## 2023-04-17

### Random Walks in the Dungeons of the Slave Lords

I recently had an opportunity to run AD&D module A4, In the Dungeons of the Slave Lords, for the first time. This is of course the culminating adventure in the classic A-series Slavers tournament, famous for stripping the PCs of literally every resource and forcing them to outhink their way through a pitch-black labyrinth after being abandoned/ sacrificed to its horrors. We chatted about it a bit on Wandering DMs the other week.

Once again, the playthrough made me realize several things about the adventure that I hadn't noticed, even having read through it multiple times since its release in 1981. (As usual, one of the pieces of dogma for this blog is: The acid test is gameplay.) One that came up in my discussion with WDM Paul is that, while the dungeon has 3 different possible exits, all the times we've run it the players have made it out through one exit in particular.

To investigate this, I took some graph-theory code I'd developed for one of my college courses, modeled the A4 dungeon as an abstract graph, and then simulated several thousand random walks starting from the entry area #1 to see the frequency that those walks run into the various exits. For this purpose, I annotated the dungeon map with extra areas 22-27 to mark otherwise unlabelled tunnel intersections (if you have your own map copy you can deduce where I put those labels, I'm sure). Then I cut out all of the mid-tunnel points that don't have any branches, places where the PCs are highly unlikely to turn back, counter to how a random walk will work (and this also simplifies the visual appearance of the graph, below). Here's the result, via the gvedit visualization tool:

Some observations: There are several interconnecting circuits in the section of areas #1-12 (top half of this graph), which allow numerous ways to navigate between those areas. But there's only one exit in that section, at area #10.

In contrast to that, there's one critical bottleneck-tunnel from area #12 to #15; that's the only way to access the other branch composed of areas #15-21 (bottom half of the graph here). Despite the difficulty in getting there, that branch includes 2 of the 3 dungeon exits (at areas #19 and #21), as well as the notable Myconid colony (featured on the cover of the module, and the only place in the entire A series where negotiation can be profitable). If players never find their way to that particular tunnel out of area #12, then they'll never see any of that latter content.

So here's the results of my series of random walks -- note this is purely random at each location, including equal chances to turn around and backtrack from any location. After 10K simulations, the number of times each exit was reached are as follows:

 Exit Reached Percent 10 5,360 53.60% 19 1,904 19.04% 21 2,736 27.36%

So broadly speaking, this model suggests that about half the time, players will exit from the top half of the graph, which means the exit at area #10. And the other half of the time, players will exit from the bottom half of the graph, with exits split between areas #19 and #21. Basically that toggle is a coin-flip over whether they take the tunnel from #12 to #15 or not. And consider that in this scenario, the players aren't allowed to map or properly orient themselves ("all directions should be given to them in terms of right and left", p. 3), so it's at least as likely that they'll circle back on their own path several times as they are to stumble onto the key connection. Indeed, it's the exit at #10 from which Paul & I have seen all of our playgroups escape (a small sample size, to be sure).

Regarding the difference between the two exits in the far part of our graph: our model makes it look significantly more likely that #21 is found than #19. On the other hand, it's the latter area that the Myconids are able to direct the players towards, which might shift some weight from #21 to #19; but on the other-other hand, anecdotal evidence suggests the Myconids are so frightening that it's rare for negotiations to be pursued with them. Since all of these factors are isolated in our lower branch, I don't think any such re-evaluation would affect the chance that area #10 is discovered first.

Here's he upshot: If you're preparing to run module A4, then you should prioritize being able to handle the #10 exit above the others, and more generally the whole branch that it's on, because it looks like a bit more than half the time that's how the action will play out. Secondarily you can prepare for running the more distant branch (with the complex Myconid area), in particular the area #21 exit, and not spend too much time thinking about #19, which seems to be a fairly unlikely exit point.

If you've played or run module A4, which exits did you personally see get used in play?

1. I wonder how sensitive your results are to the weight you give advance vs turn back? Especially at the core point. They look suspiciously close to flip a coin whether you'll exit from the top half or bottom, and flip a coin between the bottom exits, which makes me wonder if the graph matters much at all.

1. I had a version that included all the mid-tunnel waypoints and the results came out differently, so the graph does make a difference. There's also a significant (and stable) difference between #19 and #21 -- the latter being one step off a loop gives more ways to get there, for example.

2. I'm still curious about what the results would look like with different thresholds for advancing vs. retreating. My sense is that real players will keep with a direction they picked at least 2/3 or 3/4 of the time and will almost never reverse directions more than once or twice unless they really hit a dead end. But I have no idea whether that would actually change the end result.

3. For the case of a party that won't backtrack (unless forced to by a dead end), the graph can be simplified and it becomes evident that they'd reach #10 50% of the time, 25% chance of #19, and 25% chance of #21. I'd expect intermediate levels of backtracking to produce odds in between.

2. Last I ran this was in 84? So I don't recall how the party escaped the caves. However, they did beat the looters, took their stuff, and then took on the slavers. I recall that they beat them with some shenanigans, and one player used a skull as a club throughout the entire session...

1. Cool! I think you're talking about the post-dungeon expansion that comes after the tournament part (which we didn't get to in our con game).

3. I truly appreciate your view that "the acid test is gameplay." I wish more would uphold that.

Also, cool analysis! But I do wonder: why isn't there a line from 11 to 12? PCs can go that way through 14 and 13. Also, 11 and 6 are linked.

A major factor, though, is [SPOILER] that the exit at 10 may be accessible, strictly speaking, but to discover that it's an exit, PCs have to contend with a giant crab while swimming hundreds of feet underwater through tunnels with dead ends described in the module as "death traps." In the rules given, you need a CON of 20 to swim to the exit, if you make no wrong turns, so the prisoners have to figure out how to rig non-obvious airbags to get out. This ain't easy. Notably, all the pregens in the module have CON 16 or higher, except #9 who has a "mere" 15 CON. Most parties will have zero chance of getting out this way.

So: not all exits are equal and maybe DMs should not count on an exit at 10.

Off topic, you and your readers may be interested to know that this module is the target of the oldest known use of the term "railroading" for a module. Ken Rolston remarked in Dragon 133 (1988) that "A little railroading is required to set the PCs up for this scenario" coming from the previous one A3. (This is mentioned on the RPG Diegesis blog's article on railroading.)

Thanks again for the cool analysis. I ran A4 once in middle school in the early '80s, and recall none of the play.

1. Very interesting about the term "railroading"! Definitely the inescapable-capture that occurs at the end of the prior module is one of the most abrasive things that can happen in a game. I thought it would go down easier in the context of a tournament one-shot but my players were still kind of upset by it.

The link from area #11 to #6 and #12 is represented in my graph by location #24 (an unlabeled intersection in the original module). The line from #24 to #12 is the tunnel from that intersection through #13 and #14.

I almost noted that all the exits have some complicated obstacle to make use of them, so as a zero-level assumption I figure they're all about as hard to get through. #19 is hidden similarly to #10 (albeit different direction). Area #21 I was looking at and I'm not even sure how my PCs had any way to get through it.

4. This type of analysis really floats my boat. It is why I continue to deeply enjoy many of the posts from the many years the blog has been running.

As an aside, it reminds me a bit of the end sequence in BBC2's The Adventure Game from the very early 80s. Players had to negotiate a hexagonal node grid while avoiding standing on an invisible vortex that would move every time they moved. As a kid my sister and me would argue over what the best strategy was to negotiate the grid safely. No mathematics just empirical observation. No idea if either of us was right.

I've written this problem up as a D&D situation.