Sunday, August 2, 2015

New Class: Modron Mathmatician


This is what happens when a human child is raised by modrons.

They want to get a nice accountant job or something, but no one will hire them because they are weird and sleep standing up, with their eyes open, humming The Calibration Tone (to show the pentadrones that they are healthy).

Mathematicians often become adventurers in order to complete their thesis.  If nothing makes sense, they might as well go try to impose order on the least orderly places possible: dungeons.  

Map them out, make them straight, kill all demons, correct all illogical people.

Modron mathematicians are very dutiful, and most of them will constantly be writing letters home.  They'll write a letter full of the details of their new life among their fellow humans, give it to someone who looks Lawful*, pay them some money, and tell them to carry the letter to Primus, the One and the Prime.

Most of these letters are opened by the person who "looked Lawful", read, mocked, and fed to a goat.  DMs should give an insultingly small amount of XP when a mathematician spends money sending letters to Primus.  Like 10xp or something.  This is because mathematicians cannot carouse.

Primus never responds to these letters, but mathematicians are comforted knowing that Primus's behavior and responses are standardized and well-characterized.  They imagine what Primus would say if he were to read their letter, and they are usually correct.

If they ever somehow make it to level 9, they start attracting modrons and other lawfully minded folk, and they invariably found an ultra-rational town somewhere, in imitation of Mechanus.

However, some human mathematicians are more than just modron-level OCD sufferers.  Sometimes, they freak out upon experiencing the non-modron world**, and revel in their new-found freedom (which was previously more than unattainable--it was literally inconceivable).  These mathematicians are dreaded by modrons everywhere, and are known as Chaos Theorists.

This class is also appropriate for people who want to play a modron.

*There are no alignments in Centerra.  Hilariously enough, though, modrons seem to think that there are.

**Modrons are the inventors of mathematics.  They are also it's only real practitioners, and a few humans (architects, siege engineers) study under them to master their potent maths.  So, yeah, if someone knows math, it's because they apprenticed to a modron.  In fact, people often don't call it mathematics; they call it the "modron art".


This is a class about math and fiddly numbers.  Not just for the character, but for the player, too.

I was talking to +Chris McDowall about the desirability of having a complex class for people who like complex classes.  I ventured that I (sometimes) like fiddly little subsystems for classes, because then the class feels very different from other classes.  And that's diversity.  That's the freshness.  I like playing a quirky little subsystem long enough to figure out how to best utilize it.  Unravel its mysteries, so to speak.

Yes, fighters are simple and easy to understand, and I love playing fighters.  (I'm playing one right now.)  But there are people that thrive on complexity.  So, here is a complex class for people that like complex classes.  At the beginning of every turn, you have an incredibly complex little question to consider: which number should I put into my matrix?  And in the middle of each of your turns, you have another incredibly complex little question to answer: what spell or ability should I use?

It's a funky little optimization problem.  I suggest that the DM give a mathematician player a hard time limit of 30 seconds to decide those things, once its their turn.

It's a potentially powerful class, but it needs to be played like a chess game.  And more perversely: it's a very unreliable one, because it depends on getting the right numbers in your matrix at the right times.


Modron mathematicians are always watching the invisible algebra at work in the universe.  You can see the numbers behind everything.  You can see the matrix.

Think of your matrix as a bag full of scrabble tiles.  Except instead of letters on those tiles, they're numbers from 1-20.  The maximum capacity of your matrix (how many tiles the bag can hold) is equal to 7 + level + Int bonus.  If you want to gain a number but don't have room for it, you can overwrite an old number at any time.

The mathematician player will probably need a piece of scratch paper to keep track of this.

Alternatively, you could just download the mathematician tracker I made and print it out.

Gaining Numbers

Just as a modron mathematician is constantly watching the universe and discerning the underlying mathematics, so are you (the player) watching the game for any numbers that pop out.  Whenever one of your fellow players rolls a d20, ask them to tell you the natural number (what is actually showing on the die).  At the beginning of your character's turn, you can add one of those numbers that you heard about since the beginning of your last turn.  Of course, any d20 number that you roll on your turn can be added to your matrix at the beginning of your next turn.

Keep track of this.  You'll probably be adding a number to your matrix every turn.  Modrons must be ever-vigilant against the forces of chaos!

Losing Numbers

There are two ways to lose numbers from your matrix.
  1. If you have three of the same numbers (e.g. three 6s) in your matrix and you personally roll a d20 and get that number, that is a bust, and you lose all three of those numbers.  Additionally, you can't add that number to your matrix at the start of your next turn, even though you rolled it.
  2. If you take damage, look at the final damage and compare it to all the numbers in your matrix.  If there are any matches, you lose them.
Using Numbers

There are three ways to use the numbers in your matrix.  Your character cannot use any of them unless they have their math book open in front of them (usually held in one of their hands).
  1. Spend three or four number straights (e.g. 3-4-5-6) to make attack vectors.  These are basically spells that damage opponents directly.
  2. If you have 3 copies of the same number (e.g. 7-7-7), you gain a linear ability.  These are passive abilities. For example, if you have triple '7's in your matrix, you can breath underwater.  (Remember that triples bust whenever you roll that number on a d20.)
  3. Spend certain combinations of three numbers to cast non-linear spells.  For example, you might spend a '4', an '8', and a '15' from your matrix to cast invisibility.  

Attack vectors are your primary method of damaging enemies with math.  You have two kinds.

Euclidean Attack Vector
Erase 3 numbers from your matrix that form a 3-number straight (e.g. 3-4-5).  A creature or object within 50' takes math damage equal to the lowest of the three numbers.

Non-Euclidean Attack Vector
Erase 4 numbers from your matrix that form a 4-number straight (e.g. 17-18-19-20).  A creature or object within 50' takes math damage equal to the highest of the four numbers.

Math Damage
Treat math damage as non-magical slashing or spell damage, whichever is more advantageous.  If the math would deal 10 damage or less, the target can make a save for half damage.  If the math would deal 11 damage or more, the target can save to negate all damage.


Announce it to the table when you gain a linear ability and when you lose one.

Triple 1 - Can levitate (fly) at half your movement speed.
Triple 2 - Can see in the dark.
Triple 3 - +4 to save versus spells.
Triple 4 - You can add two numbers to your matrix each turn (instead of just one).
Triple 5 - Take half damage from fire.
Triple 6 - Can climb on all walls (as spider climb).
Triple 7 - Can breath underwater.
Triple 8 - +4 to save versus death and petrification.
Triple 9 - You no longer lose numbers from your matrix when you take damage.
Triple 10 - Take half damage from ice.
Triple 11 - Can burrow through dirt (not stone) at crawling speed.
Triple 12 - Can escape any grab or grapple.
Triple 13 - +4 to save versus poison.
Triple 14 - Allies within 5' of you share the benefits from your Linear Abilities.
Triple 15 - Take half damage from acid.
Triple 16 - Can swim as fast as a dolphin.
Triple 17 - Take no fall damage (as feather fall).
Triple 18 - +4 to save versus charm and mind-control.
Triple 19 - The next time you would bust one of your triplets, you can bust your triple 19s instead.
Triple 20 - Take half damage from lightning.


Spells with an asterisk are new spells, and are explained at the end of this post.  You can cast any of these spells on your turn, as long as you have the appropriate three numbers in your matrix (and remove them when you cast the spell).  So if you wanted to cast mathic missile, you would need to remove 5, 14, and 18 from your matrix.

1-5-12 analyze foe*
1-8-17 calculate attack*
1-10-14 detect magic / read magic
2-6-13 detect invisible
2-9-18  detect thoughts
2-11-15 dispel math*
3-7-14 divide health*
3-10-19 hold portal
3-12-16 integrate matrix*
4-8-15 invisibility
4-11-20 knock
4-13-17 mage armor
5-9-16 mage hand
5-14-18 mathic missile*
6-10-17 mirror image
6-15-19 multiply health*
7-11-18 prime weapon*
7-16-20 pseudo-pseudo-random number generation*
8-12-19 theorize*
9-13-20 wall of math*

true fact: modron decatons are the coolest modrons

Analyze Foe
If a creature in 50' fails its save, you learn all of its basic numerical stats: HD, max HP, current HP, armor class, attack bonus, attack types and damages, morale, speed, and intelligence.

Calculate Attack
You get +20 to the first attack you make next round.

Dispel Math
As part of casting this spell, erase another number from your matrix.  This number is X.  This spell functions as dispel magic, except that it has an X-in-20 chance of succeeding.

Divide Health 
Designate a target within 50' and an integer X.  If the target's HP is less than X, nothing happens.  Otherwise, the target takes damage equal to half of X.  They are allowed a save for half damage (one fourth of X).

Integrate Matrix
Add one number of your choice to your matrix.

Mathic Missile
As magic missile, except that it does (1d3 squared) damage.

Multiply Health
Target creature's current HP is doubled.  If this would raise their HP above their normal maximum, this spell has no effect instead.

Prime Weapon
Temporarily enchant a weapon that you touch.  Whenever this weapon deals damage that is a prime number, it deals an additional +3 damage.  Lasts 5 turns.

Pseudorandom Number Generation
Cast this spell instead of rolling a d20.  You can cast this spell even when it is not your turn.  Instead of rolling a d20, use one of the numbers from your matrix, determined randomly.

Increase the maximum size of your matrix by 5 until the end of the session.

Wall of Math
As part of casting this spell, erase another number from your matrix.  This number is X.  Creates a square wall of force at any location within X feet.  The wall is X feet on a side, and must be oriented exactly vertical or horizontal.    This wall lasts for X minutes and has X HP.

Level 1 Modron Mathmaticians roll 2x on this table.  They also start with a math book.  If they lose their math book, they can create a new one by spending a week in a library or other mathy place.
  1. Set of perfectly balanced dice.
  2. Coin that always comes up heads.
  3. Square, pyramidal hat with each side a different color (red, blue, green, yellow).
  4. Square, boxy modron mask (see #3 above).
  5. Perfectly circular protractor shield.  +1 to any task that benefits from calculating angles.
  6. Spherical, masterwork breastplate (medium armor).  With an hour of tedious reassembly, it can be turned into a working astrolabe.
  7. Abacus.  +1 to any task that benefits from counting shit.
  8. Scales.  +1 to any task that benefits from weighing shit.
  9. Prayer book containing the first 1000 prime numbers (up to 7919).
  10. Masterwork sword without any adornment whatsoever.  Like a platonic ideal of a sword.
  11. Spear with meters and centimeters marked off.  +1 to any task that benefits from calculating lengths.
  12. Jar of human nutrient paste.  Tastes awful.  Takes up space like 3 rations, but feeds you for 9 days.

Click HERE to download the mathematician tracker PDF
(You'll probably need it.)


  1. This is an interesting and novel concept, but I suspect it would require a lot of adjustment and playtesting to get it to work well.

    The impression I got was that it's not actually very powerful - especially with lots of allowed saves to reduce or nullify damage and other effects. Worst of all is a 1/20 chance every die roll of losing whatever "linear ability" you have active, which means that e.g. few people are going to want to use the water-breathing one if they suspect that anything at all will happen while they're underwater. Perhaps allowing the mathematician to sacrifice another number or two from their matrix to avoid a "bust" would help offset that?

    I just noticed that there isn't anything on hit dice, or attack or save progressions. A note on those, and perhaps some more abilities that impact the mathematician's (or even other peoples') stats - AC HP, attack rolls, saves, etc. - would help round out the character some more. Other than the number of numbers the mathematician can hold, too, there doesn't seem to be anything that scales with level, which means that after just a few levels a wizard is always going to offer more power, far more reliably, for less work.

    Note also that "breath" is a noun, and the verb is "breathe." 8^P

    I really like the idea of "non-Euclidean attack vectors," by the way. I'm picturing some very freaky stuff happening to the target of math damage... which makes it all the more disappointing that if they save they take half of low damage or none at all. (On a save, target takes 0-5 damage; on a fail, they take 1-20. Compare to a minimum-strength [5d6] fireball, where on a save each target takes 2-15 damage and on a fail, 5-30.)

  2. wow my hat tips to you on this - fits nicely into my recent modronomicon blog
    has me thinking more things for LAW to get up too...


  4. Both the thematics and mechanics here are clever, as always. Let me state this up front. Confanity critiques the mechanics well. As to the thematics, well, I feel they suit a different class.

    Exploiting repetition of integers strikes me as far less mathematician-like than it is drummer-like. (Being both, I also think the math puns are applicable to wizards in general, and that inability to carouse is a class feature.)

    The emphasis on manipulating chance to one's favor is very much a performance artist thing. Moreso than it is a 'writing a rigorous proof' thing or even a 'solving a difficult problem in a clever way' thing. (Mathematicians are lazy, in my experience. This is why they deal in abstractions all the time.)

    Drummers who deal in polyrhythms, on the other hand, are basically shuffling integers. Playing in 5 against 4 (with implicit divisions of 20), breaking a bar of 10/4 into 4+3+3 beats, etcetera. It's nontrivial to hear, let alone play, but then finally you realize how neatly it fits together...

    1. So here was my first idea for the mathematician:

      Roll, like 4d6. Through some combination of addition, subtraction, multiplication, and division of those numbers, arrive at an end number. The value of that end number determines what you do, so if you got (5 + 1) * (3-1) = 12, that 12 corresponds to a certain effect.

      So, that's one idea where the mechanics actually reflect the "doing math" thing. I didn't like that idea because (a) it makes it impossible to plan for things, because you are essentially generating random numbers and then trying to wrangle them to a goal. Inability to plan seems antithetical to a class that should be about calculation And (b) the player who plays a mathematician must then be good at math, specifically doing arithmetic quickly (which is what people think mathematicians do until they learn the first thing about mathematicians.)

      So, I like my mathematician mechanics. I'll probably rewrite it at some point, after I've playtested it a little bit. I don't see it as "manipulating chance" as much as "imposing order on a chaotic process".

      The drummer is a pretty cool idea. I can imagine a drummer class that plays around with tempo or repetition in a fun way.

    2. Ah. Then the mechanics do convey the intent, whilst incorporating voluntary risk-reward. I should not be surprised that modrons (among others) might actually believe in the theme park version of math.

      I look forwards to the results. Hm, implying manipulation of the underlying probability distribution was not my intent. 'Coming out ahead', maybe. By applying a(n orderly) strategy, yes.

    3. Tarsos came up with the idea of rolling then placing 3 to 4 D6's in a column and using the side faces to generate new information (which could fit in with the theme of your above first concept):

      I did some maths (if that is of interest) on Tarsos's concept when using Tarsos’s idea to make a PC stat generator: