# Duels & D.Sci March 2022: Evaluation and Ruleset

This is a follow-up to [last week's D&D.Sci scenario](https://www.lesswrong.com/posts/Mucvqyuo8o9ecbzea/duels-and-d-sci-march-2022-it-s-time-for-d-d-d-d-d-d-d-d-d-d): 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_mtg) where you can test your submission against your rival's deck (or against a couple other NPCs I added for your amusement, if you think yourself mighty enough to challenge those who wield the legendary power of the Sumerian Souvenirs).  

**NOTE**: Win rates in the interactive are Monte-Carlo-d with small sample sizes and should be taken as less accurate than the ones in the leaderboard.

RULESET
=======

Code is available [here](https://raw.githubusercontent.com/aphyer1992/dndsci-mtg/main/dndsci_mtg.py) for those who are interested.

A game is played as follows:

*   There are up to 6 turns in the game.
*   Each turn, each player simultaneously draws 2 cards from their deck.  (So over the full duration of the game, each player will draw their entire deck.)
*   Then, each player will simultaneously play either 0 or 1 of those cards:
    *   Every card has a mana cost, ranging from 1 to 6.
    *   On turn X, you can play a card that has a cost of X or less.
    *   If both your cards are valid plays, you will play the higher-cost one.
*   For example, if you draw a 2-cost and a 4-cost card:
    *   If it is Turn 1, you will play nothing.
    *   If it is Turn 2 or 3, you will play the 2-cost card.
    *   If it is Turn 4 -6, you will play the 4-cost card.
*   Any cards you didn't play are discarded - you will not be able to play them on later turns.
*   Note that:
    *   You cannot play two cards in the same turn, even if you would in theory have enough mana to do so.
    *   You cannot be clever about which card you play.  In some cases a lower-cost card might be better than a higher-cost card: you will play the higher-cost one anyway if you can.  If you draw two cards of the same cost, you will play one at random.
*   After both players have played a card if they can, each player calculates their Total Power by adding up the Power of all cards they have on their board.
*   If one player's Total Power exceeds the other's by at least 2000 Power, that player wins an immediate victory and the game ends.
*   If not, the game continues to next turn.
*   After 6 turns, if no player has won an immediate victory, the game ends anyway, and whoever has higher Total Power wins.
*   If players are tied on Total Power at this point, their cards clash in a mighty battle and the winner is decided randomly.

CARD LIST  
 
=============

Cards available to you were the following:

| Card Name | Mana Cost | Power | Alignment |
| --- | --- | --- | --- |
| Gentle Guard | 1   | 700 | Good |
| Lilac Lotus | 1   | 200* | Artefact |
| Patchy Pirate | 1   | 700 | Evil |
| Horrible Hooligan | 2   | 900 | Evil |
| Kindly Knight | 2   | 900 | Good |
| Sword of Shadows | 3   | 2000* | Artefact |
| Virtuous Vigilante | 3   | 1300 | Good |
| Bold Battalion | 4   | 600x* | Good |
| Murderous Minotaur | 4   | 1700 | Evil |
| Alessin, Adamant Angel | 5   | 1800* | Good |
| Dreadwing, Darkfire Dragon | 5   | 2500 | Evil |
| Evil Emperor \\[omitted for length\\] | 6   | 4500 | Evil |

*Some cards have special abilities:

*   Lilac Lotus provides additional Mana.  For every Lotus you have on the board, you have 1 extra mana each turn.  (Yes, I know this is more like a [Mox](https://gatherer.wizards.com/pages/card/Details.aspx?name=Mox+Sapphire) than like a [Lotus](https://gatherer.wizards.com/Pages/Card/Details.aspx?multiverseid=382866).  I don't need to make the hints give **that** much away.)
*   Sword of Shadows requires a Wielder.  If you have at least one Evil creature on your board to wield it, it adds 2000 Power.  If you do not, it adds 0 Power.
*   Bold Battalion draws Power from your Good creatures.  Its Power is 600 per Good creature you have on your board (including itself).
*   Alessin, Adamant Angel shows Mercy on your bad draws.  When you draw it without enough mana to play it, you shuffle it back into your deck and draw again. (You can do this many times if you are unlucky enough to draw the Angel repeatedly, but if your deck is **entirely** Angels you will draw the Angel anyway rather than getting stuck in a loop).

Congratulations here to: 

*   **benjamincosman**, who I believe was the first to identify Good & Evil and the existence of internal synergies.
*   **gammagurke**, who I believe was the first to localize the Good and Evil synergies in Battalion and Sword specifically.
*   **GuySvrinivasan**, who I believe was the first to identify the Lotus's ability.

STRATEGY
========

There were three available 'archetypes': coherent decks that fit together and did something powerful.  All ended up with a roughly 75% winrate against your rival if optimized, but they performed differently against one another.

**Good Tribal** is based around Bold Battalion.  It tries to play lots of cheap Good creatures (Gentle Guard) in early turns, and then lots of Battalions to gain high Power.  The best build for this against your rival is very simple, with 6xGuard and 6xBattalion. This gets 75.4% winrate, the best available.

**Sword Aggro** is based around Sword of Shadows.  This time, your goal is to get cheap Evil creatures to wield Sword of Shadows, and then try to use the Sword's very high score for its cost to win on turn 3 or 4.  The best build for this against your rival is 3xPirate, 5xSword, and 4xAngel.  (The Angels make your lategame a little more reliable, and don't get in the way of your early game thanks to their ability).  This gets 74.6% winrate.

**Lotus Ramp** is based around Lilac Lotus.  Your goal is to play Lotuses in the early turns and use them to play out large late-game threats like the Emperor.  The best build for this against your rival is 5xLotus, 3xAngel, and 4xEmperor.  This gets 74.5% winrate.

When these decks as-written play against each other, their relative speeds lead to some rock-paper-scissors (where being slightly stronger and slower than your opponent advantages you as you end up with more power, but being much stronger and slower disadvantages you as you can lose before getting off the ground):

*   Good Tribal has a slight advantage over Sword Aggro by being slightly slower and stronger (~55%)
*   Sword Aggro has a slight advantage over Lotus Ramp by being much faster and weaker (~55%)
*   Lotus Ramp has a substantial advantage over Good Tribal by being slightly slower and stronger (~63%)

It is possible to build these decks differently - most noticeably, you could build more defensive Lotus Ramp decks (with more Angels or even Vigilantes, and fewer Emperors).  This improves the matchup against Sword Aggro and other fast decks substantially, but worsens the matchups against Good Tribal, other Lotus Ramp, and any other slow decks.

Particular congratulations are due here to **gammagurke**, who managed not only to identify these three archetypes but to actually give two of them exactly their correct names.  (Sadly, 'Evil Equip' doesn't quite work out as a name when the deck often contains more Good creatures than it does Evil ones).

I was expecting Good Tribal to be the simplest available deck, and for Sword Aggro and particularly Lotus Ramp to take the most work to optimize - it seems I was mistaken in this regard, and many players submitted Sword or Lotus-based decks while no-one submitted a Good-based deck.

PVE LEADERBOARD
===============

*Note: all winrates below were Monte-Carlo calculated rather than explicitly derived. *

Submitted decks were as follows:

**abstractapplic:** Sword Aggro (3xPirate, 3xHooligan, 4xSword, 2xAngel)

**gammagurke:** Lotus Ramp (5xLotus, 2xPirate, 3xAngel, 2xEmperor)

**GuySrinivasan:** Dragon Ramp (6xLotus, 4xDragon, 2xEmperor)

**jsevillamol:** Knight Aggro (1xPirate, 9xKnight, 1xBattalion, 1xEmperor)

**Maxwell Peterson:** Sword Aggro (6xPirate, 2xSword, 1xMinotaur, 3xAngel)

**Measure:** Lotus Midrange (3xLotus, 2xPirate, 1xSword, 1xVigilante, 2xAngel, 1xDragon, 2xEmperor)

**Pablo Repetto:** Lotus Aggro (3xLotus, 3xPirate, 2xSword, 4xAngel)

**Yonge:** Lotus Midrange (2xLotus, 1xPirate, 1xHooligan, 2xVigilante, 1xMinotaur, 2xAngel, 1xDragon, 2xEmperor)

| **Player** | **Winrate** |
| --- | --- |
| **Optimal Play** | **75.4%** |
| abstractapplic | 68.46% |
| GuySrinivasan | 66.16% |
| Measure | 61.38% |
| Maxwell Peterson | 61.06% |
| gammagurke | 59.00% |
| Yonge | 57.76% |
| Pablo Repetto | 52.57% |
| **Random Play** | **40.5%** |
| jsevillamol | 31.39% |

Congratulations to all submitters, in particular to **abstractapplic** (whose Sword Aggro build was fairly well-tuned despite the Hooligans not being quite optimal) and **GuySrinivasan** (who managed to place a very close second despite playing an archetype I didn't even think existed).

PVP LEADERBOARD
===============

*Note: all winrates below were Monte-Carlo calculated rather than explicitly derived.*

*~~**Note: The commentary below should be considered non-final for a few days to give people time to point out that I've misread the decks they submitted/added up win percentages wrong/made other obvious mistakes.  If I have messed something like that up I'll have to recalculate, so don't count on victory/defeat until some more eyes have confirmed.**~~*

Submitted decks were as follows:

**abstractapplic:** Sword Aggro (3xPirate, 3xHooligan, 4xSword, 2xAngel)

**gammagurke:** Lotus Ramp (6xLotus, 2xAngel, 4xEmperor)

**GuySrinivasan:** Dragon Ramp (6xLotus, 1xMinotaur, 5xDragon)

**jsevillamol:** Knight Aggro (1xPirate, 9xKnight, 1xBattalion, 1xEmperor)

**Maxwell Peterson:** Sword Aggro (2xPirate, 4xHooligan, 2xSword, 4xAngel)

**Measure:** Sword Aggro with Emperors (4xPirate, 4xSword, 1xVigilante, 3xEmperor)

**Pablo Repetto:** Lotus Aggro (3xLotus, 3xPirate, 2xSword, 4xAngel)

**Yonge:** Lotus Midrange (2xLotus, 1xPirate, 1xHooligan, 2xVigilante, 1xMinotaur, 2xAngel, 1xDragon, 2xEmperor)

Standings were as follows:

| **Player** | **abstractapplic** | **gammagurke** | **Measure** | **Maxwell Peterson** | **Yonge** | **GuySrinivasan** | **Pablo Repetto** | **jsevillamol** | **Total Score** |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| **abstractapplic** | 50% | 56.44% | 55.51% | 59.99% | 59.4% | 59.78% | 68.85% | 85.62% | **4.96** |
| **gammagurke** | 43.56% | 50% | 53.28% | 51.37% | 67.67% | 58.18% | 60.17% | 82.46% | **4.67** |
| **Measure** | 44.49% | 46.72% | 50% | 50.99% | 52.98% | 56.78% | 59.87% | 78.97% | **4.41** |
| **Maxwell Peterson** | 40.01% | 48.63% | 49.01% | 50% | 53.28% | 53.91% | 60.98% | 82.4% | **4.38** |
| **Yonge** | 40.6% | 32.33% | 47.02% | 46.72% | 50% | 51.45% | 56.43% | 74.96% | **4.00** |
| **GuySrinivasan** | 40.22% | 41.82% | 43.22% | 46.09% | 48.55% | 50% | 53.58% | 70.46% | **3.94** |
| **Pablo Repetto** | 31.15% | 39.83% | 40.13% | 39.02% | 43.57% | 46.42% | 50% | 71.15% | **3.61** |
| **jsevillamol** | 14.38% | 17.54% | 21.03% | 17.60% | 25.04% | 29.54% | 28.85% | 50% | **2.04** |

**gammagurke's** Lotus Ramp deck was designed to try to prey on other midrange and ramp decks by going over the top with more Emperors - sadly, there were many Sword-based aggro decks and fewer midrange and ramp decks, making this otherwise-reasonable deck poorly positioned for the opponents it actually faced and pushing it back to second place.

**Measure** and **abstractapplic** both submitted solid Sword Aggro lists, but **abstractapplic**'s was somewhat better-tuned and came out on top.

Congratulations **abstractapplic**!  Once you've figured out what theme/work* you want to request an upcoming scenario be based on, PM or comment and I'll try to get it to happen.  I can't promise it'll happen soon (it'll take some time to write one of these, I have at least one other scenario that'll likely get posted before it, and other people may also submit some), so you'll end up waiting most likely a few months.

**Ability to select a specific work is contingent on me being familiar with that work and thinking I can write a scenario based on it.*

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?

It also looks like we had a few new players.  Congratulations to you, and I hope you enjoyed the game - if you liked it, the sequence [here](https://www.lesswrong.com/tag/d-and-d-sci) contains past scenarios, and you can subscribe to that to get notifications when new ones are posted (I try to make sure this happens around once a month).

Thanks for playing!