# Ars D&D.Sci: Mysteries of Mana Evaluation & Ruleset

This is a follow-up to [](https://www.lesswrong.com/posts/cesr2yGoZ2y327qKQ/d-and-d-sci-divination-nine-black-doves) [last week's D&D.Sci scenario](https://www.lesswrong.com/posts/9P4yLsfhj2Jjm4yqg/ars-d-and-d-sci-mysteries-of-mana): if you intend to play that, and haven't done so yet, you should do so now before spoiling yourself.

There is a web interactive [here](https://aphyer1992.github.io/dnd_mag) you can use to test your answer, or you can read on.

RULESET
=======

Mana
----

Your initial studies of mana missed out something - there are actually **six** kinds of mana, not five, arranged in three opposed pairs:

*   Fire and Water mana are opposed.
*   Earth and Air mana are opposed. 
*   Light and **Dark** mana are opposed.

Total mana of all six types is 150, at the time of the scenario the strength of Dark is **17. **

You didn't in fact need to figure this out to solve the puzzle, but it would make many things fit together better - understanding what spells were powerful when and how elemental counters work is likely much easier once you understand this.

Congratulations to **abstractapplic**, who was the first to comment on this, and to **simon**, who had a fairly comprehensive analysis of the mana types.

Spells
------

Spells are distinguished by two things:

*   Their associated mana types (each spell has two associated mana types, and each pair of mana types that aren't opposed to one another has one associated spell).
*   Being an attack or a defense spell (six element pairs have attack spells, six have defense spells, with each element having two attack and two defense options).

**simon** made an excellent chart of the spells, which I am shamelessly stealing rather than drawing my own:

![](https://i.imgur.com/papsVEf.png)

Source: **simon** posted this at https://imgur.com/a/eUzxY9p

Mage Spell Preparation
----------------------

Mages prepare spells mostly randomly, with two caveats:

*   A mage will always bring one attack and one defense spell.  The third spell can be either type.  This was for good reasons - bringing no attack spell makes winning impossible, while bringing no defense spell makes winning unlikely.  Nobody submitted an answer with no attack/no defense, though **GuySrinivasan** briefly considered it.
*   Mages dislike Dark spells, and bring them only half as often.  This set up some skew in how likely to win different spells were, based on elemental counters.

How a Duel Works
----------------

*   Each mage starts with 100 Health.
*   A random mage wins the initiative and attacks first:
    *   He selects one of his attack spells to attack with.
    *   His opponent selects one of their defense spells to defend with.
    *   The attack spell's power is equal to the sum of the powers of the two elements it uses (e.g. Merinita's Mud Missiles at the time of your duel uses Water 39 + Earth 26 = 65 Power).
    *   The defense spell's power works similarly, but any element it shares with the attack spell counts as 0 (fire cannot block fire), while any element it has that opposes one in the attack spell counts double (water is extra good at blocking fire).  For example, if you defended aginst Merinita's Mud Missiles with Logain's Lava Levee, you would count Fire twice (24+24) but Earth zero times, for total power 48.
    *   The attacker rolls 1d\[Attack Power\], while the defender rolls 1d\[Defense Power\].
    *   If the attacker rolls higher than the defender, the defender takes damage equal to the difference.
*   Then the other mage attacks, and they take turns attacking until one of them hits 0 Health.

When a mage has multiple attack/defense spells, he doesn't have the benefits of your research, but he still has some ability to sense intuitively how strong each spell seems to be and to see how well it is working against his opponent.  

This means that he will be *more likely but not certain* to use the stronger spell,  using it more often proportionally to how much stronger it is.  

For example, if he has one 60-power attack spell and one 40-power attack spell, he will attack with the stronger one 60% of the time and the weaker one 40% of the time.   If one of his defense spells has 40 power against his opponent's attack and the other has 10, he will use the stronger one 80% of the time and the weaker one 20% of the time.

STRATEGY
========

ATTACK
------

Your opponent has one Defense spell: Solar Shield (Fire/Light).

The attack spells you could bring were:

| Spell name | Elements | Attack Power | Defense Power |
| --- | --- | --- | --- |
| Balefire Blast of Bonisagus | Fire/Dark | 41  | 36  |
| Flambeau's Flying Fireball | Fire/Air | 50  | 18  |
| Hylenion's Hammer of the Heavens | Air/Light | 44  | 24  |
| Merinita's Mud Missiles | Water/Earth | 65  | 66  |
| Olorin's Obsidian Onslaught | Earth/Dark | 43  | 60  |
| Rainbow Rays of Rahl | Water/Light | 57  | 48  |

These spells varied on power level (some using stronger kinds of mana than others), but more importantly varied on how well they performed against your opponent's defense (e.g. Merinita's Mud Missiles is the most powerful attack available, but it lets your opponent defend with doubled Fire plus Light, giving your opponent even higher defense).

The best available attack is Flambeau's Flying Fireball, which manages a reasonable 50 Attack Power while minimizing your opponent's Defense Power (denying him Fire mana and allowing only weak single-counted Light mana).

Bringing a second attack is suboptimal - since your master won't change his usual spell-selection behavior, any other attack spell you bring will make him use fewer Fireballs.

DEFENSE
-------

Your opponent's attack spells were Merinita's Mud Missiles (Earth/Water, 65 Attack Power) and Flambeau's Flying Fireball (Fire/Air 50 Attack Power).  You were looking for defense spells good against both of them - unlike attacks, however, bringing two defenses can be valuable for you, as your master has some ability to pair the right defense against each attack (since if a defense is high-powered against one attack and low-powered against the other, he'll be more likely to use it against the first).  

It's more important for your defenses to be good against Merinita's Mud Missiles, as it's  your opponent's higher-power attack, making it both more dangerous and more frequently used.

Your defense spell options were:

| Spell Name | Elements | Power vs Mud Missiles | Power vs Flying Fireball |
| --- | --- | --- | --- |
| Alatar's Abyssal Armor | Water/Dark | 17  | 95  |
| Crystalline Citadel of Criamon | Earth/Light | 18  | 70  |
| Logain's Lava Levee | Fire/Earth | 48  | 52  |
| Solomon's Solar Shield | Fire/Light | 66  | 18  |
| Vaporous Vambrace of Verditius | Water/Air | 52  | 78  |
| Wicked Wiskeria's Wall of Wailing Winds | Air/Dark | 69  | 17  |

Vaporous Vambrace is the stand-out defense spell, with strong defense against both your opponent's attacks.  

While they make you a bit more vulnerable against Flying Fireballs, adding in Wall of Wailing Winds (or, as a second-best, Solar Shield) substantially improves your defense against the more dangerous attack of Mud Missiles, and your master will **usually** be smart enough not to use them against Flying Fireballs.  Adding either of these spells results in slightly better defense than just Vaporous Vambrace alone.

Optimal play was therefore to bring:

*   Flambeau's Flying Fireball
*   Vaporous Vambrace of Verditius
*   Wicked Wiskeria's Wall of Wailing Winds

This gives your master an 83-84% winrate.

LEADERBOARD
===========

*N.B: winrates here were Monte-Carlod rather than calculated.*

| **Player** | **Spell 1** | **Spell 2** | **Spell 3** | **Win Rate** |
| --- | --- | --- | --- | --- |
| **Optimal Play** | Flambeau's Flying Fireball | Vaporous Vambrace of Verditius | Wicked Wiskeria's Wall of Wailing Winds | **83.5%** |
| **gammagurke*** | Flambeau's Flying Fireball | Vaporous Vambrace of Verditius | -   | **82.7%** |
| **gammagurke*** | Flambeau's Flying Fireball | Logain's Lava Levee | Vaporous Vambrace of Verditius | **80.1%** |
| **abstractapplic, simon** | Flambeau's Flying Fireball | Rainbow Rays of Rahl | Vaporous Vambrace of Verditius | **72.1%** |
| **GuySrinivasan** | Flambeau's Flying Fireball | Logain's Lava Levee | Rainbow Rays of Rahl | **62.7%** |
| **Yonge** | Alatar's Abyssal Armor | Rainbow Rays of Rahl | Solomon's Solar Shield | **55.4%** |
| **Random Spells (min 1 Attack & 1 Defense)** | ?   | ?   | ?   | **40.2%** |
| **Entirely Random Spells** | ?   | ?   | ?   | **33.2%** |

*In addition to selecting a list of 3 spells, **gammagurke** identified the best 2 spells, and considered asking their master to bring only 2 spells.  I apologize for not making it explicitly clear whether this was allowed, especially since the optimal 2-spell selection performs very nearly as well as the optimal 3-spell selection.

Congratulations to all players, particularly to **gammagurke** (who submitted the closest-to-optimal 3-spell selection as well as his suggestion of an even-closer-to-optimal 2-spell selection).

FEEDBACK REQUEST
================

As usual, I'm interested to hear feedback on what people thought of this scenario.  If you played it, what did you like and what did you not like?  If you might have played it but decided not to, what drove you away?  What would you like to see more of/less of in future?  Do you think the underlying data model was too complicated to decipher?  Or too simple to feel realistic?  Or both at once?  

I'm particularly interested in how the existence of Dark mana felt from a player perspective.  I wanted it to be a discovery players could make after exploring the data a bit that would make a lot of different things fall into place, but given that multiple people commented on it very quickly I may have made it too obvious.  (In my defense, the last of these scenarios I did also had such a discovery embedded in it, and that one no-one got, so I may have overcompensated in the opposite direction).