Wednesday, August 3, 2022

Anti-THAC0 Attack Mattrices

Anti-THAC0 Attack Matrices

The Path of THAC0

Before it was D&D, it was called Braunstein, and was a miniature wargame (like Warhammer) but with special focus on individual hero units who gained special equipment and levels of experience as the war campaign progressed.


In these days, the word "dice" meant normal, cubical six-sided d6 dice. So when Dave Arneson, the first DM, needed a mechanic to resolve hand-to-hand single solider combat, he needed a way to compactify all of the complicated reality of damage done by a man with a heavy piece of metal in his hand trying to strike another man bound in metal plates, and he had to use six-sided dice to do it.

Single-soldier war games

Fortunately, Gygax and Perren had recently published their Chainmail fantasy battle rules, which included a very handy table for single combat. War games were played with painted miniatures. Each miniature clearly held a weapon, and clearly wore a form of armor. The Chainmail man-to-man matrix relates the odds to hit each class of armor (mail, plate, etc) for each class of weapon (pole arm, axe, etc.), based on a roll of 2d6.

So look at the particular weapon the figurine is swinging, the particular class of armor the other figurine is wearing, find the intersection on the matrix, then roll 2d6 and beat that number to hit.

from Chainmail, 1971

If you look at the matrix, you'll notice some things. One, it should now be clear where "studded" armor came from -- it's a visual description of a figurine wearing brigandine. Two, either there is a typo in the pole arms row, or they are impossibly (and ahistorically) bad at hurting plate armor. Three, some weapons are better at some armor but worse at others, and this is nonuniform. Notice the easy time daggers have against unarmored persons but impossible odds against plate; and compare to the flail, which does not strike the unarmored as easily, but is otherwise adept at hitting everything. Four, there are no numbers given to armor class, but a name -- it's the class of armor the figurine is wearing. The weapon class does have a number, which is a rough rank-order of length from shortest to longest.

There is also a section of the rules in Chainmail describing combat procedures. Defenders with a significantly higher weapon class (meaning longer weapon) always get to strike first on the first combat round, but after that the benefit is always to the lower-class weapons. A dagger wielder, for instance, gets to make three attacks against the pikeman's single attack -- and each dagger strike is equally as lethal as the pikeman's attack.

None of this is terribly accurate, but it's a first step to include man-to-man combat into a war game.

From war games to roleplaying games

When it was turned into D&D, the game began using a d20 to resolve hits, and weapon classes vanished. Armor classes stayed, where again armor class is a category: plate; plate+shield; leather+shield; etc. Instead of weapon being essential, your character level was important. All weapons were basically identical; hit the same, did the same damage, etc. Magic swords struck as though by the next level tier. Pole arms were slower... but had identical to
-hit odds and damage, raising the same obvious question of why using pole arms at all when daggers are clearly superior.

OD&D rules, taken from tametick

It is clear the matrix has been made more uniform, in that armor types have a clean linear progression from no armor up to plate and shield in each of the level tiers, with the target number going up by 1 as class decreases (better armor). From one level tier to the next, all numbers uniformly drop by 2 until the minimum of 1 is reached. The exception is for level 16+ (close to godhood), where a 1 is sufficient to hit most ACs.

By the time of AD&D it was even more uniform, with AC a true abstract numerical value divorced from armor category, spanning from 10 to -10. The only non-uniformities are the "repeating 20s" on the sides. All notion of grit and granularity has been abstracted away. This is the fighter to-hit matrix. Wizards have their own matrix, equally as uniform but all the numbers are higher; it is this matrix but all rows shifted down.

1E attack matrices, as in original DMG

From tables to equations

The wizard and fighter matrices match up by just shifting the matrices up or down. Similarly, the distinct rows in the fighter matrix all map to each other by just shifting up or down.

Shifting the rows up or down is the same as adding some amount to the AC.

Some intelligent person realized this means you only need a single row in this matrix. If you know what number you need to hit some AC, then to hit the next best AC, you just add one to that number. To make the math somewhat easier, memorize just the row for AC zero. If you need an X to hit AC 0, then you need a roll X-Y to hit AC Y.

The roll you need To Hit AC 0. This is the infamous THAC0.

You can just learn the single number, your THAC0 at current level, and completely drop the attack matrices. Now you only need the equation.

Your THAC0 decreases as you level, which means it becomes easier to hit things. Lower AC is better, just as lower THAC0 is better. But that's confusing, and requires subtraction. Why not use addition and let higher be better?

The Core Mechanic

Believe it or not, it took two decades for D&D to finally adopt ascending AC (so higher AC is better armor) and replace THAC0 with an attack bonus (so higher bonus is better chance to hit). By the time they did, it was 3rd edition, and the game now coalesced around the Core Mechanic we know today: roll 1d20, add any modifiers, and meet or beat the AC.

The success of every task, from battle to lock-picking to song-playing, is expressed in the form

Pr(success) = 5%*(20 + bonus - DC).

That is all we can ever have.

What began as a chaotic, fluctuating matrix turned into a uniform matrix, then turned into a simple linear equation, then into the Core Mechanic. And that is basically where RPGs are today. We no longer use the word, but the d20 mechanic is along the path of THAC0.

Smoothing, simplifying, unifying led us down this path. We are now in a place where it is difficult to imagine deviating from the d20 Core Mechanic. Even Indie RPGs trying to snub their noses at 5e end up essentially reproducing its gameplay.

To truly escape the monotony of the Core Mechanic, let us walk back up the path we took, and try another path.

The Path of Anti-THAC0

We begin again with the single combat melee matrix from Chainmail, reproduced here:

AC unarmored leather shield only leahter+shield mail mail+shield plate plate+shield
dagger 6 7 8 8 9 10 12 12
hand axe 7 7 8 8 9 10 11 12
mace 8 8 8 9 8 8 7 8
sword 7 8 8 9 8 9 10 11
battle axe 8 8 8 8 7 7 9 10
morning star 6 6 7 7 6 7 8 8
flail 7 7 7 7 6 7 6 7
spear 8 8 9 9 10 10 11 12
pole arms 6 6 6 7 7 8 9 10
halberd 8 8 8 7 6 6 7 8
2-handed sword 6 6 6 6 5 5 6 7
mounted lance 5 5 5 5 6 7 8 9
pike 8 8 8 8 8 8 9 10

This matrix isn't the one we want to use (flails are absolutely not God's gift to fighters), but we want to use a matrix like this.

Using a matrix allows us to express any kind of relation between armor and weapon and level --- not merely simple linear equations, but quadratic, exponential, sinusoidal, whatever. Rather than smoothing and simplifying the table, let's build off the philosophy of it, and accept unpredictable relations between to-hit odds, armor, and weapon class.

In D&D, the characters gain experience. We expect more experienced fighters to be more effective at hitting. So the simple matrix of Chainmail might work well for the level 1 soldiers it originally represented, but needs to expand beyond this.

The level 2 matrix will have different numbers, but is otherwise similar. Now imagine stacking level 2 on top of level 1, then level 3 on top of level 2, etc. We end up forming a 3D cube of numbers.

Then different slices of the cube would give:
  • for a given level, target roll for each weapon to hit against each armor
  • for a given weapon, target roll for each level to hit each armor
  • for a given armor, target roll needed for each weapon at each level to hit it
I think the first two are the most useful. The player character sheet can retain a matrix of weapon class vs armor class for the PC's current level. Whenever the PC gains a level, update the matrix. In addition, unique or magical weapons can be printed onto index cards, listing the name, properties, and also including the level vs. armor matrix for this particular weapon.

Scaling in attack effectiveness seems like a fighter thing. I don't know why a wizard, cleric, or thief should get better at fighting. Let's say only fighting men and dwarves (maybe hobbits) get new attack matrices. It is a class feature specific to fighters.

In principle, fighting men and dwarves could even have their own attack matrices, so that e.g.. dwarves are more effective with hammers and less effective with daggers. But this is becoming overkill. We will use the same attack matrices for humans and demihumans.

Matrices remove crunch

THAC0 is crunch. Matrices remove crunch. The anti-THAC0 core mechanic is: roll 2d6, look on the table, compare to the table. You do not need to track STR and level bonuses, DEX bonuses, damage type vulnerabilities, or any of that. You roll, you look.

The only mental effort involved is looking for the row/cell intersection. Is this really more mental effort then addition/subtraction and bonus tracking?

Matrices can express varying weapon difficulty

Fighters won't necessarily progress with all weapons uniformly with level. For instance, a pitchfork isn't the sort of weapon one improves with much. You stick 'em with the pointy end, and that's about it. A peasant can use them about as well as a knight. That doesn't mean pitchforks are particularly great in the hands of peasants or knights.

The weapon matrix for a pitchfork might look like this:
AC unarmored leather shield only leahter+shield mail mail+shield plate plate+shield
level 1-3 8910105101313
level 4-5 7999591212
level 6-7 7989581212
level 8-9 6878571112
level 10 6866561010
The logic of the table:
  • very high levels might get better at jabbing than others, but overall progression is slow
  • defeating a guy with only a shield does sound like something a more experienced fighter would be able to handle better
  • mail has tiny gaps, and piercing weapons can often penetrate these gaps, so mail is susceptible to a pitchfork
  • mail and shield can't be worse than just shield by itself
  • plate is impervious to a pitchfork, unless you are skilled enough to hit exactly right
We could compare this to a weapon like a two-handed sword, which in the hands of a peasant is little better than a sharpened stick, but in the hands of a knight is a powerful weapon. The weapon matrix for a two-handed sword might look like this:
AC unarmored leather shield only leahter+shield mail mail+shield plate plate+shield
level 1-3 578910111313
level 4-5 4678891212
level 6-7 3456681212
level 8-9 3334451012
level 10 2223341010
The logic is as follows:
  • anyone swinging a sword at an unarmored man is probably going to kill him
  • at extreme levels, cutting flesh and cutting animal hide are basically the same, and are very easy
  • mail is effective at blocking slashes, but experienced swordsmen can learn to exploit weaknesses
  • shields are no match for an experienced swordsman
  • plate is essentially impervious to swords, except to the very skilled

This shows how matrices could be used to give non-linear, non-uniform level progression stats for different weapons.

Matrices can express weapon specialties

I've been treating plate as somehow impossible to hit, but now consider a weapon like a warhammer, which is specifically meant to damage plate:
AC unarmored leather shield only leahter+shield mail mail+shield plate plate+shield
level 1-3 881010810911
level 4-5 779989810
level 6-7 66886879
level 8-9 55775768
level 10 44663467
The logic here:
  • a warhammer is meant to pierce armor, and views hide or plate or mail as equally piercible
  • a warhammer is not meant to pierce a shield, so shields are effective defenses
  • plate is more difficult to pierce than mail
To go completely crazy, consider a magic sword, which cuts through all materials and can only be stopped by catching it on a shield first:
AC unarmored leather shield only leahter+shield mail mail+shield plate plate+shield
level 1-3 11551515
level 4-5 11551515
level 6-7 11551515
level 8-9 11551515
level 10 11551515
The logic here:
  • anyone swinging this swings it just as well, with or without skill
  • armor is irrelevant
  • only a shield can catch it, and even then odds are high the shield is negated anyway
(I do not recommend giving this sword to any characters in a game.)

Matrices create strategy

In D&D, there is very little difference between a maul and a battle axe. Attack bonuses are the same, damage die are the same, damage bonuses are the same. The maul might do double damage against a stone golem and the axe double damage against a flesh golem, but overall the difference is so rare that it is not worth lugging both a maul and an axe around everywhere.

Real medieval combatants carried several arms. A pole arm for charges, a sword for up-close battle, a warhammer for damaging armored foes, a dagger for grappling. They carried these because some weapons were efficient, others weren't, depending on how the enemy was armed.

Real medieval combatants took time to strap many peices of weighty metal plating all over their body. Metal gloves, metal greaves, metal shoes, metal skirting, metal breastplates, metal arm covers, all of which needed to be strapped in place by someone assisting. They did this because, covered in armored plating, they became nearly impervious to all but specialized weapons or incredibly well-aimed blows.

Matrices, which can easily capture the different effectiveness of weapons, helps recapture this notion of strategic choice of arms.

The downsides of matrices, and solutions

Attack matrices have downsides. Obviously, or we'd never have left them.

Matrices can't exist in your head

The simple linear equations of the Core Mechanic can be computed on the fly in your head in almost no time, requiring memorizing only a single number (your total bonus with this weapon). Tables require space (either physical space, or monitor and hard drive space), they require look-up (looking up the table and then looking up the correct cell), and they can't be predicted. Even the single, simple table of OD&D was pushed down the path of THAC0 to make gameplay faster and simpler.

The matrices could be memorized, but that's unrealistic.

Only one row of the matrix is needed at a time, the one corresponding to the PC's current level. To avoid the mental energy of lookup, the needed row of the attack matrix should be printed on a character sheet or other clearly visible, central location.

Proliferation of matrices

Proposing a distinct to-hit matrix for every weapon, with varying level progression and varying damage per armor class quickly leads to too many tables. It is also a burnout for DMs, who have more work to do just to give out a new weapon or suit of armor.

Special to-hit matrices then should be for special weapons. For all normal, mundane weapons, have a single matrix. Below is my version, adapted form Chainmail but with some variation:
AC unarmored leather shield only leahter+shield mail mail+shield plate plate+shield
dagger 7 8 7 8 9 9 12 13
hand axe 6 7 8 8 9 10 11 12
club 5 6 9 9 8 9 13 13
mace 8 8 10 10 8 10 9 11
sword 5 8 9 10 11 11 13 13
2-handed sword 5 7 8 9 10 11 13 13
battle axe 8 8 8 8 9 10 11 12
spear 8 8 9 9 10 11 11 12
poleaxe 7 7 8 8 8 9 8 9
pole arms 8 8 8 9 9 10 11 12
pike 8 8 8 8 9 10 11 12
mounted lance 5 5 5 5 6 7 8 9
I'm not proposing these as the set of numbers, just as an example.

On this table, fighters add a simple level bonus to their roll. A little bonus goes a long way on 2d6, so I recommend being sparing with any bonus. Perhaps fighters should roll:
  • 2d6
  • d6+d7
  • 2d7
  • d7+d8
  • 2d8
increasing with level.

All classes except Fighter (and possibly Dwarf) roll on this matrix with no bonus. On weapon-specific tables, they either roll on the level 1 column, or possibly even just roll on the standard table for the same weapon type.

Rather than mace and morning star categories, they are club and mace. A club is any purely blunt bluedgeoning instrument, while a mace is any blunt weapon with spikes or flanges affixed, intended for piercing or destroying armor. This category includes morning stars. Flails have been removed; medieval flails, if they existed, were mostly bludgeoning implements, as clubs; but if you want spikes on yours, use the mace row. The category of pole arms includes halberds, along with war scythes, billhooks, etc. Separate categories are listed for spears, pikes, and poleaxes, due to their importance in different aspects of medieval warfare. A battle axe is a Dane axe, bearded axe, or other such implement requiring two hands but with a haft shorter than a poleaxe.

Pikes are really intended to battle against cavalry, and the mounted figure columns aren't shown here. This is perhaps an oversight on my part, as it is certainly reasonable to consider certian classes of monsters (and not only centaurs) as roughly equivalent to fighting an armored man on horseback. For instance, Chainmail counted a Balrog as two heavy horse. You would imagine pikes would serve a similar usefulness against such monsters.

You will notice that plate is incredibly hard to strike. That's because it is. They wore it for a reason. This should be taken into account in armor prices and availability. Plate requires specific tailoring to an individual, which should be extremely expensive, requirng a professional armorer and apprentices working for several weeks. Even if found in a dungeon, it needs to be fit by an armorer, or else it counts as mail.

A future addition might be a distinction between suits of plate, and mere plate pieces as armor, such as only a breastplate. It is really only a suit of plate that deserves such impossible odds of damage.

Not represented by these tables are considerations such as weapon range and differing weapon damage dice. A weapon might have a harder time striking, but make up for it by carrying a larger damage die.

These are the anti-THAC0 attack matrices. Instead of simplifying mechanics, they deliberate invoke more complexity through tables. They do not require mental math, but do require table lookups. They allow for strategic weapon and armor choice, and give fighters an additional combat advantage over other classes. Not only do fighters have more choices for strategy, they also become more proficient, using new tables, as they increase in level.

Saturday, July 9, 2022

Seiges & Sappers: the D&D from a parallel universe without Gygax


A little while ago, someone posted this blog post asking this question:
"A game designer from a parallel dimension with no D&D nor Gygax is tasked with designing a game supporting common OSR principles. What would such a game look like?"
The original intent of the question was to remove deadweight mechanics form the game. Ideas that started with Gygax and early versions of D&D, that no longer make sense, but that have stuck around because of their historical inertia.

As an example, clerics as PCs and wizards who can't heal. It would make sense for wizards to have healing magic, and the only reason they don't seems to be to stop them from intruding on the cleric's space. But why is there a cleric in the adventure to begin with? Because one of Arneson's friends wanted to play Van Helsing from the Hammer movies while they were fighting a vampire named Sir Fang (yes, that was really the vampire's name) . That's why there is a cleric class in D&D, and it continues to exist because of inertia.

Remove that history and re-make the game again, and you'd probably drop clerics and give wizards healing spells.

But I was actually more intrigued by the literal wording of the prompt. A parallel dimension with neither D&D nor Gary Gygax. What is this dimension, and what kind of game can come out of it? Let's imagine a universe where we are making the first roleplaying game, where D&D has never existed, and where Gygax also doesn't exist. What does the first roleplaying game out of this universe look like?

What About Arneson?

The first and obvious answer is that this would be Arneson's Braunstein game. The history of D&D has many sad turns, and one of those is how Arneson was pushed out of the game he co-founded. Braunstein was the earliest role-playing game. It was still mostly a wargame and played with wargaming rules, but had a focus on individual soldier units who persisted from battle to battle. Arneson used a collection of house rules and pointed referee calls to adjudicate the entire game, cribbing notes from various sources. But one of those sources was Chainmail, a set of rules for miniature wargames with medieval and fantasy armies, written in part by... Gary Gygax.

Because there is no Gygax, there is no Chainmail, and Braunstein as Arneson once played it can't exist. A very similar game can, but not the exact game.

We can see from this example how the lack of Gygax has more implications than just the lack of the original DMG.

The Wargame Roots of the Hobby

The challenge now, in this world without Gygax, is to task a "game designer" with creating a version of D&D. But what even is a "game designer"? To do this thought experiment right, I think we have to first explain how we choose a person to be a "game designer", and how the designer even knows what is it they're being asked to design.

Historically, D&D developed out of wargames. What began as games played on a table with hundreds of tiny tin soldiers rolling dice to fire at one another, gradually began to focus on a few hero units. Soon it was only about those pieces. One battle took them through some underground dungeons of a castle, and the players enjoyed exploring it so much that it became its own thing. However, that doesn't mean that's how role-playing games have to develop in every universe. Let's think of some alternatives.

One alternative would be a board game designer. This gets at the mechanical side of RPGs. There are many board games today rivaling the complexity of D&D or war games in terms of mechanics. But board games at the time of D&D are things like Candyland and Monopoly. There is a board game called Dungeon! that was made with inspiration from Arneson's games and is probably the closest look at what a D&D based on board games would look like without Gygax. The board represents rooms in a dungeon with each space a flagstone, and players move their meeples through the dungeon opening doors and fighting monsters. Treasures and spells are represented by cards or tokens, you roll a die to move in the dungeon, and you draw an encounter card at each room. It might eventually evolve into something like HeroQuest.

Another alternative could be actors from a radio show. This gets at the narrative/simulation side of RPGs. We ask the radio show actors to improv, pretending to be knights in a dungeon. Keep in mind, the concept of "knights in a dungeon" makes no sense at this point, as D&D has not been invented. Mechanics would not be the same, because rolling to hit isn't acting. Tracking initiative isn't acting. You could introduce a random element, but it would more likely be drawing situations out of a hat. Not rolling for damage. It would be a "game" in the sense the players would be "playing" and otherwise engaging imagination. A referee could be introduced to judge if the imaginary situations were resolved suitably, to add a "winning" element. But this is nothing really like D&D.

I think the only pre-existing concept that combines the mechanics of a game while having the freedom needed for narratives, is going to be wargaming.

The Pitch

There is no Gygax, so there is no Chainmail, so there are no printed rules for fantasy wargaming. Wargaming at this stage is about reenacting the battles of Napoleon or Roman conflicts or naval skirmishes. Wargamers take historicity very seriously, and consider their game very high-mindedly as a mix of historical pursuit and practical strategy. The armies are supposed to represent historical army sizes, and the goal is to explore how the battle might have gone differently. The soldiers are fighting on fields of battle, against other humans, with possibly some camels or elephants in the mix. No trolls, no dungeons, no dragons.

To get this game off the ground, you have to anchor it in elements of real historical battles taking place in the medieval era.

There are also usually only two players, representing "generals" of the opposing sides, as in chess. They aren't joined together fighting forces of darkness. To make this more like an RPG, you'd need a reason to remove the "general" element to focus on individual initiative more than central command.

My idea is to ask the wargame designer to create a campaign scenario focusing on just a few individual soldiers who are sent on some kind of recon or sabotage mission taking them through underground tunnels. These pieces are part of an army laying siege to a castle, and have been sent in through a discovered secret entrance that should bring them up inside the castle. The battles will use the usual war game rules, but scaled down for smaller numbers of individual troops.

This is anchored directly to real medieval battle simulation, and also provides an excuse to remove the element of a general sending instructions to troops. Each player can be a single soldier, or a small squadron of soldiers.

This game would be extremely deadly. Individual soldiers in a traditional war game are one-hit-wonders. Most of the game would be about sneaking and avoiding confrontation while in the tunnels.

The only characters would be soldiers. The idea of a priest going down into a dungeon to infiltrate a castle is actually really stupid. There are no wizards because there were never any real wizards in historic medieval battles. The only other PC class that might join would be akin to a thief, based on the engineers in wargames who traditionally man the siege engines. These engineers are there to help remove rubble, open doors, or otherwise undermine inside the castle, but are basically worthless in a fight.

You and your fellow soldiers were given the instructions to explore these tunnels for a way inside the castle, and once inside to open the gate from within. You will not be able to communicate with any commanding officer while inside, and you do not know what awaits you within the tunnels. You have with you a team of engineers. It is your duty to guard them to the inside of the enemy castle, so they can sabotage once inside.

This game will be called...

Seiges & Sappers

Let's look at what the game mechanics would be.

The Base Ruleset

Arneson began Braunstein with some inspiration from Chainmail. While Chainmail was the first printed ruleset to describe medieval fantasy battles, it was not the first printed ruleset for medieval battles. It was actually not even the first set of fantasy rules.

On the "Playing at the World" blog , the author has posted a magazine spread from before Chainmail, showing fantasy battle rules by Leonard Patt of the NEWA, which lays out most of the same principles that Gygax adapted in his fantasy supplement. This supplement referred to itself as based on the NEWA Ancient rules, which, as far as I can tell, are the WRG Ancient rules . The 6th printing, which is apparently the most famous, is available for sale here via print-on-demand. I own a pting copy of 6th edition, as well as their fantasy ruleset, "Hordes of the Things," which post-dates D&D by several years.

 

from Playing at the World

Chainmail was originally published in 1971. Sometime after this, Arneson began using some of the rules in his Braunstein games. He later contacted Gygax to explain his new concept, and he and Gygax codified his game notes into the game that would be published as Dungeons and Dragons in 1974.

The first edition WRG Ancient rules are the ones closest to this time frame that I have seen, published in 1969. These are available for free on the WRG website, in the history section. Our parallel-universe Arneson would have had access to these before beginning Braunstein, so I will take these as the wargame rules he starts with as he begins adapting to individual soldiers.

The WRG rules are written assuming two players (or at least two teams) in competition. In this game, several players may be on the sabotaging team, and at most one will play the soldiers of the castellan. In this case they will have separate, identical maps and sit at separate tables, while an impartial Referee coordinates all battle between the two as they explore the tunnels. The lone castellan has the advantage of far, far more soldiers than the saboteurs. However, it would probably be simpler to also have the Referee play as the castellan, to avoid a second map and table.

These rules are incredibly crunchy. They are supposed to span a time period from pre-Roman to the Islamic conquest, including territory from India to northwest Europe. There are tons of stipulations for all the different soldier types represented, with rules to go with them. The 6th Edition massively simplified the rules around soldier types to a few basic rules that are easier to keep track of. But beginning with the 1st Edition rules, we will need to make some simplifications.

The WRG Rules Adapted to PCs

Pages 2 and 3 discuss army creation. To begin, each player has some amount of points with which to make a squadron. While competition games suggest 800 points, this scenario allows only 20 points per player. Each player can choose to be regular or barbarian. Whichever picked, all soldiers must be of that type; this choice has an impact on troop morale and discipline that can impact combat. The options for soldiers are limited to: Soldier Prices
Regular Barbarian
light war engine 15 --
super heavy cavalry 12 15
heavy infantry 8 9
medium infantry 4 3
light infantry 4 3

as they appear on page 3, however with some explanatory notes. This designation of type is called the soldier's class.

It's important to note, the designation of "barbarian" is used here in a historical sense, not in terms of pulp fiction stories from the 1930s. It refers to people living mostly in tribal or village collectives who have been called to war by a cheiftain. As opposed to regular standing armies paid for with levied taxes gathered by an empire or other complex government. The main advantage of barbarians is that they have a larger variance of results in reaction and combat results.

As detailed on page 2, light war engines are assumed to have a crew of 2. So this option actually means a team of two engineers, who will have special thief-like skills to be described later. Note barbarians cannot have engineers, and only have fighting units.

As also detailed on page 2, superheavy cavalry are armored cavalry whose horses are also clad in heavy armor. In the game world, these are knights, who have the social rank to afford all of this war gear. They cannot bring their horses into the passages with them, but they do have many benefits to fighting not given to other classes, including the highest AC.

Heavy infantry wear metal armor over their torso and either have a larger shield or are more skilled in using the shield, so start with higher AC than light infantry.

The light infantry wear leather jerkins and possibly light shields. These soldiers are trained to fight as skirmishers, so have some additional speed over heavy infantry and are best suited to scouting ahead in the tunnels. Medium infantry are armed like light infantry, but fight in close ranks like heavy infantry and have slightly better shields.

This game is still a wargame, so miniature figurines are still important. Each figurine represents a PC, and a given player may have several PCs. The PCs are armed with whatever their figurines are armed with, and should correspond visually to the class each figurine represents. In the rules on page 2 it is stated that each figure represents 20 men, but here in the tunnels it is 1:1, where each figurine is a single soldier.

On page 1 it is explained that soldiers armed with only a sword are assumed to also have some sort of throwing weapon. Soldiers armed with only a bow are assumed to be carrying a side-arm in case of melee charges.

So we now have something like class. Your class is your literal class of soldier: cavalry, infantry, engineer. You can be a trained regular, or a barbarian taking up arms. There are no magic users or priests down here, because why would there be. There are soldiers and undermining engineers, and that's what we need for the sabotage mission.

On page 6 there is an additional sort of "class," this referring to the quality of the soldier.

A Guard and Household troops of the highest calibre
B Elite regulars, personal followings of barbarian war leaders
C The great bulk of trained troops other than those above
D Levies, barbarians, etc. of known fighting value, but not highly organized or disciplined
E Levies, peasants, etc. loosely organized, and of doubtful fighting value

This classification impacts response to both battlefield instructions and charging attacks, similar to morale rolls in D&D, and will be called the morale stat. Different classes will have different starting morale stats.

Each figurine represents a single soldier. However, in the WRG rules it is assumed that a single figurine stands in for as many as 20 soldiers. That figurine then has a certain number of casualties it can suffer, corresponding to the number of men in that battallion, as described on page 16. All soldiers will start with 1 casuality, but as they level they will be able to gain even more casualties. This is how we get hitpoints.

Not only that, but the number of soldiers in a battallion also impacts the number of casualities the battalion inflicts in combat, as detailed on the combat table on page 16. Each figurine represents a single soldier, so will only roll from the first column of that table. However, as the PCs fight more, they will become more adept, so could end up counting as multiple men in combat.

So we now have PCs with class, level, and stats. As you explore the ruins, you gain experience, which can later cause your stats to increase. Let's turn these into classes.

Player Character Classes

There will be five classes. The cavalry option becomes the Knight, the heavy infantry and medium infantry options become the Guard (differing only in their starting equipment), the light infantry becomes the Scout, and the war engine becomes a set of two Engineers.

Soldier Type Price (Regular) Price (Barbarian) Corresponding Class
Light war engine 15 -- Engineers (2)
Super heavy cavalry 12 15 Knight
Heavy infantry 8 9 Guard
Medium infantry 4 3 Guard
Light infantry 4 3 Scout

Below are details for the classes. The armor class corresponds to the column header on the table on page 13, the weapon class to the row on the same table. The weapon class given to each class is regardless of whatever they have in their hand. Movement per turn is taken from the table on page 11. The # Own Figures corresponds to the column headers on page 15, and the Casualties to the number of casualties this figure can suffer before being removed.  The Distance Detected refers to the ability to move silently, and how far away castle troops can hear the soldier moving, under assumptions of deliberately trying to be stealthful and hide in the dark.

The Knight

Unit Price
12/15
Armor class
Plate (as SHC)
Weapon class
10
Morale score
B
Casualties
2
# Own Figures
2
Movement per turn
40 yards
Distance detected
30 yards

The knight is the only unit capable of fighting from horseback. In the underground passages, that is not likely to come up. The knight has superior arms and weaponry to other classes, as reflected in the armor and weapon classes and corresponding factors.

The Guard

Unit Price
8/9 (for HI) or 4/3 (for MI)
Armor class
Plate (as HI) or Leather (as MI)
Weapon class
9
Morale score
C
Casualties
2
# Own Figures
1
Movement per turn
40 yards (as HI) or 60 yards (as MI)
Distance detected
20 yards (as HI) or 10 yards (as MI)

The guards can be more or less armored, with corresponding price difference. A MI who finds plate armor during the adventure could advance to HI, if desired.

The Scout

Unit Price
4/3
Armor class
Leather (as LI)
Weapon class
6
Morale score
D
Casualties
1
# Own Figures
1
Movement per turn
80 yards
Distance detected
3 yards

These figures might be archers. If archers, use Weapon Class 11.

The Engineer

Unit Price
15/- (for 2)
Armor class
Leather (as LI)
Weapon class
11
Morale score
E
Casualties
1
# Own Figures
1
Movement per turn
60 yards
Distance detected
10 yards
Engineers are capable of several important skill actions, including
  • Pick lock
  • Disable trap
  • Set trap
  • Remove rubble
  • Controlled burn or material
These are resolved similar to combat. For each, the Referee sets a casualty rating (CR) for the skill to succeed, the Engineer rolls for the random factors, the Referee applies any pertinent tactical factors, and the casualty table on page 15 is consulted for success.

Orders and Reaction Rolls

Orders (page 4-9) in the WRG Ancient rules are of prime importance. This introduces an element of confusion, where troops will not necessarily behave the way you want them to. This makes sense ofr a General (C in C) giving commands from afar through messengers, but does not make sense for controlling individual units. Every PC will always be exactly aware of what the player wants it to do. However, pending Reaction Tests, the PC may be overwhelmed with fear or overboldened with courage, and not behave as desired.

The Reaction Test on page 7 is to be implemented as described. These are situations where a player wishes to move a PC into some form of harm, or the PC has been suffering harm. Failing the reaction roll means the troops are frightened by combat and do not respond as instructed to an order, or over-succeeding means they start charging the enemy, disregarding orders. The procedure in item 5 describes how to roll the dice to determine success. Possible factors impacting this test are given on page 8. Then page 9 gives two tables to consult; first roll on table 1, then continue rolling on table 2 until the PC is no longer fleeing/advancing.

Combat

Combat is governed by the Casualty Calculation matrix on page 15. The columns correspond to the number of soldiers in the battalion. In these rules, use the # Own Figures stat corresponds to the columns to use.

First consult the weapon factors table. For ranged attacks these are on page 12, and for melee on page 13. Look at corresponding weapon class (the numbered rows), and search over to the armor class of the attacked figured (eg. SHC, HI, MI, etc.)

Next consult the tactical factors on page 14.

Next generate the random factor. This is the difference of two dice, labeld red and black. For barbarians, the black die is a normal d6. For a regular, the black die is an averaged die numbered 2,3,3,4,4,5. The red die is an averaged die for both types. The black die minus red die is the random factor.

The disorganization factors seem to be irrelevant.

Add the weapon, tacitcal, and random factors together for the total factor. On page 15, consult the corresponding row and column in the Casualty Calculation table for the number of casualties inflicted on the unit. Remove figurines as necessary.

The Castellan

If the Castellan is not simply the Referee, then he is limited to an army of 50xN points, where N is the number of saboteur players. He can buy any units, but with the obvious restriction that elephants and horses will have difficulty fitting in the tunnels. Each figurine of the Castellan represents five soldiers, but otherwise follows the usual WRG rules for figures.

The Castellan has prior knowledge of the tunnels, but not of the location of the saboteurs. He will only be made aware of the saboteurs when a unit in his control encounters them in the tunnels. Likewise, the saboteurs will only be shown the part of the tunnel their figurines can see, and have no idea where Castellan figures might be located.

If the saboteurs plan and successfully execute a sneak attack to subdue a Castellan figure before the figure can sound an alarm, the Referee should not tell the Castellan this until it becomes discoveredby another piece, and move that figurine as normal as though it still responded.

Conclusion

So that's my game idea.

The result is something very much like OD&D, and can begin expanding in similar directions. I have not included any fantasy, but there are definitely inroads for it as players start exploring deep into underground ruins beneath castles. A troll, for instance, might have stats like an elephant figure, or an orc like a barbarian heavy infantry.

If there were to be wizards, they would be introduced largely in-line with their original role to serve as artillery in a fantasy battle. I don't think Vancian magic would ever get invented a second time. I think wizards' spells would operate similar to soldiers' weapons, being rolled on specialized tables.

I don't think clerics would get introduced.

As the PCs progressed across missions, they would gain battle experience, becoming hardier and deadlier warriors. They would see increases to the Casualties, # Own Figures, Morale score. As they discovered new items in the underground ruins, they would improve their weapon or armor class.

I think as people began to grow to this idea, players would want more customization options to increase the realism of exploring the underground. More soldier classes would be invented. People would start publishing dungeon tunnel plans for others to use.

This game is deadly, will have a focus on player skill over PC ability, and will be driven by exploration rather than combat, as combat can be so deadly. I think it would count as an OSR.

What do you think?

Friday, July 1, 2022

The Acrobat and the Flea -- The Unexplored Science in Stranger Things



I just finished watching what is available of Stranger Things Season 4, and planning to watch the rest tonight.  I've been meaning to comment on the show for a while.  There are a lot of really neat ideas present in the series, that sadly I don't think get fleshed out as much as they could have been.

I was inspired to finally start writing some commentary by a scene near the end of vol 1 of season 4.  That is your spoiler warning.

Saturday, June 25, 2022

God and the Law of Identity

 I remember my first few years as a grad student, a professor reassuring my friend and I that no physicist ever gained true expertise in the topics by taking the classes.  We'd learn the subject matter, but the real mastery would come when we had to teach it.  Since about January my wife and I have been teaching a Sunday school class on logic and critical thinking, and even though the subject matter is pretty basic, I'm finding more insights into the topic that I just hadn't noticed before.

One of these is with the Law of Identity, which is our next topic.  Stated, the Law of Identity sounds really dumb: "A thing is itself, and not anything else."  This apple is this apple, and not a banana.  This apple is this apple, and not that apple.  It applies to claims, as well.  The claim that the sky is blue, is the claim that the sky is blue, and not some other color.  It's the claim that the sky is blue, and not that my car is blue.  And if we disagree on what is meant by "the sky" (do we mean the night sky?) or "blue" (my wife says this color is "blue"), the language disagreement doesn't make the claim itself ambiguous or unknowable.  My claim still means what it means.

I was thinking recently how this applies to God.

What do we mean when we say the word, "God"?

There are some people who claim the word "god" is so ambiguous that's it impossible to know if a god exists or not.  It has truth to it.  What a bronze age European tribesman meant by "god" is vastly different, in terms of category, from what a Muslim means by the same word, or what a Vedic Hindu means by the word.  The ideas are not comparable enough for a single, common word to be applicable to all three.

The confusion over what the word signifies is especially true for Christians, with our storied history of violating the Commandment against graven images.

One of the most famous centers for Christian worship in the world has on its ceiling this painting:


And this painting has spawned a thousand memes.

When I say the word "God", I get the sense that many people think I mean this guy here depicted in this painting.

God is a man.  God is a man in the clouds.  God is a white man with a long flowing beard living in the clouds, wearing a robe and rope sandals.

That is not what I mean by the word "God."

Saturday, April 23, 2022

No One Should Care What Kate Turabian Thought About Style

I have recently had to write and turn in my dissertation.  To do this, I had to adhere, at least somewhat, to the stylistic whims of Kate Turabian.  Which has been a painful process.

Who is Kate Turabian?  She is a former bureaucratic pencil-pusher who leveraged her tiny bit of control over dissertation layout into a world-wide empire enforcing her anal-retentiveness about margin widths and heading formats through a book she wrote explaining how she liked things to be.  Because she had to approve dissertations at the University of Chicago, students had to do whatever she said to graduate.  She herself never even finished college, and never wrote a dissertation.  She certainly never wrote a college term paper using her made-up style.  She just made others follow it.  Margins on the left should be 1.25" while the right 1"?  Appendix titles are only 1" from the top margin, but chapters 2"?  It doesn't matter if it makes sense, you just have to do it, or you can't get your PhD.  

And that's all her wikipedia page should say about her.

You know the security guard who thinks because he technically has a badge that he can commandeer your car?  That's Kate Turabian, but with academic writing.

Except she's worse.  The one security guard is the one security guard.  But imagine that one security guard writes a manual, "A Manual for Guards of Security," setting himself up as the world expert on how to properly guard buildings and parking lots, and it involves asking three hundred questions, checking the glovebox, and making the driver submit to a field exam, and now every security guard in the entire country insists he has to do this because it's part of the manual, and you have to let him because he decides who gets past the turnstile.  That's Kate Turabian, but with academic writing,

You spent six years taking classes in natural sciences, performing research, analyzing data, manipulating equations, connecting theory and experiment.  You've presented your work to audiences of scientists, written papers in journals, and finally defended your dissertation research to a committee of professors.  

But then after all of that, the real task is an old lady with a ruler, who is going to tell you there should be indentations after subsections but not subsubsections (because obviously).

Now, I should be more fair.  In principal, I understand the need for standards.  Subsections should not be set with bold in one place and then italic in another.  You should be able to distinguish a subsection from a section based on the heading.  The margins shouldn't be so wide that the page is mostly blank space.  I get that.  And since most normies use Microsoft Word instead of TeX to write absolutely everything (I've had students hand in C code written in Word), I can understand why some set of rules is important.

And in the age of typewriters, when students had to manually set bold, italic, etc., I understand that making a list of which to use where helps to standardize everything.

But if students follow a consistent style, if they use structural organizational tools in their word processer to automatically control style, if things look professional and organized, if the term paper conveys the information without distraction over formatting, then it doesn't matter if page numbers are centered on the bottom or typeset to the top left.

And that, arguably, is one of the places where obsession with Turabian style falls on its own sword.

The point of standardizing style should be to make the formatting disappear, leaving only the text.

If a professor is going to pull out a ruler to measure your term paper to make sure it's a 4ex indentation in a new paragraph, then it is serving the opposite purpose.

Kate Turabian had some opinions about how papers should be formatted.  At one point, students at the University of Chicago had to care about her opinions, because she loved using her power over them to make everyone respect her opinions.

All of her opinions were arbitrary.  They were based, ultimately, in her whim, in what she thought looked prettiest.

A lot of her choices do NOT look the prettiest.  Most of her choices look butt-ugly.

Her insistence on ragged-right typing instead of justified text maybe made sense with typewriters, but not in the age of computer typesetting.  Her choices for title headings are dumb, changing from emphasized, to not emphasized to emphasized.  A paper typeset using her rules looks unprofessional, like some hack who doesn't know how to use a word processor wrote it up, pressing each key with his index finger.  Like a rough draft of a 5th grade book report before your mom spellchecked it.

Turabian style looks unprofessional.

And yes, those are also my subjective opinions.  And my subjective opinions are equally as valid as hers.  The only difference from her is I'm not trying to force all of academia to adhere to my subjective opinions.

Were I to receive a term paper written in Turabian style, I would just grade the content of the paper.  I wouldn't tell the student he has to go retype it in TeX using Computer Modern font and standard report class outlines for sections and subsections.  I wouldn't  pay attention to how ugly and illegible it looks.

But people in the Turabian cult do.

Why does the Turabian cult exist?  Why do we continue to care about her opinions?  She has passed from her post in Chicago, and no longer holds power over grad students.  She has passed from this world, and can no longer hold out her ruler of terror to tell us the margins are too wide.

Why do we continue to care what she thought?

It is of course unsurprising that a low-level pencil-pusher, with no formal education and completely unqualified to comment on academic writing, but with supreme power over those with the highest level of education, would make up and enforce and insist on all manner of arbitrary and stupid rules as though they descended from on high.  That's going to happen.  It's part of human nature.

What is impossible to understand is how she indoctrinated so many academics into this cult of hers.

I would like us, as a country, to just move on.  Instead of enforcing some dead woman's arbitrary opinions, let's just instead ask for consistency by asking students to use internal organization tools in the word processors, rather than laying everything by hand.  And if it's typeset in TeX or similar, then you can be assured it will have consistent style and organization.

Friday, April 15, 2022

Twelve Years a Grad Student

I drew this on a white board at my 
last school, in 2013.  Nine years later
and I slayed the dragon.
I recently finished my PhD in physics.  My particular field is astrophysics, and my thesis topic was on Newtonian and relativistic white dwarf asteroseismology.  All I have left to do is get past the whims of Kate Turabian, whose opinion on formatting people for whatever reason care about.  

The first post on this blog was almost ten years ago, while I was a grad student.  Inspired by some of my classes and books I was reading, I had some crazy ideas mixing science and fiction and wanted to post them somewhere.  The most famous of those crazy ideas was about the Berenst#in Bears, which is now a meme far beyond my mere tiny blog.

Ten years ago I was a graduate student.  One week ago, I was a graduate student.  In fact, I started graduate school in 2010, meaning I have been pursuing a PhD for for twelve years (eleven not counting my year teaching high school).  

I have been twelve years a grad student.

I figured, given the momentousness of the situation, I would reflect on this overlong time.

Thursday, October 29, 2020

Trying to decode The Beginning Place by Ursula Le Guin

 I recently reread this favorite of mine.  My copy is an old, worn paperback I purchased at a used bookstore in the middle of nowhere in Georgia.  The cover art shows the two man characters Hugh and Irena lost wandering in a forest, Hugh dressed in the vest from Tembreabrezi with the ceremonial sword drawn, and Irena in the red traveling cloak the inn lent her.  I've seen other covers for the book, and this one blows the others away.  It is apparently also the author's favorite, because it's the one she shows on her website.



This book, especially with this cover, might make you think this story is in the same genre as Narnia or Bridge to Terabithia.  It is and it isn't.  For one, this book is not meant for children.  It's actually too mature for young adult.  It'd be better for students just entering college.

If you recently read this book and are trying to understand it, or read it long ago but didn't really get it or don't remember much, I'm going to offer an explanation for the story that should help it make more sense.  (Spoilers below)

To enjoy this book, you need to understand that it is not the same kind of book as Narnia.