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:

AD&D Module A4 Random Walks 

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?