and pick stance 2 from discipline A. Lets say you pick stance 2 from discipline B.
• Turn 4, you can now only pick from Discipline C. Can't go back to A and you used up B. Lets say you pick Stance 1, discipline C.
• Turn 5, you are now stuck with Stance 2, Discipline C.
• If you did 1 from A Turn 1, 1 from B turn 2, and 1 from C turn 3, turn 4 you'd be stuck with 2 from C and then turn 5 have nothing.

Because of the way this is going to be what separates wheat from chaff and really will put a skilled/practiced custodes player above the rest, because thinking through the order and timing when you want to land your key Kat'ah is going to be crucial. Lets show you some decision trees to demonstrate the point.

Complicated yet?

Okay so that one was a joke first attempt one of my team mates made, but it illustrates the point (as a side note, the guy who drew that has a Master's degree in Math, the only reason he doesn't have a doctorate is he was tired of school, and he currently teaches Math at a collegiate level... so yeah, color him not a fan of this system). I made a cleaned up version in power point.

So that decision tree has 72 nodes in it. That is 72 different decisions you can make with Ka'tahs once you have chosen them. It would be more if we had 6 turns, but the game currently ends Turn 5. This leaves you with some routes that end before using the 6th stance available to you, while some routes you have no stance in turn 5 because you burned through your Ka'tahs fast.

There is fortunately an easier way to look at it. Back to my Math friend

So in this simplified trace path, you start on A1 or A2 on Turn 1 and each arrow represents a new Turn of the game. And you have to remember, you can never go back wards. 

But it really isn't that simple now is it. This represents once you have picked your Ka'tahs. What we need to talk about is permutations. We are in an N choose r situation, where we know r to be 3 (Primary, Secondary, Tertiary), but we don't know what N is. Now based on the preview we know there are 3 Ka'tahs minimum, but also based on the preview I am going to assume there are more. Now I'd venture that there are no more than 6 Ka'tahs for a total of 12 stances. This fits the potential for randomly rolling for a Ka'tah and stance as part of some crusade mechanic or something. There could be less, but likely no fewer than 4, and there could be more, but I am willing to bet no more than 6 Ka'tahs to choose from. We always get 6 powers in a discipline. We always get 6 Warlord Traits. 6 fits the design prerogative of Warhammer 40,000. 

So assuming 6, that is 120 permutations of Ka'tahs. To do the math, that is 

• 6!/(6-3)! = 120
• (6 x 5 x 4 x 3 x 2 x 1)/(3 x 2 x 1) = 120
• 6 x 5 x 4 = 120
• 720/6 =120

Now lets go look at that visually.

That is 8,640 nodes. Or 3,840 pathways to play the game.

8,640 potential decisions you as the player should understand the consequences of before the game starts. That is 3,840 courses of action that will play out on the table. Even if we used the simplified table, that would be 1,680 nodes for 6 Ka'tahs.

Or as I like to think about it, one node for each name Constantine Valdor has. Which is now canon.

Yes it is.

Now, yes, you don't actually need to know the whole diagram, and you can be flexible and reactive on the decision tree to a degree. And for sure, there will be some Ka'tahs that are OBVIOUSLY better than others, and that's also not to mention that people will have their own personal favorites, leading them to ignore other Ka'tahs all together 99% of the time.

But what you need to understand is that from all that potentiality, each decision you make locks out more and more of the totality of potential, and from the beginning of the game you may choose 3 Ka'tahs that result in this table...

When you really needed a subset down here to achieve victory.

See as you pick yohr Ka'Tahs, you rapidly winnow options available. Without consodering order if you pick one Ka'Tah, you instantly eliminate 30 tables here. Down to 90. Another Ka'Tah and you are down to 24, or 1 row above. You're third and you are down to 6. Start ordering them, the moment you set a primary you are at 2 tables left, and then your secondary selection drives which table you are on.

And there in lies the rub. For a "streamlined" game, this is an INCREDIBLY HIGH amount of decision making and comprehension of potential choices and their impact that is required by the player, and it really does set up for those with the natural ability to understand this, or those who are more experienced in its use, to be better than everyone else. And that is not a system that is friendly to new players, nor is it really friendly to casual players. And IMO to be a good mechanic is a game claiming to be streamlined, it should do both those things.

I can also almost guarantee this will slow game play as people go back and forth agonizing over which Ka'tahs they should select, what order to place them in, and then which stance they should use each turn.

And to complicate it all even further, I am willing to bet there will be

• A stratagem allowing you to use both Stances from a Ka'tah in a turn
• A stratagem allowing you to reuse a previously used Ka'tah and/or stance

And I am sure that won't complicate the matter...

And oddly enough your Primary Ka'Tah isn't even your most important. You can only acces it T1 and T2, and you can leave it as early as T2. Your secondary is where it is at since you can time it to be T2, 3 or 4. So whatever stance you want to hit the hardest, make it B1 or B2. Your second most important Ka'Tah is actually your Tertiary for the same reason prett much. You can access it T3, 4 and 5 if timed properly. THIS is what I am talking about when I talk about more some players really using Ka'Tahs to a degree that others can't. Understanding when and where to land their Ka'Tahs.

Now this also means, it may be a little easier to choose though. If a Ka'Tah is obviously a Defensive/Movement buff, it may always be just clear to use it as a Primary for Turn 1 and 2 access. Where as your shooting ones may be best as Secondary and your Assault or Scoring ones as Tertiary. Really narrows you down on the table faster.

I also want to take a moment here to point out though that while this is supposed to represent a Martial prowess and flexibility as unparralled by any others, it is really actually super rigid mechanically. Those potential stratagems aside, lets say I pick a stance from a Ka'tah that would shut down a rerolling hit/wound deathstar character. Lets say its the second stance in that Ka'tah I have used, so I have to move onto a new Ka'tah next turn. Now I selected this in my command phase, so in my opponents turn he knows I have that selected... so he just chooses not to charge this turn. Next turn, I have to choose a new Ka'tah and uh-oh... it is one for dealing with hordes. Now my opponent in his turn charges that character into me and destroys the squad by rerolling everything.

Some bunch of ultimate badasses I was, not able to adapt to the situation when faced with a combat monster instead of the chaff infantry I was planning for.

And to me, this really underscores the complicated nature of the system and what I was saying earlier. You make one bad mistake about what order to put your Ka'tahs in at the start of the game, you are now locked into that mistake for the entire game and may potentially not be able to recover from it. And that is a hallmark of a bad game mechanic IMO.

Will Ka'tahs be useful? I'm sure. But useful doesn't mean good mechanically. Back when space marines got 500 free points in Rhinos and Razorbacks, that was useful, but terrible for the game. When you could have untargetable assasins, useful but bad mechanically. Ka'tahs don't seem to that level, especially since they aren't unfair to your opponent it seems, but they still seem off and rough on their own player.

Will they be fun? IDK. This is where I think you'd need to look more specifically at the Ka'tahs themselves. However, no matter what they are, I am sure there could have been a more fun way to implement them, because this...

This give me a migraine. 

SOLO: A SCIENCE STORY- 12 Parsecs Conundrum

With each new Star Wars movie that comes out, I find myself being critical of the Science in it. I understand is it Space Fantasy and should not be taken seriously. And I don't. I LOVE Star Wars and find each of them highly entertaining in their own way. But that does not mean that I can't be critical of certain details THAT RUIN THE TOTALITY OF STAR WARS.

A hint of where I am going with this

Hold on, I don't mean to say this franchise we LOVE is ruined. But take a moment to read my previous Science based posts about how Star Killer base is ultimately a worse weapon than the Original Death Star and how I predicted how the infamous Solo shield bypass maneuver makes the "War" part of Star Wars pointless by itself being a super kamikaze weapon. Then my next post about how said Kamikaze maneuver in TLJ was not NEARLY powerful enough and is really a better move than using something like the Death Star.

See what I mean when I say "Star Wars is ruined"?

What are my qualifications to talk about such things? Well I am a member of the 501st legion (AT-AT driver), own all the old dictionaries and technical books and have watched the movies like a million times...

Oh, you mean the science part. Well I have a Master's Degree in Applied Physics, specifically focused on shock physics/weaponeering. I guess that counts for something.

ANYWAY, let me tell you that even though the new Solo: A Star Wars story "fixed" the Parsec conundrum of time vs distance, it still leave a huge gaping hole in the form of WHY IS A PARSEC EVEN A UNIT OF MEASURE TO THEM!

For those not in the know, a Parsec is used to measure the distance to another star using the  reference dimension of AUs, which is the specific distance between our Earth and our Sun. It's more of a perception of scale dimension, because when you are dealing with the space between astronomic bodies in the universe normal units give no concept of scale.

Which is funny because Parsecs don't either because of how ridiculously big space is. See below

__________________________________________________________

That line above, well it isn't a line..... its a triangle

for the parsec calculation for the closet star

And actually its worse than that. 1 AU is 4.8481e-6 Parsecs. If that line is 1 pixel thick, I would need a line 4.8 million pixels long for it to work. 

Now you might say maybe its the the parsec of a different planet and its sun. Well fine maybe that's what's supposed to be, but that is the measurement equivalent of measuring feet using your actual foot. They aren't all the same, so you "6 feet" would be different than mine. Or Bigfoots for that matter.

They are both "One Foot" right?

Point is, in a Galaxy with tens of thousands of planets and thousands of species from all over, it would be weird to base the standard unit of measurement off of any one planet.

Now you may say "What about Coruscant" and that is kinda fair. It has only been the seat of the Republic and the Empire for a little over 1,000 years.... however there was Hyperspace Travel well before that (it is over 4,000 years old by the time the First Order comes into existence). So it would likely have to be something well before that. And in the wake of the Galatic Civil War, Coruscant stops mattering. In the end it is just silly to base a galactic standard off the orbit of a single planet.

A more appropriate unit would be based on a degree of rotation of the galaxy, or a distance between the 2 brightest objects, or the distance you cover at hyperspeed in a galactic day (whatever that standard is. We are only covering one here). Basically something a little more galactically tangible.

So now that I have ranted about why a Parsec is even a measure of distance in the Star Wars universe, lets go into why doing the Kessel Run in 12 of them is still relatively dumb.

And I know the line is LESS than 12 Parsecs, but 1- he admits he was rounding down in SOLO and 2- it is easier for me to just use 12 moving forward.

First of all, Han Solo took a shortcut. He is bragging he is so fast, but really its just a different distance? Would a marathon runner be like "I'm so fast I ran those 26 miles in 15 miles"... No. That just means you cheated. Sure its awesome Han was able to take a short cut the the Maw, but not really relevant to his speed.

Up until this point, I haven't said how far a Parsec actually is. Well for our purposes, lets say that this is a magical universal constant, so it exactly matches our Parsec. That would mean a Parsec is 3.262 Light Years (which is another reference specific to Earth, but that is beside the point. It works for my purposes here). That means 12 of them is 39.144 Light Years. FYI, the Star Wars Galaxy is only 120,000 Light Years wide, meaning that Han's Kessel Run covered ~.01% of the breadth of the Galaxy. The NORMAL Kessel Run is 20 Parsecs, meaning it would be ~.016% the breadth of the Galaxy or 65 Light Years. So roughly the Galatic Neighborhood. For reference, the nearest star to Earth is Proxima Centari and it is 4.25 Light Years away. Now whats odd is the Kessel Run is through that huge cloud, called the Akkadese Maelstrom. What we see in the film is on the way in, they make these short skips through hyperspace and then fly a little in real space, and on the way out our heroes do alot of initial flying in real space, then one long shot jump in Hyperspace. Now the Falcon is actually slow in realspace. It does a made up speed of "3000 G" to a Tie Fighters "4,150 G". Now it does have a atmospheric speed of 1200 KPH, but this is Space. Lets say G is once again magically related to our accepted G on Earth. 9.81 meters per second per second... yes per second per second. Its acceleration. So it is silly for speed. But lets just call it a constant 9.81 meters per second for this rating. That means the Falcon at sublight speeds goes 29.4 Km/s. That is fast... but light is 300,000 Km/s. FYI the fastest ship we ever launched, the New Horizons probe, only did 16 Km/s. So, that means even at full blast sublight, Han did NOTHING to chip off the distance. Every minute of realspace flight he does only saves him .6% of a light second of travel. Not light year. Light second. Meaning most of the flight through this "Maelstrom" actually had to be through stable, reliable and LONG hyperspace corridors. I am talking on the order of distance between stars long. So really it doesn't make sense IMO. 

So lets talk about  Hyperspace speeds. There is a pretty cool article where someone deduces the actual speed of the Millennium Falcon. I'll let you read it, but essentially he uses the scale of the galaxy and an estimated times to travel from Tatooine to the space formerly occupied by Alderaan. He comes up with 25,000 Lightyears per day, and then equates that to ".5 past lightspeed", which it really isn't, but that could just be Jargon. It would mean 20k LY/day is .4, 15k LY/day is .3 etc. etc. Kinda like a Warp Factor from Star Trek.

So with that in mind, that means it would take the Falcon normally only about 4 minutes of Hyperspace Travel,  plus whatever realspace time, to do the Kessel Run, but Han managed to get it done in just 2.25 minutes. Big Whoop. No one cares.

BUT in the Movie Solo, these scenes are several minutes long. But we can just attribute most of that to hyperspace. As i showed earlier, realspace travel offers no real savings in comparison to the scale hyperspace crosses.

SO now lets back track. Lets say he did that Run in 3 to 5 minutes of hyperspace, ignoring the realspace time. Seems plausible based on what we see on screen. Now we will use our known speed of the Falcon based on other ON SCREEN references, at 25k LY/day. That means 1041 LY/hour, meaning he had to travel between 52.05 to 86.75 light years in his Kessel Run.

This would make a Parsec between 4.34 Light Years and 7.23 Light Years in Star Wars scale, given that he covered 12 of them in that distance. That is 132% to 222% what a Parsec in relation to Earth is. Now using Pythagorean geometry, we can find out just how close to a star Han's parsec reference planet is.

Turns out that is only 124 to 206 million miles away from their star. For comparison, the Earth is 93 million miles from the sun. Mars is 129 million miles and the Asteroid Belt is 205 million miles from the Sun. That is 1.33 AU to 2.21 AU for our star wars reference point.

So not too extreme...

But while thats within the realm of possibilities...

Why would you brag so much about only being like a minute faster that the other guyn especially if once you come to real space, the real time eater in Star Wars space travel, you are pathetically slower than everything else. Your minute leg up over 99.9999% of the journey means nothing if it takes you 10 minites more than the other guy to do the the last .0001% of that trip.

The physics (or lack there of) of Star Wars: The Last Jedi (Hyperspace Kamikaze)

Let me first say, that I LOVED The Last Jedi. I think it is great. If you don't, then fine. But this is not the time or place to discuss whether the movie was good or not (though I probably have more posts coming on that). Now is the time how to, once more, explain how the latest movie RUINED ALL OF STAR WARS...

Needless to say, but... spoilers ahead!

A few Disclaimers

1- Let me reiterate, spoilers for the movie lie ahead, so if you haven't seen it, stop reading and come back after you do (go ahead and join us/follow us on facebook or twitter!)
2- The movie is AMAZING. Anytime here that I say that "Star Wars is ruined" I don't mean it literally.
3- I am not guaranteeing full accuracy of this. I do this just because I am really nerdy and think about these things... A lot of approximation and some rounding goes into this sort of math. I am not doing SCIENCE. I am writing a blog post. But I do try and make sure there is some "weight" to the numbers I do throw around.
4- And before you go "This guy doesn't know anything," or "I know physics better", I'll just say I have an MS in Applied Physics, so I have a decent grasp of this kind of stuff.

If you recall two years ago, I did a similar piece after the Force Awakens.

The physics (or lack there of) of Star Wars: The Force Awakens (Starkiller Base and the Solo Maneuver)

Let me say first you should probably read that, especially the part on the "Solo Maneuver". But in case you don't want to spend the time doing that I will sum it up here

1- Going Lightspeed through shields makes them useless
2- Even if "Hypserspace" allows you to not interact with matter, there has to be a transition speed between 0 and c (lightspeed).
3- Why slow back down? Why not just stay at .99c and run into things. Gives you LIGHT SPEED MISSILES.

So, I guess I predicted that didn't I... because that's EXACTLY what happened in Episode 8.

Vice Admiral Holdo takes her flagship, the Raddus (named after Admiral Raddus from Rogue One) and RAMS IT RIGHT INTO THE FIRST ORDER FLEET.

This. In space.

So four things to take away from this scene
1- This is the ONLY moment in Star Wars with NO SOUND. Everyone knows there is sound in Star Wars space! But seriously, its funny how this moment, despite every other flaw, actually does follow one real scientific truth. "In space, no one can hear you lightspeed kamikaze"

2- Why aren't lightspeed droid missiles a thing. SERIOUSLY. Even if they aren't that small. A-Wing sized I guess. That is big enough for a hyperdrive AND would be pretty devastating. Good enough to kill a Superstar Destroyer, good enough for me. Lets put it at  conservative 10 tons. That's as much as an F-16 fighter jet about, so seems good. So 9,200 kg ish.

Now I could go into alot more ballistics and impact physics. It's actually what I got my master's degree in. However, for simplicity here we are just going to go with the super simple equation for kinetic energy.

Next we establish what c is. Rounded up its about 300,000 km/s.

So going .99c puts us at 297,000 km/s.

Now do the math and we get 4.06 x 10^20 JOULES. Or 406 EXAJOULES. That's a lot of energy in that A-wing sized droid controlled missile.

So step that up to the Raddus. Extrapolating from some of the largest warships in the world, Nimitz Class aircraft carriers (100k tons-ish), I would put the 3500m long, 460m tall, 700m wide Raddus at about 1.5 x 10^11 kg. That's a lot of mass.

Rough math for its kinetic energy in the same situation, 6.6*10^27 joules. Or 6.6*10^15 terajoules. Or finally something manageable... 6,600 yottajoules. yodajoules? (1 yottajoule is 1 SEPTILLION joules).

The death star, well that operated at 225,000,000 yottajoules. So the Raddus ramming manuever is only 1/34,090th as powerful as the Death Star.

But that is still 17.36 TIMES MORE ENERGY THAN THE SUN PUTS OUT IN A SECOND. And we were AIMING IT AT A SHIP. For all its mass, the Supremacy is about one trillionth the mass of Alderann. So if Alderran was instantly obliterated by a weapon only 34,000 times more powerful, I think 1 trillionth the mass is no issue for instant obliteration of a weapon 1/34,090th the Death Star.

But even if it DID hit a planet, it would be a cataclsymic event.

To put this into perspective, a 1 megaton nuclear blast would be 418 Terajoules, making a 1 kiloton blast 4.18 terajoules. This would make the blast at Hiroshima about 63 Terajoules.

The A-wing hyperspace missile droid collision would be 6.4*10^6 times more powerful than Hiroshima. The Raddus is at 1.05*10^14 times more powerful than Hiroshima. A Turbolaser is suppossedly 200 gigatons around the time of the clone wars, so that makes it 8.36*10^19 joules, or 1.3*10^6 times more powerful than Hiroshima.

Directly comparing the two, the A-wing is 5 times more powerful than a Turbolaser and the Raddus is 7.9*10^7 times more powerful than a Turbolaser. And shields stop Turbolasers.

But for even more perspective, the Asteroid that killed the dinosaurs was only 1x10^9 times more powerful than Hiroshima. That's right, an the Raddus running into Earth at 0.99c would be equivalent of 105,000 Dinosaur killing asteroids...

Really makes you wonder if the Death Star was necessary after all... (hint, it wasn't).

Now in both these cases, the A-Wing and the Raddus, imagine that much force being transferred in an infinitesimal moment. That's ALOT OF FORCE. Makes the lightside and the darkside insignificant in comparison.

It wouldn't just cut the ships in two. It would OBLITERATE THEM. Nothing would have survived on the supremacy. Sure there are other articles out there saying they aren't sure it would go down the way it did in the film. I am hear to tell you that it MOST CERTAINTY WOULD NOT. And not for the same reason as that other article. They have no clue about hypervelocity impacts. Because the real killer here is the shockwave propagation through the Supremacy. And with that big of an impact at those speeds, it would be tremendous. Nothing would have been left of either ship.

Though nothing would have happened to the surrounding star destroyers UNLESS spall shot off at near light speed into them.

Basically, Hyperspace Missiles are the single greatest weapon that can exist in Star Wars.

To reiterate from my last Star Wars phsyics post, they have the added benefit of
-You can strike from ANYWHERE IN THE GALAXY
-Your enemy cannot detect you
-You are moving too fast for anything to stop you even if it could
-There are no (known) defenses for this. Han proved shields don't work, so what else is there?

3- Objects in Hyperspace must not interact with mass, and only energy some how?

So its established in Episode 7 that to get through the shield (an energy field) Han has to be in hyperspace. And we know that gravitational fields can rip ships out of hyperspace or prevent them from jumping into it from back ground lore and the cartoons (Interdictor cruisers people).

And Holdo looks like she is only ACCELERATING to Hyperspace in The Last Jedi, and not yet at it (thus why I did everything above at 0.99c and not 1.0+).

Bust most importantly, even if my math above is just rough approximations and doesn't fully encapsulate the complexities of light speed collisions, I think it does well enough at demonstrating the energy involved is ENORMOUS.

So even if not specifically used militarily, why is this not used by Terrorists? Or more to the point... why does it never happen accidentally.

All it would take is a miscalculation or a computer error and BAM, Coruscant is gone as some lowly junk goods trader plows into the planet for coming out of hyperspace 2 seconds too late. But that never happens right? You never hear of the planets that are vaporized by accident.

To expect all calculations across the galaxy are always perfect to avoid such accidents is just too much to assume. It would require ultra precise numbers, and incredibly precise locations... in a Galaxy KNOWN to have uncharted star systems. Beyond that, it would require the impossibility of a perfect, synchronized time reference point. But we are talking about FTL and interstellar distances soooooo that can't happen. Relativity says that the clocks will never match.

Also, those computers would have to be BEASTLY. And based on what you SEE in Star Wars... they don't have computers that powerful. I mean, they have to access the Death Star plans on Scariff in Rogue One with an Analog System. The schematics for the Death Star have all the resolution of late 1970s computer graphics (lol).

So if these accidents COULD happen, they WOULD have happened, and you would see A LOT more precaution in regards to Space Flight, particularly around Coruscant in the prequels. The fact that you don't means it can't be a concern. Meaning that once at Hyperspeed, objects cease to interact with each other physically.

Its like it must be a parallel reality or something they travel through, where you can go faster than the speed of light and yet not have relativistic repercussions, maintaining a bubble of reality around your own vessel in order to return to the proper time, covering vast interstellar gulfs of space in a fraction of time it would actually take even at the speed of light...

Sound familiar?

Last take away from that scene
4- The tacticians and military scientists of the Star Wars universe are idiots for not realizing any of this.