# D&D.Sci Release Day: Topple the Tower Analysis & Ruleset

This is a follow-up to [last week's D&D.Sci scenario](https://www.lesswrong.com/posts/ucJrRBu2KxmAJHRTs/d-and-d-sci-release-day-topple-the-tower): 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/dndsci_sts) you can use to test your answer, and generation code available [here](https://github.com/aphyer1992/dndsci_sts) if you're interested, or you can read on for the ruleset and scores.

RULESET
=======

As you climb the Tower, you will gain in Power. The way this works depends on your class:

*   A Mage begins with 0 Power and gains 3 when they level up.
*   A Rogue begins with 3 Power and gains 2 when they level up.
*   A Warrior begins with 6 Power and gains 1 when they level up.

Floors could contain Enemies, Campfires, or Treasures.

A hero successfully Toppled the Tower if they defeated the Boss on the final floor, and failed if they were defeated (either by the Boss itself, or on an earlier floor).

ENEMIES
-------

Each enemy has a Power:

| **Enemy** | **Power** | **Floors** |
| --- | --- | --- |
| Gremlin | 0   | 1   |
| Acid Slime | 2   | 1-2 |
| Cultist | 4   | 1-3 |
| Jaw Worm | 6   | 2-4 |
| Slaver | 8   | 3-5 |
| Sentries | 10  | 4-6 |
| Gremlin Nob | 12  | 5-7 |
| Chosen | 14  | 6-7 |
| Shelled Parasite | 16  | 7   |
| Bronze Automaton | 16  | 8   |
| The Collector | 18  | 8   |
| The Champion | 20  | 8   |

When you encounter an enemy, roll **1d3 plus your Power minus the enemy's Power:**

*   +3 or higher: you defeat the enemy effortlessly. You beat it and move on to the next floor, but you don't level up and your Power remains unchanged.
*   +0 through +2: you defeat the enemy cleanly, with enough difficulty that you also level up. You move on to the next floor as above, but also gain Power based on your class.
*   -3 through -1: you defeat the enemy with great difficulty. You move on to the next floor as above, and gain Power as above, but you also become Wounded. If you are Wounded a second time, you will be defeated.
*   -4 or lower: you are defeated immediately.

For example, if each starting adventurer encounters a Cultist (Power 4) on the first floor:

*   The Warrior rolls 1d3 plus their Power of 6, getting 7-9. All of these rolls defeat the Cultist too easily, and do not level up. They move on to the next floor with a Power of 6.
*   The Rogue rolls 1d3 plus their Power of 3, getting 4-6. All of these rolls defeat the Cultist cleanly, and level up. They move on to the next floor with a Power of 5.
*   The Mage rolls 1d3 plus their Power of 0, getting 1-3. All of these rolls defeat the Cultist with difficulty. They move on to the next floor with a Power of 3, but Wounded.

By contrast, if they encounter a Gremlin (Power 0):

*   The Warrior again fails to level up, moving on with Power 6.
*   However, the Rogue now also fails to level up, moving on with Power 3.
*   The Mage rolls 1-3. 2/3 of the time, they level up and move on unwounded with Power 3. 1/3 of the time, they too fail to level up.

The Boss at the end works like a regular enemy but is a bit stronger than usual for its floor.

CAMPFIRES
---------

At a campfire, a hero does two things[^7ip9w7999cb]:

*   They Smith their equipment to grow stronger, gaining +1 Power.
*   They Rest, and are no longer Wounded if they were before.

TREASURES
---------

A hero who picks up a Treasure gains Power:

| **Treasure** | **Power** |
| --- | --- |
| Cloak of Protection | +3  |
| Boots of Swiftness | +3  |
| Ring of Resistance | +2  |
| Potion of Healing | +2  |
| Adamant Armor | +1 (but +4 for Warrior) |
| Enchanted Shield | +1 (but +3 for Warrior) |
| Dagger of Poison | +1 (but +4 for Rogue) |
| Vanishing Powder | +1 (but +3 for Rogue) |
| Staff of the Magi | +1 (but +4 for Mage) |
| Tome of Knowledge | +1 (but +3 for Mage) |

  

STRATEGY
========

The general strategy was to try to stay alive while building up Power. Different classes cared about these two things different amounts:

*   The Warrior almost never died until the boss, or at least until very late floors, thanks to their early strength. However, they gain power very slowly. The only way to get >1 Power on a floor as a Warrior is a Treasure, and enemies frequently give 0 Power if you overpower them too hard.
*   The Mage could easily beat the boss if they leveled a lot, but had trouble doing it without dying.

Overall the Warrior mostly wanted to avoid weak enemies and look for campfires/treasure, while the Rogue and especially the Mage wanted to pick enemies at the right strength for them to level up.

The best enemies to fight were ones whose Power was exactly 1 greater than yours, as this guarantees that, regardless of your roll, you will beat them without being Wounded but while still leveling up. Enemies stronger than that will sometimes Wound you; enemies weaker than that will sometimes fail to level you up.

The Rogue in particular could benefit from paths where they gained 2 Power/level but fought enemies 2 Power higher each time, letting them beat enemies at exactly that sweet spot of Power over and over.

Getting to the boss, you would like to either have Power of \[BOSS POWER - 4\] and be Healthy, or Power of \[BOSS POWER - 1\] and be Wounded. This means that not being Wounded for the boss is extremely valuable, and a Campfire that heals you before the boss is effectively +4 Power.

With optimal play, the basic map could be beaten 100% of the time by any of the three classes:

*   The Warrior avoids enemies as much as possible, taking a path composed mostly of Campfires to ensure 1 Power/floor:
*   *   Enchanted Shield (+3 Power = 9)
    *   Campfire (+1 = 10)
    *   Jaw Worm
    *   Campfire (+1 = 11)
    *   Campfire (+1 = 12)
    *   Campfire (+1 = 13)
    *   Campfire (+1 = 14)
    *   The Collector (14 + 1d3 vs 18 means you will be Wounded, but will always survive)
*   The Rogue heads over to the far right to ensure they get the treasures there, then has just enough Power to win even while Wounded:
*   *   Tome Of Knowledge (+1 Power=4)
    *   Jaw Worm (worst-case is you roll a 1 and get Wounded, +2 Power = 6 but Wounded)
    *   Jaw Worm (worst-case is you roll a 3 and fail to gain Power)
    *   Dagger of Poison (+4 = 10)
    *   Cloak of Protection (+3 = 13)
    *   Chosen (13 + 1d3 vs 14 means you will always win cleanly and level up, taking you to 15 Power)
    *   Shelled Parasite (15 + 1d3 vs 16 means you will always win cleanly and level up, taking you to 17 Power)
    *   The Collector (17 + 1d3 vs 18 means you will always win cleanly)
*   The Mage picks up an early Tome and then tries to level a bit safely and then heal at Campfires before the boss:
*   *   Tome of Knowledge (+3 Power = 3)
    *   Cultist (3 + 1d3 vs 4 means you will always win and level up, taking you to 6 Power)
    *   Jaw Worm (worst-case is you roll a 3 and fail to gain Power)
    *   Sentries (6 + 1d3 vs 10 means you become Wounded, but level for +3 to 9 Power).
    *   Sentries (9 + 1d3 vs 10 means you will always win cleanly and level up, taking you to 12 Power)
    *   Campfire (no longer Wounded, up to 13 Power)
    *   Campfire (no longer Wounded, up to 14 Power)
    *   The Collector (14 + 1d3 vs 18 means you will be Wounded, but always survive).

In the Ascension 20 map, there was only one 100%-winrate approach, which relied on using the Rogue to chain together early fights at the right difficulty to level rapidly, and then pick up the treasures near the end:

*   Acid Slime (worst-case is you will fail to level, staying at Power 3)
*   Cultist (3+1d3 vs 4 means you will always win cleanly and level up, taking you to 5 Power)
*   Jaw Worm (5+1d3 vs 6 means you will always win cleanly and level up, taking you to 7 Power)
*   Sentries (worst-case is you will roll a 1 or 2, taking you to 9 Power but Wounded).
*   Campfire (+1 = 10 Power, no longer Wounded)
*   Cloak of Protection (+3 = 13 Power)
*   Vanishing Powder (+3 = 16 Power)
*   The Champion (16 + 1d3 vs 20 means you will be Wounded, but always survive).

It was possible to reach at best an 89% winrate with the Warrior or a 55% winrate with the Mage on this map.

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

Almost all players submitted the same solution, optimizing for the Warrior, which was not quite perfect on the A20 map but could still do very well. (This is what I get for not cruelly making sure that there wasn't an easy second-best path through the A20 map, alas).

**Yonge** defeated the regular tower with a Rogue, and then used the same Warrior solution as all other players for the Ascension 20 tower.

**joseph_c** boldly tried a Mage solution, which wasn't quite as good but still performed fairly well.

| **Player** | **Base Winrate** | **A20 Winrate** | **Combined** |
| --- | --- | --- | --- |
| **Optimal Play** | **100% (Any)** | **100% (Rogue)** | **100%** |
| abstractapplic, faul_sname, Measure, simon, Unnamed, Yonge | 100% (Warrior, Rogue for Yonge) | 88.9% (Warrior) | 88.9% |
| joseph_c | 77.8% (Mage) | 59.3% (Mage) | 46.1% |
| **Random Play** | **20.3%** | **8.6%** | **1.7%** |

Congratulations to all players! Extra congratulations are due to **Unnamed** (as the first person to find the strong Warrior lines that most player ended up using), to **abstractapplic** and **simon** (who did a lot of investigation of the mechanics, even if it sadly did not end up boosting their winrate).

DATASET GENERATION
==================

Previous heroes have wandered through the Tower without knowing where they're going. Each floor had:

*   A 25% chance of a Treasure.
*   A 5-35% chance of a Campfire (more likely on later floors).
*   A 40-70% chance of an enemy (more likely on earlier floors), with each of the three enemies that could appear on that floor being equally likely.

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

As usual, I'm interested to hear any other 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 scenario was more complicated than you would have liked?  Or too simple to have anything interesting/realistic to uncover?  Or both at once?  Did you like/dislike the story/fluff/theme parts?  What complexity/quality scores should I give this scenario in the index?

[^7ip9w7999cb]: Yes, they do both of these things. Did I predict the Tent?