Monday, May 16, 2016

Arena v1.11: Man vs. Monster, Pt. 2

Last time we convinced ourselves that the Monster Level Matrix given in OD&D Vol-3 is, to be honest, irreparably broken and in need of a fix. Here we search for a revised table to use in its place. Previously I'd contrasted the alternatives that followed, as in Holmes' Basic D&D and Gygax's AD&D Dungeon Master's Guide (link). My impression at that time was that Gygax's AD&D table was such an incredibly radical swing in a direction away from OD&D, and the Holmes' table appeared to be a balanced medium between them, that the latter seemed to be the better choice.

Here I'll consider the AD&D table more closely, partly because it has the Gygax imprimatur on it (and also I want to avoid any psychological Framing Effect). First, recall the OD&D matrix:


Compare to the equivalent table in the AD&D DMG:


This latter table is much more forgiving. Of course, it's stretched the monster levels out from 6 to 10, and it uses a d20 instead of a d6, but that's not what really interests us here. On the 1st dungeon level, where OD&D includes 2/3 of the possible monster levels, AD&D covers less than 1/3 (equivalent to permitting only monster levels 1 or 2 in OD&D; so the danger level is approximately half or less). In OD&D, the danger level rapidly ramps up, because of the way dungeon levels are batched up starting at the 4-5 tier and so forth; in AD&D, levels are kept distinct up until level 10, so a much more gradual increase can be drawn (except for the completely bizarre joint step at dungeon level 2-3, which skips having a 20 in the monster level IV column; Odin only knows how that came about). And while OD&D ends up with the only possibility being top-level encounters by the end of the table, AD&D always keeps at least a 1-pip chance for any lower-level encounters down to level I (including the possibility of maybe very large collections of goblins, skeletons, or giant ants, say).

So what I decided to do was linearly translate this AD&D table back into the OD&D format. The process was like this: (1) Interpolate a distinct row for dungeon level 2 in the AD&D table. (2) Separate the AD&D table out into "pips" value difference in each cell. (3) Transform the pips in the 10 columns of AD&D into 6 columns for OD&D (e.g., OD&D monster level 1 gets the pips from AD&D column 1, plus 2/3 the value of column 2; OD&D column 2 gets pips from AD&D as 1/3 column 2, all of column 3, and 1/3 column 4; etc.). (4) Scale the pips from d20 to d6 with a 6/20 multiplication in each cell. (5) Sum the values back up sequentially on each row for d6 roll ranges. You can see all the details in an ODS spreadsheet at the end of this post, but the end result of the translated AD&D table looks like this:


Dungeon levels 1 & 2 end up looking identically, by which I'm not hugely offended. Due to the lower granularity of the d6, we don't have space to maintain every single possible monster level on the deeper rows of the table, but that's not a huge tragedy, either. In general this sort of looks like the inverse of the original OD&D table (just a few options in the top-right, with most of the level possibilities covered on the bottommost row).

Now, let's load this as a data file into the Arena simulator, in place of the original OD&D Monster Level Matrix, and see what the resulting population of Man-vs-Monster gladiator combats produces. This is done with 10,000 fighting men in the list, over 100 years, fighting 24 times/year (biweekly), with age effects implemented, and the standard 5% chance for a magical boost on each level-up:



Now, that looks like a more reasonable population (i.e., a game that's not entirely suicidal to play). It's still a significantly more risky path than the Man-Vs-Man game we looked at two weeks ago. No one here has reached Name Level, and most fighters do not survive to the age of 30 years. But at least it covers most of the D&D span of levels, Superheroes are at least possible, and at least one figure did see 34 years. I think we can conclude that Gygax's table in AD&D is not too generous; it's still a very highly risky path to fame and fortune; if anything, one might argue that it should be softened some more to actual produce a Lord or two over the course of a century. But it's not completely the holocaust that the OD&D table was.

One thing you might notice here in the chart is the drop-step at fighter level 2. This isn't because level 2 is too dangerous, but rather just the opposite; it's an unusually easy level to survive and graduate, so most members have quickly moved on to level 3 at this point. This is because of two reasons here: (1) Although the fighters are about twice as durable as when they were 1st-level, they are still rolling on the same row of our Revised Monster Level Matrix, and (2) The way the geometric XP tables are constructed in OD&D Vol-1, it doesn't take any more XP to graduate 2nd level than it did 1st (2,000 XP in each case).

In conclusion: This is something I can live with for my game. My plan is to paste this into my custom print of the OD&D ruleset and use it in place of the original Monster Level Matrix. Be cognizant that while this game is at least conceivably survivable (for a time), it is still too risky to reflect the demographics of groups of Men in the upper world; for that, we will continue to look at the Man-vs-Man results from earlier (and as in the Marshal application, etc.).

Below, the software package you can use to play with this yourself. As before, if you have Java installed, you can download and unzip the first file, which includes Arena.jar and associated data files. You'll need to run it with several command-line parameters to get useful output, for example the command

java -jar Arena.jar -n=1000 -m -a -rys 

will run the simulator respectively with 1,000 men in the list, fighting man-vs-monster (instead of man-vs-man), with aging effects applied, and reporting yearly updates and summary statistics at the end. To switch from the original (brutal) OD&D monster level matrix to the revised one, rename the included data file MonsterLevelMatrixRev.csv to MonsterLevelMatrix.csv and run it again (or modify the data file to whatever format you prefer). A complete listing of all the available command-line parameters is as follows:


Usage: Arena [options]
  where options include:
        -a apply aging effects
        -b base type of armor (=0-3, default 3)
        -f fights per year (default =24)
        -m man-vs-monster (default man-vs-man)
        -n number of men fighting (default =100)
        -p percent chance of magic per level (default =5)
        -r reporting types
                s summary statistics    y year-end info
                d detailed data         k monster kills
        -s start level for fighters (default =0)
        -x use revised XP award table (from Sup-I)
        -y number of years to simulate (default =100)



Have fun! And tell me if you find any other interesting discoveries that I've overlooked.




2 comments:

  1. Dan that's awesome. I love it. It's apparently quite different than the old D&D trope of dungeon level = monster level.

    One question though, I don't pretend to have more than a superficial understanding of the math, but I wonder about how you translated the AD&D monster levels into OD&D monster levels. Unlike the OD&D levels, he AD&D levels are based on experience point ranges, so I would think to translate from one to the other accurately, you would need to calculate the AD&D exp values of each OD&D monster level, and then figure out the % of each OD&D ml is of the OD&D total, and then map those percentages onto the AD&D level exp total and see what AD&D Monster Levels fall within the 6 percentage ranges of the OD&D levels.

    Feel free to tell me I'm overcomplicating it. :)

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    1. Glad you liked it! :-D

      Here's a simple answer to the monster-level question (I think): I just didn't change the "Monster Level Tables" at all from OD&D Vol-3, p. 10-11. Kobolds are still categorized as monster level 1, wraiths level 4, giants level 6, etc. The only thing I adjusted was the "Level of Monster Matrix" as above, which determines which (unchanged) Monster Level chart you should consult.

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