Saturday, November 4, 2017

A Rule for Shields from Descending Armor Class, Applied to Ascending Armor Class

I've been playing 'D&D 'ever since I was a young boy and found my dad's Dungeon Master's Guide on his bookshelf (the original, by Gygax).  I was still too young to understand a lot of it (Gygax opens with a discussion of uniform vs binomial probability distributions...), but I spent hours of days flipping through the pages, looking at the pictures and reading the descriptions of a fantastic world.  It inspired me to make my own games about exploring through planned dungeons with friends and having them use ability scores to get through.

By the time I was old enough to try to really figure out the rules, version 3.0 was out, which made a lot of changes.  One of the biggest was replacing the original Descending AC and THAC0 system with the slightly more intuitive Ascending AC system.  This system always just made sense to me, whereas DAC and THAC0 always seemed weird and complicated.  I never understood how DAC worked, and never really saw a good explanation of it, and so just never used it.  It was only recently, when getting into old school tabletop RPGs, that I decided to look up an explanation of how DAC and THAC0 used to work.

In the process, I found there are all kinds of debates about which is better, which frankly is stupid because unless you're using the original B/X table-lookup method (which does not correspond to any simple linear equation), then THAC0 and DAC is exactly identical to Attack Bonus and AAC.  Algebraically, one is just a different way of writing the same equation.

Let DAC = Descending Armor Class, AAC = Ascending Armor Class, AB = Attack Bonus.

In 1e/2e rules, where unarmored DAC is 10, to determine if you hit, you roll 1d20 and check if
1d20 >= THAC0 - DAC.
If it is, then you hit.

In 3.0/3.5 rules, where unarmored AAC is 10, to determine if you hit, you roll 1d20 and check if
1d20 + AB >= AAC.

Notice, if you use the conversion
AAC = 20 - DAC
AB = 20 - THAC0
then this latter method just gives
1d20 + 20 - THAC0 >= 20 - DAC
which, after you cancel the 20's and move the THAC0 over is just
1d20 >= THAC0 - DAC.
So both give the exact same thing.  (That's actually the condition you use to find this conversion.)

I guess the real argument is over which is easier to use.

I have always thought AAC is the most intuitive, because better should be bigger!  An AC of 200 sounds super tough, while an AC of 0 sounds like you have no armor.  That's what made the most sense to 8-year-old me, anyway; whereas I only understood the Descending system after growing up and getting a bachelor's degree in mathematics.

That doesn't mean DAC doesn't have some benefits, though.

The idea of the DAC system is that your armor class represents the chance to hit you, as opposed to a score needed to hit you.  Smaller AC means a smaller chance to hit you.

DAC works by effectively treating the wearer's armor class as a modifier to the attack roll, and has a constant DC of 20 for every attack -- so an attack roll could also be expressed as
1d20 + AB + DAC >= 20.
This, I think, makes a bit more sense of the Descending system.  The smaller DAC,  the harder it is to hit.  This is also a pretty intuitive way to phrase it.

It is also possible to easily phrase things in terms of "chance to hit" with the DAC system.  Calculate Attack Bonus as
AB = 21 - THAC0 + modifiers
Your chances to hit the target are
so if you have an AB of 3 and are trying to hit someone with DAC 4, then you will succeed 7/20 times, or 35% of the time.  This leads to a different way to run attack rolls, which is a hit on
1d20 <= DAC + AB,
so roll under or equal to the sum of DAC and Attack Bonus, consider a 1 (an "ace") to be a crit; a fumble is now a 20.  Of course, this requires calculating Attack Bonus differently (consistent with OE and B/X rules of DAC 9 for unarmored), which means the normal Attack Bonus from standard d20 rules is increased by 1.

At first glance it seems crazy, but after some thought it actually makes a bit more sense than the old method, since it correlates more directly with probabilities to hit.

One other cool flavor feature of DAC is that it makes a clear demarcation between natural and supernatural, as even full plate armor with a shield and high DEX only brings you to 0 DAC.  To get anything below 0 DAC, you have to have magical enchantments.  If a creature has a DAC of -4, it is immediately put into the category of otherworldly and you know to expect a difficult battle.  Whereas the equivalent AAC of 24 just isn't as neat.  It's just 4 higher than 20.  There isn't any clear, non-arbitrary line between what is naturally achievable vs. what is the result of powerful magic.

None of this is actually the point I wanted to address, though.

What I actually wanted to talk about is an interesting house rule I came across for shields that depends on the DAC system.  I saw this rule on stackexchange when looking for info on DAC.

The rule figures that shields get a lot of disrespect, only offering a single measly point of AC bonus.  In reality, shields were a crucial part of armed combat.  To make them a bit more awesome, this user made the house rule that a shield halves your DAC.

So if you are unarmored (DAC 10), your DAC with a shield is 5.  If you're wearing chainmail (DAC 4), your DAC with a shield is 2.   If you're in plate (DAC 2) your DAC with a shield goes down to 1.

It's a pretty neat rule idea.  You can see some of the limits, though.  For one, it seems way too powerful at higher DAC.  Someone with a DAC of 18 (representing I guess someone stark naked, bound at the ankles, with a target painted on them and a magic curse) gets lowered to DAC 9, the same as wearing padded armor.  For two, at higher AC, it stops working, and then starts hurting.  Someone with a DAC of 0 gets no benefit from a shield.  Someone with magical armor granting them DAC -2 is actually hurt by the shield, up to DAC -1.

Despite all that, though, it's not a bad rule.  It's simple, and makes shields a bit more special.

The original poster said this was one of the benefits of DAC, because there was no simple way to do this with AAC.  Which of course is wrong.  Doing the math on paper, this rule amounts to: halve your AC, then add 10; that's your new AC with a shield.

In an equation,
 New AC = 10 + 0.5*(Old AC)

The hard part (dividing by 2) is present in both, whereas adding ten just amounts to mentally placing a "1" digit in front of 1/2 your AC.  It's barely "math" and more like squinting.  If your AAC is 12, then half is 6, goes to 16.  If you AAC is 18, then half is 9, goes to 19.  It's basically the same difficulty as the original method.

Working this out, you will see corresponding limitations.  After AAC 20 (corresponding to DAC 0), a shield stops being useful and becomes detrimental, whereas someone with the miserable AAC of 2 (DAC 18) gets brought up to a whopping AAC 11 (DAC 9).

But, it still gives a neat take on the shield.  Most neat of all is that it suggests a way to grade shields.  This works for DAC or AAC, but I will just use AAC to illustrate.

Rather than all shields halving your DAC, you can instead say that different shields give a different fractional modifier.  The three that seemed to work best (numerically) were 2/5, 1/2, and 3/5 shields, which alter ACs as
New AC = 10 + 0.4*(Old AC)
New AC = 10 + 0.5*(Old AC)
New AC = 10 + 0.6*(Old AC)
I'm not exactly sure what to do with rounding (truncate, round up, round the way you learned in chemistry class?) and the original poster didn't specify and only used even numbr examples.  (The corresponding benefit to DAC, if frac = fractional benefit, is frac_DAC = (1 - frac_AAC), i.e. 2/5→ 3/5, 2/5 → 3/5).

A chart of how these work is as below (I use rounding down)
Old AC   0   1   2   3   4   5   6   7   8   9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
2/5 10 10 10 11 11 12 12 12 13 13 14 14 14 15 15 16 16 16 17 17 18 18 18 19 19 20
1/2 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22
3/5 10 10 11 11 12 13 13 14 14 15 16 16 17 17 18 19 19 20 20 21 22 22 23 23 24 25
This adds that bad shields (crappy wooden ones, say) not only give you less of a bonus, but they stop being useful sooner; whereas good shields (magical mirror shields, say) not only give you more of a bonus, but continue being useful even for higher ACs.

You could also decide that above the limit of usefulness, the  shields just give a static +1 bonus.

The limit of usefulness is calculated as 10/(1 - frac) rounded down.

The major problem is this really is not easy to do in your head.

The math is much easier when the multipliers are 1/something, like 1/4, 1/3, 1/2.  However, these cut off in usefulness far too soon (13 for 1/4 and 15 for 1/3 respectivly); though if you resolve to use a constant bonus thereafter, it may be worthwhile.  The table is
Old AC 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
1/5 10 10 10 10 10 11 11 11 11 11 12 12 12 12
1/4 10 10 10 10 11 11 11 11 12 12 12 12 13 13 13
1/3 10 10 10 11 11 11 12 12 12 13 13 13 14 14 14 15 15
1/2 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20

which carries up to just past where the shield "bonus" becomes detrimental.  Notice the bonus increases by 1 in integer steps or 5, 4, 3, and 2.

The cutoff of usefulness to certain shield classes makes some roleplaying sense.  If you are wearing rune-enchanted plate made of star-iron from the realm of Fey, but also carrying a shield made of tanned hide stretchd over a bone frame that you got back in the first dungeon off a liazardman -- then really, why bother with it?  It's time to throw that shield away and get a better one.  But if you have a shield made of the same rune-enchanted star-iron, then it also makes sense that this shield is awesome and contributes to protect your character even into supernatural AAC levels.

At the same time, if you've got nothing but a big solid moveable wall to hold up in front of yourself, you're going to rely on it an awful lot.  You can kind of see this, in that Greek hoplites wearing leather armor carried giant shields to battle, whereas the classic tourney knight in full plate wasn't above grabbing his opponents sword with his hand midswing.  And even if you're naked and bound at the ankles and magically cursed to absorb all thrown projectiles, ducking behind a piece of wood will still help you deflect a lot of the blows.

So I think an idea that works, using different shield classes, is to have the shield cut off when it cuts off, and provides no benefit to AC after that; not even a constant +1 benefit.

To put everything together: rounding down and cutting off, the table works out to:
Old AC 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
1/5 10 10 10 10 10 11 11 11 11 11 12 12 12 13 14 15 16 17 18 19 20 21 22 23
1/4 10 10 10 10 11 11 11 11 12 12 12 12 13 13 14 15 16 17 18 19 20 21 22 23
1/3 10 10 10 11 11 11 12 12 12 13 13 13 14 14 14 15 16 17 18 19 20 21 22 23
2/5 10 10 10 11 11 12 12 12 13 13 14 14 14 15 15 16 16 17 18 19 20 21 22 23
1/2 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 21 22 23
3/5 10 10 11 11 12 13 13 14 14 15 16 16 17 17 18 19 19 20 20 21 22 22 23 23

Beyond AAC 23, you need a really incredible shield for it to be worth anything compared to your crazy-powerful armor.

A 1/5 shield seems kind of worthless -- maybe this is an old oaken branch your PC picks up in desperation.  A 1/4 shield might be leather stretchd over a wooden frame or made lashed bones.  A 1/3 shield might be a simple wooden shield, made of a solid flat piece of lumber.  A 2/5 shield might be a banded wooden shield made of planks of wood fixed together by a metal frame.  A 1/2 shield can be a shield made of steel or other metal.  A 3/5 shield may be magical or of superb craftsmanship.

There are other ways to give shields back the respect their deserve.  You might consider damage reduction, and in particular the "Shields Shall be Splintered" rule.  These have the benefit of being a bit simpler to implement.

Or if you're not above some 6th grade Algebra at the game table (or look-up), then consider the option above.

Wednesday, October 25, 2017


test for commenting

Update: I think I figured it out.  Comments should work better now.

From my phone I can comment.  From my computer, I'm only able to  comment if I use a separate page for  comments.

Sunday, September 24, 2017

The Baker and the Beast

I have an idea for a movie.  It's a moving tale of passion and vocation.  I've pitched it to my wife and a few friends, and all agree, it's pretty brilliant.

Since it infringes on all kinds of Disney copyright, and since the premise is kind of ridiculous, it will never actually be made into a movie.  So I figured I'd just pitch it here.

The genesis.

So, I hate pop music.

I am very susceptible to having songs stuck on my head.  And I absolutely hate it. For this reason, I despise pop music with the burning fury of a thousand suns.  I will not enter stores playing pop music, because then I'll have these obnoxious jingles stuck in my head for months.  Solid months.

So I developed a coping mechanism.  When a song gets stuck in my head, I gradually deform the lyrics to make the song stupider and stupider, until it more accurately reflects the worthless string of noises it so truly is.

It's kind of childish, but it makes me feel better.  If I have to be infected with these memetic viruses from every store corner and coffee shop, at least I can mock the virus.  I'd mock the flu too, if I could.

Back to the movie idea.

I went to see Beauty and the Beast a few months ago when it came out.  They repeat the animated Disney version with the classic soundtrack, but in live action and with some slight tweaks to the story.  They seem to have attempted to answer some of the fan speculation questions that Cracked reposts every four months, like why the enchantress cursed all the servants for what the prince did, and they added a lyric here or there, but mostly the same story and same songs from my childhood.

One of the songs from the film got stuck in my head.  The opening song, "Bonjour," where Belle is walking through the village openly dsparaging the simple townsfolke as "provencial" for having to actually work for a living to support their families, instead of getting to read books all day and refuse to do chores.

The song isn't really as dumb or obnoxious as pop music, but it was in my head, nonstop for weeks.  And when I have an earworm eating my brain I start getting a tad resentful.  So I started changing the words to the song.

But by changing those words, I changed more than just the intro song.  I actually changed the direction of the entire plot, which lead to a completely different movie.  A movie called:

The Baker and the Beast

We open in a small town in post-Revolution France.  A girl stands outside and begins singing just as the sun rises, and people pop out of their windows to great the day with "Bonjour!"

The song begins "There goes the Baker with his tray like always..."

But then rather going on to talk about anything else, the song keeps following the Baker, talking about how awesome his bread is.  People are clamoring for it.

"I'm a baker that is true,
And baking's what I do!
Baking in this small provencial town."

The Baker is actually an exceptionally talented artesan who dreams of baking out in the great wide yonder, of expanding his craft beyond the usual French breads and pastries, but feels constrained by his town.  The townsfolk love him, praising him in song,

"Look there he goes the man who bakes like magic,
Something about how he kneads the dough
And it's flaky and its rare
And there's flavor here to spare
It's really quite incredible....

Eventually the Baker sets off for the next town over, looking for new flavors and techniques to try.  He wants to perfect his mastery of the craft.  But when wolves attack his carriage, he flees, taking refuge in a haunted castle ruled by a terrible Beast.

Long ago... or, I guess, maybe like ten years ago... the castle was the home of a terrible, spoiled, bratty prince who cared for nothing and no one but himself.  He was ill-tempered, vain, and selfish.  One day an enchantress came to the castle asking for shelter from the cold, and when the prince turned her away, she cursed the prince to become a terrible Beast, and the servants of the castle to be turned in to common household items.  The prince was to remain in such a state until he reformed his ways, until the gruesome Beast outside no longer matched the person inside.

The Baker is imprisoned by this Beast, until the servants come to learn that he is an artesan and a very skilled baker.  The castle is lying in ruins, but the servants hope that if the Baker can take over their kitchen and bring his exceptional talent and drive to the kitchen, more guests will start coming to try to food and maybe the Beast will develop better hospitality.

They invite the Baker to dinner and implore him to stay at the castle as the cook in a musical number, singing,
"Be our chef!
Be our chef!
Use our ovens to their best!"
Eventually the Beast finds out about this and is furious.  Until he tries one of the fresh-baked loaves right out of the oven that the Baker hands to him on one of those wooden spatula things.  The bread is steamy, and flakey, and the dough parts like butter in the Beast's hands.  It's the best bread he's ever eaten.  He's so impressed that he agrees to let the Baker sleep in a room in the castle and have free reign over the castle's kitchen.

It turns out the castle's kitchen is enormous, with all kinds of specializd equipment the baker has never even seen before.  It has stocks of ingredients from places in the world he's never heard of.  He's like a kid in a candy store.  He's like  an atypical bookish girl in a giant library.  The baker takes off, trying everything, a dash of this here, a dash of that there.  He's trying so many new things.  He's growing as a cullinary artist, and for the first time feels unrestrained by the small town where he used to work.

The Beast watches the Baker cooking, and his passion for the craft really moves him. The Beast has never cared about anything in his life in half as much as the Baker cares about making bread.  It's a strange thing for the Beast.  Why is this guy so excited about it?  How does he take such joy in it?

The Beast is curious, and goes from watching in the door to actually standing in the kitchen, untilfinally he asks the Baker to explain what he's doing.  The Baker starts to show him.  Eventually, after a few more days like this, the Beast asks if he can try kneading, and the Baker tells him to wash his hands and dive in.

The Beast isn't the best baker in the world, or even a remotely competent baker, but through this simple activity, something kind of clicks.  He'd been brought up in the lap of luxury, never even refilling his own cups.  But doing this simple work with his hands, he sees a pleasure in it.  When his first attempt at bread comes out of the oven and he sees something he made with actual value, his heart warms.  The Beast starts to understand something about passion in life, and vocation, and persuing excellence at what you do.

The Beast tries baking a few more times, but then moves on to other hobbies like wood working and finds himself more suited to it.  Each day, as he sees how hard it is to make an S-curve in a chair, he starts to appreciate more the luxurious mansion around him and the craftsmanship and care that went into adorning his castle.

While all of this is going on, by the way, the villagers have gotten worried about their Baker.  In particular, one man, Gaston, is concerned because he had been talking to the Baker about investing in his bakery.  Gaston recognized the Baker had exceptional skill, and wanted to use that skill to start a chain of bakeries throughout France with the Baker's recipes.  So he was trying to convince the Baker to accept him as a business partner for a hefty sum of money.

When Gaston learns that the Baker is actually at the castle baking for someone else, he whips up the villagers into a frenzy about the Beast and they march off to kill it.  A fight breaks out at the castle betwen the vilagers and the enchanted servants, but in the end the castle prevails and the vilagers are driven off.

The Beast, who sacrificed himself to protect the Baker, is magically transformed back into a human, now that he has learned the value of hard work.  The rest of the servants revert back to their old selves in their human bodies.  The Baker and Prince live on as friends in the castle, spurring each other to greater excellence in their respected crafts.  The Baker becomes the most famous baker in all of France, while the Prince becomes quite good with woodworking and even sees some demand for his furniture over in Italy.

Everyone lives happily ever after.  Except for Gaston, who falls off a high ledge and dies.

But everyone else lives happily ever after.

So, that's my movie.  What do you think?

Monday, September 18, 2017

Replies not working

I just want to apologize to people who have commented and I haven't replied.  For some reason, Blogger is eating my reply comments, so that after I hit "submit" the reply doesn't get saved to the server.

A similar problem also happens to people trying to comment on older posts with lots of comments.  I can't complain about Blogger, it being free and all, but I will need to look into my server situation and perhaps go with a different hosting platform.

UPDATE: I think the problem is my computer's browser (safari).  I tried updating all of my computer's software, but it still doesn't work very well with Blogger.  I have tried responding to some comments three or four times now, and this is really frustrating.

Sunday, September 17, 2017

I am a monotheist about Zeus

Growing up in the time I did, I have had plenty of chances to hear atheists -- on talk shows, PBS documentaries, classrooms, debates, YouTube videos, internet forums -- present their arguments, and I've heard almost all of them by now.  There are especially some arguments that get brought up rather frequently, and then keep getting repeated for years later.

There's one in particular I want to address, the "One God Further" argument.  I believe the argument originates with Richard Dawkins, but I have certainly heard Christopher Hitchens and others make similar arguments on stage.  This argument is that we are all atheists about most of the gods anyone has ever claimed to believe in.  I'm an atheist about Zeus, Hercules, Mithras, Minerva or any of these other figures.  Dawkins simply goes one god further than I do.

And so, to clarify this issue once and for all, let me just resolutely state that I am not an atheist about Zeus.

I'm really not.

I am a monotheist about Zeus.

My issue with Zeus isn't that he's clearly ridiculous and there's no evidence for him.  I mean, yeah, Zeus is pretty ridiculous and there's no evidence for him.  But that isn't really my objection to Zeus worship.

My objection to Zeus worship is that Zeus isn't the kind of thing that should be rightly called a god, or the kind of thing that should be worshipped.

I believe in one God.  One, singular.  No more, no fewer.

That number isn't just a coincidence.  The uniqueness of God is part of my belief.  I didn't begin with a big list of deities, then go on down the list checking them off in order, until it turned out I only checked the box for one.

"Hmmm... Athena... no.  Next."

"Okay, Achilles... lemme think.... nah."

"Next on the list, Odin.  I'm going to do with no here."

"Moving on: Jehovah.  Huh.... yeah, yeah, sure.  Why not, right?"

"Okay, next one up is... Ahura-Mazda.   Yeah... yeah, I'm not really feeling it, going with no...."

That didn't happen, and the difference between Dawkins and I is more than just a single checkmark on that list.

Now, if I know internet atheists, they are leaping up, shouting "Aha! So you admit it! You didn't even evaluate all the other gods! You just picked the one you heard of!"  But hold on, guys.  Lemme get to the end first.

Prior to the rise of monotheism, it was pretty easy to merge religious traditions.  Jupiter and Zeus are basically interchangeable names for the same "guy", and half the Greek gods usually get called by their Roman counterpart's name instead.  You go up to Germany, they called their thunder god "Thor"; go over to India and he's called "Indra."  If you met someone with a different pantheon than you, you either merged them by changing names, or you expanded both pantheons to account for the new gods.

Polytheism works like that because of what gods are in polytheism.  A god in polytheism is some powerful entity that has some manner of control over some area of life.  And there are a lot of areas of life.  If the people in Norway have a god of frozen tundra, and the people in Egypt have literally never heard of frozen tundra, then the first time an Egyptian hears about frozen tundra and its god from a Norseman, the Egyptian doesn't have to stretch his beliefs to imagine that such an entity exists up there in the Nordic cold.  Afterall, there's a god in the Nile River, there's one in the Earth, several in the sky, one in the desert -- why not one in the tundra, too?

If you ask a ancient Roman pagan if he believes in Thor, he might reply that in his country they know Thor as Juptier, and yes, he does believe in him.

If you repeated this very thorough list of deities to the ancient Roman pagan, he might reply that he hadn't heard of some of them, or knows some by other names, or thinks some are limited to areas outside of his home, but never that he categorically disbelieves in all of them.

I do.  I categorically disbelieve in all of them.  You don't need to list them, but it's neat that you did.  I categorically disbelieve in every single pagan deity on that list.  There are ancient cultures whose mythology vanished in the mists of time, the names of whose gods have been forgotten for millennia, and I also categorically disbelieve in all of those gods, too, without even having heard of them.  Some day in future people will make up new gods that no one has ever worshipped before, and I already disbelieve in those gods, too.

Why?  Because I'm a monotheist.  I disbelieve in all of these gods because I believe that God is absolutely unique in his nature from every single other thing in existence, and that these properties which make God unique are also what make God worthy of worship and worthy of the title "God."  The so-called "gods" of polytheism don't exist, but even if they did then I still wouldn't worship them because they aren't entities worthy of my worship.

The argument between Dawkins, Euthyphro, and me isn't really about the number of deities, as though the solution is to go out and count them.  It's about the nature of deity.  It's an argument about what makes something divine.

So what do I think, and how is it different from what Dawkins and Euthyphro  believe?

I believe that at a certain point, there was no such thing as time or space or matter or energy.  There was no universe.  There was no "before" or "after".  There wasn't even a void, as though there sat a giant blank nothingness waiting for something to come in.  None of it.  There was only God.  God preexisted everything, and then God created every single thing in the universe.  There is nothing in the universe you have ever seen that was not created by God.  The moon?  God.  Angler fish?  God.  Flesh-eating bacteria?  God.  Galactic clusters at the limits of our satellite telescopes?  God.

God eternally preexisted time itself, and created every single thing in the universe.

This entity that I call God is an entity entirely unlike anything else in creation.  He can't be compared to creation, or pictured in terms of his creation.   He's not a "guy in the clouds."  You can't draw God; you can't even really make analogies to God.  He is entirely, completely other.

God doesn't live "in the sky" as internet atheists are so fond of insisting.  God doesn't live "anywhere", because God exists in a way that the question "where" doesn't make sense applied to him.  God exists in a way that the notions of "future" and "past" are irrelevant.  God exists completely differently than we do, and so doesn't exist in any particular place.  He isn't an object in the universe -- not even an object in the sky!  All those atheist critiques of "skyfairies" and "sky daddys" and "invisible sky giants" are really good critiques of Zeus and Jupiter and Thor, but really, really crappy critiques of monotheism, because that isn't what monotheists believe in.

God isn't an object in the universe, because God created the universe and preexists the universe.  It is proper both to say (in one sense) that God is nowhere in the universe, and also correct to say (in a different sense) that God is everywhere in the universe.  Nowhere, in that he isn't an object like a tree or a person that you can find over there on that hill or that river or that planet; everywhere, in that God's nature and attributes permeate his creation and are visible to us here and everywhere in it, and that God has full awareness and power over the entire scope of the universe at every instant.

Let me be clear: I don't mean that God is just a really powerful person.  Like a dude who's really strong -- so strong he can't die, so powerful he can make everything.  The difference between God and man isn't like the difference between a bear and an ant, that the ant is just smaller and punier than the bear; it's more like the difference between the Law of Noncontradiction and an ant.  The difference is about category and nature.  God is in a different category altogether from his creation.   And God alone is in that category.

The most profound difference is that God is a se -- a term from the Latin meaning "of himself," defined well by the Catholic Encycopedia.  This phrase refers to God's complete self-sufficiency.  By that, I don't mean God  can take care of himself alone in a cabin in the woods and make his own candles from beeswax.  The point is more philosophical.

If you see a house in the middle of nowhere, you know that someone built the house.  A house isn't the kind of thing that just appears.  But much more than that, the house is made out of wood.  In order for there to be the house, there must be trees.  In order for their to be trees, there must be soil and water and sunlight.  In order for soil and water and sunlight there have to be stellar nuclear processes that bind protons and neutrons into heavier elements.  In order for their to be stellar nuclear processes there have to be physical interactions like gravity, the strong nuclear force, and electrodynamics.  And on and on, lower and lower, deeper under the hood.

A house requires an explanation, at several layers.  You can't just have a house without first having an entire universe.  Things like houses and neutrons aren't ontologically self-sufficient, and require appeal to other factors to explain how they exist.

God isn't like that.  He's the deepest under the hood it goes.  God is a se.  He's of himself.  God contains within his own being the cause and explanation of his being, and doesn't need anything else.

This is, by the way, why I object to the existence of things like the Flying Spaghetti Monster.  Not because I pick and choose what to believe in, but because the Flying Spaghetti Monster is a big ball of pasta with two meatballs.  Pasta is made of wheat; meatballs are made of animal flesh.  Wheat requires sunlight, water and soil and carbon dioxide; ground beef requires fields of grass and water and oxygen, along with butchers and meat grinders.  The flying Spaghetti Monster is made of things (and those things are made of other things), and so the FSM is itself just some thing in the universe like a rock or a hill or a tree or Zeus; not the a se Creator of time and space itself.

Pictured: A thing made out of things located in time and space
Not pictured: Aseity

Unless the spaghetti is all just a symbolic way of representing the Deity I described... in which case: sure, I believe in the FSM; I just think it's a very irreverent and disrespectful way of depicting the Deity.  But if that's all the FSM is -- just a blasphemous way of portraying God -- then it loses a lot of its zing, really.  It isn't even a clever blasphemy.

God being a se is the fundamental distinction between God and creation.  Nothing in the Universe is a se -- everything you've ever seen "rests" (ontologically speaking) on top of something else -- and many things you can't see likewise rest on top of something else.

The Bible expresses this truth about God in several places, but the most profound is in the revelation of God's name to Moses in the burning bush.  You've probably heard the basics of the story in Exodus (maybe in this scene from Prince of Egypt): Moses is out by himself, he sees a bush burning with fire but not consumed by it, and he goes to it to see what's going on.  A voice speaks to him from the burning bush, and tells Moses to go tell Pharoah to let the Hebrews go free.  Moses says he'll go, but he wants to know which god this is he's talking to, so that when he tells Pharoah that a god sent him, h'll be able to clarify which.  So he asks for God's name.  The name God tells Moses is "I AM THAT I AM" (traditionally written in small caps).  God tells Moses to say that "I AM" has sent him.  God identifies himself not as the sun god, or the moon god, or the wind god, or the sea god, or the earth god, or the star god, or the fire god.  Instead he uses the verb "to be".  God isn't any particular god; God just is.

That's what I believe about God.  Because I believe that God is that way, that means I also believe that anything that isn't that way, isn't God.

Zeus was born, and had three brothers.  He became king of the sky, not because he created the sky, nor because Zeus is the principle of the sky, but because his brothers let him pick his kingdom first -- the sky was already there waiting for him.  Athena sprang out of Zeus' head.  Aphrodite grew out of Cronus' severed penis thrown into the ocean.  They all began to exist, and many of them ceased to exist.  Pagan gods are things that can be born, and things that can die.  They are just creatures, just things, that exist in places in the universe.  None of them created the world -- they were all born inside the universe and just stumbled onto their respective domains.  They are therefore, by definition, not truly gods.

Notice, this categorical denial is entirely indifferent to whether they exist or not.  If you could find Thor and lock him in a scientific laboratory and have him shoot magic lightning from his mighty hammer Mjolnir, and verify for a fact that he's there and his hammer is shooting magic lightning, then that would be really interesting.  I would believe that Thor existed -- or something like Thor.  I still wouldn't think Thor was a god.  I still wouldn't worship Thor.

I wouldn't worship Thor because, you see, I'm a monotheist.

In a similar situation, it's entirely possible Dawkins would worship Thor, because there he has finally got the evidence he's been asking for.

The difference between Dawkins and me here is more than just a single check mark on a list of names.  It's a difference of fundamental philosophy.

Dawkins disbelieves in Zeus because Dawkins is committed to naturalism and empiricism, and so far has not uncovered compelling evidence for Zeus' existence -- or more likely, because Dawkins believes the supernatural is scientifically untenable and cannot exist.  I disbelieve in Zeus because I'm committed to monotheism, and creatures like Zeus are just that -- creatures, and not gods.

So I'm not an atheist about Zeus.  Dawkins doesn't just go one god further on the check list than I do.  I can't use my reasons for disbelieving in all the other alleged deities out there to also understand why atheists disbelieve in mine.  Because the reasons Dawkins and I have for disbelieving in all those pagan deities are categorically different.

So, I hope I've cleared things up.

I'm not an atheist about all these other gods and don't reject them all for anything close to the reasons Dawkins rejects them.  I'm not an atheist about them.

I'm actually a monotheist about them, and reject them because I believe in monotheism.

Monday, August 7, 2017

Easier way to replicate funky dice for DCC RPG using regular d6s

I recently came across the Dungeon Crawl Classics RPG and have been pretty hooked by the game since then.  The game introduces a lot of very interesting new mechanics into an over-troped hobby, most notably the magic system, the level-0 funnel, the Warrior's Might Deeds, and the dice chain, all of which bring back some of the spice of adventure and originality.

The dice chain is an original game mechanic.  While everyone who has played an RPG is familiar with a modified roll like d10+4 -- that is, roll a ten-sided die and add four to the result -- DCC offers an alternative way to express modifications in terms of changing the die you use, either up or down the dice chain.  The dice chain is
which, if you're familiar with gaming dice or 3D geometry, you realize includes a lot of shapes that don't exist.

In the D20 system of games (such as D&D since 3.5 or Pathfinder), whenever your character attempts something they need to roll for, you most commonly roll a d20 -- a twenty-sided die -- and add whatever modifiers, and try to beat a Difficulty Class for the attempt.  The DCs are usually such that, for instance, a DC 15 is a fairly difficult check.  If you are rolling a check for something you character does well, you will get a positive modifer that you add to your result (like +2, or +6), and if rolling a check your character does poorly, a minus modifier (like -4).  DCC offers an alternative way to think of bonuses and penalties in terms of the dice chain.  Rather than subtracting a modifier, they may ask you to instead roll a d16 to represent low training; or instead of adding a modifier, to roll a d24 or a d30.  Rather than just making your result higher or lower, it actually changes the probabilities by decreasing of increasing the range of possible results.  If the check is DC 15 and you have to roll a d16, success becomes very rare.  If you get to roll a d30 instead, then what is normally a fairly difficult task suddenly seems to your character like no problem.

While it's a brilliant mechanic of the game, after some reading online, I've found that it's also the single most maligned mechanic of the game and represents a pretty big barrier to people joining the game.  Not because they dislike the dice chain in itself, but because where the heck do you get a 16-sided die???

While such dice do exist, they aren't usually available at the Friendly Local Gaming Store.  The standards -- d4, d6, d8, d10, d12, d20 -- can be found at pretty much any game store or online for very cheap, whereas these so-called funky dice are usually only available from small boutique stores online, and aren't cheap.  If you live in the UK or Australia or elsewhere outside the US, then just the shipping costs can be way more than $20.  This represents a pretty big barrier to a lot of people to starting the game.  If you can't get the tools, you can't play the game.

Goodman Games needs to consider offering at least just the crucial d14, d16, d24, d30 to come with the book (or perhaps in a starter set), but until they do, let me offer some ideas on how to simulate funky dice so you can still play the dice chain, at least until you decide to get the actual dice.

There are some ideas on how to do this in one of the earlier sectons of the DCC RPG book, but frankly it's kind of complicated, inelegant, and involves things like ignoring a roll of 8 on a d8 (sure to go over great with players -- especially when they then proceed to roll a 1).

Here are my ideas on how to get around this.  While your Friendly Local Game Shop may not have a 16-sided polyhedron, they almost definitely carry blank d6s (or can get them to you very cheaply).  My work-arounds will involve only modifying blank d6 dice to simulate the funky dice.

Note, there are also dozens of dice roll simulators out there that will simulate any dice roll for you.  These are for people who really want to maintain the "feel" of rolling at the table, without springing for expensive dice.

Reduce the Dice Chain

Firstly, use a "truncated" dice chain.  Part of the reason for the funky dice is to make the transition between dice more smooth.  The biggest offender is the jump from d12 to d20, since the rest go in increments of 2.  The smaller funky dice add some extra smoothness at low numbers, then the d14 and d16 give some transition steps before the d20.  Notice, the jump from d16 to d20, and then d20 to d24 on the dice chain is already a step of 4.  So one possibility is to drop d14 and d7 from the dice chain, while still retaining a bit of smoothness.  (The reason for this is that these are impossible - or very hard- to simulate effectively).

So the new, truncated dice chain is
which, you're noticing, still includes dice like d3 and d16.  I'll tell you how to simulate this next.

Make a d2

The d2 isn't part of the dice chain, and doesn't come up very much in gaming for some reason, but we're going to make some anyway.  This is basically just flipping a coin.  Say that heads is 2 and tails is 1, and you have a d2.  If you'd like, get a wooden or plastic chit and write each side.  While that's as good a d2 as any, flipping a coin doesn't "feel" the same as rolling a dice.  If you have a blank d6, then you can make a d2 by marking it with three 1's and three 2's.  Now you can roll it like a normal die and get the same distribution of results.  Another option is to paint one half green (as an example) and the other half red, and treat green as a 2 and red as a 1 -- this allows you to also use it as a d3 by marking each face with a number, but more on that later.

Make binary dice

A d2 offers two options, and with two options, your standard geek should be reminded of binary.  A binary die is basically a d2, but with 0 and 1 instead of 1 and 2.  I will be calling this a db.  You can make it in any of the ways you make a d2, just number differently.  More effectively, use the coloring option above.  Make the 1s green and the 0s red -- or make the 1s green circles and the 0s red Xs, or the 1s blue and the 0s yellow, or make the 1's a smiley face and the 0's a frowny face.  Using coloration instead of specific numbers will let you use this as either a d2 or a db as needed, and will also let you use this as a d3.

Make a d3

A d3 is actually pretty standard -- some game shops may already be selling these as a d6 numbered 1-3 twice.  If you look closely in the d6s, you will might find some.  If not, they can be created very easily by modifying a blank die.  They can also be coupled to serve as a d2/d3.  I have one that I bought in a store, where half is red and half green, with the numbers 1-3 on the red half and 1-3 on the green half, which serves double duty.  You can also do this simply without modifying a blank die by just rolling a regular d6 and splitting up the range.  Either take 4-6 to be 1-3, or divide the result by two, rounding up.  If taking 4-6 to be 1-3, consider marking those sides as a reminder.

Make a d5

The rule book suggests rolling a d6 and re-rolling on a 6.  Besides being fiddly, one major problem with that is that 6 on d6 is the highest roll.  So a player rolls high, but rather than getting to savor this lucky stroke, they instead have to roll again.  You could avoid this by rolling d6-1 and re-rolling on a 0.  It's the same thing, mathematically, but now they don't feel as bad re-rolling that 1.  But it's even more fiddly now.

This is actually pretty easy, though.  Roll a d10, and take 6-0 to be 1-5.  Or roll a d20 and take 6-10, 11-15, 16-20 as 1-5.  Consider marking those ranges in a different color as a reminder.  You can also roll d10, divide by 2, and round up; or roll d20, divide by 4, and round up.

Make a d7 and a d14

I have no idea how to get this one with dice.  The problem is that 7 is prime and 14 is just 2x7.  This is why I considered dropping them from the dice chain.  If you have a d14, then a d7 is the same procedure used to get d3 from d6, or d5 from d10.

While they can't be effectively simulated with dice (the DCC suggestion is quite fiddly) they can be simulated with other means that were used back in the heyday of RPG gaming during the Great Dice Shortage of '79.  These include spinners, or drawing numbered chits out of a bag.  Another possibility is to make a spinning top/dreidel/teetotum numbered 1-14.  You can get a normal top and -- as evenly as possible -- square off the top edge into 14 notches.  If you go with chits, a spinner, or a top, then the d14 is the only one you need to make, as d7 is then just 1/2 of d14, and the rest can be made with d6s.

Or just consider dropping d7 and d14 from the dice chain.

If you follow the rule book's suggestion for the d7 to use a d8 and re-roll on an 8, then take my suggestion and instead roll d8-1 and re-roll on a 0.  There still isn't any non-fiddly way to get a d14 without rolling d16 or d20 and dropping lots of rolls.

Make a d16

This one requires the binary dice.  Make four dbs.  You will need to make all four visually distinct.  You might have four different base colors, or use four different coloration schemes (viz. one is red numbered 0,1, another is yellow numbered 0,1; or, one is red/green, the other is yellow/blue; or more clear, one is labeled 1000, 0000, the other 0100, 0000, the other 0010, 0000, then 0001,0000).  With these, we are going to create a binary number between 0 and 15.

The logic is similar to the d% by rolling 2d10.  If you understand rolling a tens place with one d10 and the ones place with another d10 to get up to 100, then you should be able to understand rolling four db to get up to 16. When you roll d% from 2d10, then you usually specify, say, the red die is tens, the blue ones.  Or, nowadays, a lot of d10s are numbered 10,20,30,...90,00 to specify they are for the tens place in a d% roll.

The distinction in the four dbs is the same here, except we're distinguishing binary digits.  So the red dice is the 1's place, the blue dice is the 2's place, the green dice the 4's place, and the yellow dice the 8's place (for example).  In this way, you can get d16 by rolling four db, interpretting as binary, and taking 0000 as 16 (similarly to how 0,0 with d% is takn as 100).  Line them up in order, and then the conversion from binary to decimal is as follows:
0001 -  1
0010 -  2
0011 -  3
0100 -  4
0101 -  5
0110 -  6
0111 -  7
1000 -  8
1001 -  9
1010 - 10
1011 - 11
1100 - 12
1101 - 13
1110 - 14
1111 - 15
0000 - 16
Now you have a d16.  (Many of your players will already know this conversion table cold, this being a game by and for nerds).  Consider writing the correct order of the dice down on paper in clear view (e.g. yellow, green, blue, red), perhaps with a visual aid showing their correct order by color, so debates of which is which don't break out; draw squares of the appropriate color on paper in order and have players place the appropriatly colored die on each square.  Numbering with all the zeros (as in 0100, 0010, etc.) also works.

You could also just roll one db four times, starting at 8's digit and going down.  imagine the tension when three 0s come up before the final roll... will it be 0 and give a crit, or a 1 and give a fumble...?

Make a d24

This one is probably the most complicated of the suggestions.  There are two standard shapes for d24, one of which is basically a d6 with square-based pyramids glued onto each side.  That's the one we are going to simulate using a marked d6 and a d4.

Get a blank d6 (preferably a larger one), and divide each face into trangular quarters.  In the central corner of each triangle on each face, write a number 1-4.  Now fill in the numbers 1-24 in each triangle.  The d24 is simulated by rolling the marked d6, then rolling a d4 to determine which of the triangles from the shown face is the result.

The trick here is *how* you put the numbers on the faces.  You want to spread them out as evenly as possible, preferably so that the sum of the numbers on each face is as close to equal as possible.  Might take some thinking to get right.  One possibility I worked out is shown here, so that each face sums to 50 and each opposing triange sums to 25.  The pips are used to indicate the d4 roll for that face.  Since each number 1-24 has only one possibile roll, this gives the same distribution as rolling a d24.
If necessary, cut out and fold over d6 t o see how this fits together

Another obscure option, using the same dice, is to work in heximal notation.  This will probably be way more conceptually confusing to your players, but would work.  Roll d4-1 to represent the 6s place, and a standard d6 as the 1s place.  While binary gets used frequently in computer science, so that the binary d16 not much of a stretch, heximal notation is pretty much useless, and mostly just a neat footnote after learning binary and hexadecimal -- so even most big-time nerds will still get tripped up on heximal notation.  Marking a blank d6 is probably the easier route.

Make a d30

If you get how two d10s can be a d%, then you can understand that a d30 only needs a d3 and a d10.  Consider making a special d3 numbered 0-2 instead of 1-3, and take a result of 0,0 as 10, 0,1 as 1, 1,0 as 20, 1,1 as 11, 2,0 as 30 (and the rest in the obvious way).  This isn't very different from the suggestion in the rule book, except that by labeling the d6 0-2, you make it a bit more obvious.


That's it.  Using only blank d6s from the Friendly Local Game Shop, you can make d2s, d3s, and dbs, and most of a d24, which, together with the "usual" polyhedral dice, can simulate the same rolls as the real thing.  The d14 remains more elusive still, but its place can be dropped from the dice chain without too much shock to the system, if absolutly necessary -- if a d14 is called for, go down to d12 or up to d16 instead.

I think these rolls are a bit less fiddly than the suggestions in the DCC rules book.  The binary dice for d16 probably isn't conceptually simpler, but it involves a lot less rerolling on high rolls, and has the benefit that the result is your result (just in a different number base system).

I should note again at this point, that every one of these can be simulated on a computer without needing to mark any dice at all.

They can also all be simulated with numbered spinners, bags of numbered chits, or with a numbered spinning top/teetotum (a d10, for instance, is just a sort of two-sided top, and the standard 14 and d16 in most DCC dice sets are likewise two-sided tops).  If you have access to wood- or metal-working equipment, you may find the numbered top method to be a more effective method for all of these; just divide the top circle into the proper number of sections and file it down.

All of these are methods for generating uniformly distributed results in the desired ranges.  The numbers generated will have equal probability for each number, as though they were rolled with a fair dice with the desired number of sides.

This should at least help get you started in DCC, at least until you decide if you'd like to shell out the extra money for the funky dice.

If you decide to buy the funky dice, note that d14, d16, d24, and d30 are the only ones you really need, with the lower funky dice being readily generated from these and the standard polyhedra by halving the result.

Hope it helps potential DCC gamers get over that hurdle.

Friday, July 28, 2017

Learning Fortran is a waste of your time

Suppose you are an advanced student of physics, and you're just beginning your first research experience with a new professor.  You're excited about the opportunities this means for your future, fascinated by the implications of the research, and anxious to please.  Your professor tells you you need to run a computer simulation, and this is also exciting; you've never used a computer as a computer before -- usually just as an internet browser.  To get you started, he points you to a reference text with some sample code, or sends you one he has on his hard drive somewhere.

This code will be written in Fortran.  They all are.  All legacy codes are Fortran.

So what is Fortran?  Fortran is a high-level programming language designed back in the 50's.  Here "high-level" means that it is not assembly language, and the programmer does not directly interact with machine elements like bits, bytes, or memory addresses, though Fortran is much "lower-level" than most modern languages like Java or Python, meaning it is only just a step or two above machine code.  The name "Fortran" is short for "Formula Translation," as the language was intended to more directly translate a mathematical formula into computer code; Fortran allowed, for instance, an entire mathematical expression to be written out as a single line of code, as opposed to assembly, which would require multiple lines of register swapping and simple operations to acheive the same result.

You'll get the sample code and look at it, and it will be completely incomprehensible.  They all are.  All Fortran codes are incomprehensible.

Why is this?  There are a lot of things that contribute to the issue.