Friday, February 27, 2015

Dice Set Comparisons

A wonderful comparison by Stephen Dickson of the WizDice 100-pack, versus the Chessex Pound-o-Dice. See his site on imgur.com for close-ups and analysis (link). More of this, please!

Wiz Dice 100-Pack


Chessex Pound-o-Dice



Monday, February 23, 2015

When an Inch is Not an Inch in AD&D

I've said this a few times in the past, but it always seems to get lost in a larger discussion, so I'll make one post here to highlight the issue. In Gygax's AD&D, one scale "inch" is not one inch on the tabletop.

Now, everyone knows in AD&D that when the book says 1" it means 10 feet in the dungeon, right? But look at DMG p. 10, under "Use of Miniature Figures with the Game", where it says that 10 feet will be 3 actual inches on the tabletop. So 1" = 10 feet = 3", or in brief, 1" = 3". Now that's a clever trick!


If you wonder why that contradiction could ever be permitted, recall that Gygax clearly stated that his circle had entirely eliminated using miniature figures by the time they started the role-playing game they called "Dungeons & Dragons" (link). So use of miniatures was really a vestigial organ, not truly playtested or maintained in the ruleset, and this section really exists in the DMG to promote the business case of selling branded miniatures (see the all-caps-and-boldface parts of the following paragraphs, and consider later Games Workshop and WOTC business plans). Gygax may have written it, but he didn't use it.

So while the 1" scale in the Chainmail mass-warfare game represented an actual inch on the tabletop, by the time of AD&D the 1" scales given for movement, missile fire, spell area and ranges, special monster powers, etc., are effectively purely abstract units, representing 10 in-game feet and nothing else. They don't indicate anything in particular for the tabletop -- for that purpose, you'd have to convert each book scale 1" to an actual 3" on the playing surface, or at least so says the Official Advanced D&D Dungeon Masters' Guide. (Compare in spirit to: moneys of account.)

Primarily, this insanity is why I highly recommend that O/AD&D be fixed, as in later editions (Moldvay Basic, 3E D&D, etc.), to use 1" = 5 feet for scale, in both book and tabletop, so as to avoid the Euclidean space-warp effect that most people can never get their heads around.


Monday, February 16, 2015

Archery – Field Experiment

My current house-rules for archery are based on a combined mathematical model and game simulation program (link). This is the fruit of quite a bit of analysis on the archery game (search the blog for "archery", you'll find lots of posts). The most important observation is this: shooting man-to-man and shooting at an army are totally different tasks (the former may be impossible to hit, while the latter impossible to miss, at the same range).

This is based on some pretty good data in Dragon #58, originally from the book Archery, on hit rates for Grand Masters at different ranges (think: top-level fighters with several bonuses). Not having specific hit data, my model for beginning bowmen (1st level fighters?) was very roughly estimated by recent GNAS scoring, and guessing they're maybe one-tenth as accurate as Grand Masters. The table below recaps the expected hit rates from both the game rule model and the bivariate normal physics simulation. But were those reasonable assumptions?



Obviously, the only way to approach this scientifically is to run a test in the field (like, an actual field). At the end of August I visited my folks' place in Maine and got out my very old bow and arrow kit and set up a target to see whether my own accuracy broadly matched this math model. The equipment is a 30-year-old Bear compound bow with a 28" draw at 60 pounds (with no maintenance ever having been done in those 30 years; in fact, it spent several winters in an outdoor shed), shooting 32" target arrows. I made a 2-foot radius target (to match the old GNAS competition), and took a series of 10 shots each from 10, 20, and 40 yards distance (to match the increments in the prior D&D model). Due to time constraints, I didn't take any practice or warmup, and I haven't done any shooting in at least several years (and I've never done it with this target size or range).

Now technically the first thing I did was set up the target and several bales of hay in back of a metal trailer and shoot one flight of arrows that I had to start with. Each of these shots went entirely through the target, hay, into the side of the trailer, and entirely shattered from head to tail. So I didn't count those, and had to go down to the Kittery Trading Post to get another batch of arrows. Later that afternoon, I was back with this setup:



Here are the two flights of 5 arrows each, shot from 10 yards. I easily hit all ten times, although several of the arrows flew entirely through the target. Notice that even on the second set of 5 my accuracy was noticeably improved, grouping the arrows closer to the center of the target.




Here are the  shots from 20 yards. Again I hit the target all 10 times -- although more of the arrows are disappearing through the target. I think I started getting a fuller draw at this point, because on the second set of 5 every one of them flew entirely through the target.




At this point I started shooting from 40 yards away (from way down in the field, actually). Here I only got 2 arrows out of 10 to actually go in the target. Generally I was aligned correctly, but my shots were mostly falling low/short, although I'm sure that would improve if I got more practice and got the ascension right.




So, an admittedly small sample size, with very old equipment and an unpracticed shooter, but that's all I could accomplish on the particular day. Let's compare the results to our prior model:

That's not a perfect match, but the numbers do seem to moving in generally the same direction. Based on my experience that one day, I really couldn't miss an immobile target of that size from 10 or 20 yards distance. From 40 yards I was hitting a bit less than predicted for a "3rd class bowman", but I'm pretty sure with a little more practice at that range I could start doing much better than that, likely above 30%. (As a comparison, the next day I spent most of the afternoon shooting from 30 yards, and I felt like I nearly couldn't miss once I had the range down; over about 100 shots I missed only 2 or 3 times, for a 97-98% hit rate. The house rule game model would predict a 55% success rate, and the physics-model simulator about 48%.)

Generally it seems like with a little practice, my hit rates are better than predicted, which could be due to a number of factors: (a) I underestimated the skill of GNAS 3rd-class bowmen, (b) I have better equipment than that used for the base data (the Archery book was published in 1894), (c) I'm a better archer than expected -- seemingly the least-likely hypothesis.

Coincidentally, a neighbor's son who is entering high school as freshman came over the next day with his own archery equipment, and it was kind of stunning to see how the equipment and style has all changed completely in the 30 years since I got my own bow. His bow is much lighter and smaller (half the draw weight) with a bunch of built-in sights and range-finders and whatnot. Shooting is done with a bent left arm (whereas I need a big leather guard to prevent injury) and a loose grip, letting the bow fall out of the hand loosely on a cord after the shot (whereas my heavier bow would likely break my wrist if I tried that). Plus a trigger-button release is used, whereas I mostly chewed a hole through a leather glove and my fingers over the afternoon. He took a few shots and obviously had much greater accuracy than I was getting, which speaks to the rapidity of how much the discipline can change due to technology in a fairly short time.

Anyway: What we clearly see in the experiment is that hit rates may be 100% at close ranges, and then very rapidly drop off to near-zero with just a few doublings of range. Even if I could practice more at the 40-yard range, I'm sure that shooting from 80 yards out at a single man-size target would be practically impossible for me. But the flip side is that it would only take a few doublings in target size (4 or 8 men deep or wide) and I'd be back to automatically hitting on almost every shot. So in broad strokes the math does seem to be winning, and generally predict the overall dropoff in accuracy from shooting at a small target at distance.

Got any more data?


Monday, February 9, 2015

The Fellowship by Michael Shorten

In line with the idea from the last post that there will probably be more Book of War stuff coming up this year, here's the first thing. A month or two back Michael "chgowiz" Shorten sent me a draft of a set of expansion rules for BOW that he calls "The Fellowship" which addresses one specific, sometimes hotly contested, limitation -- the fact because of the 1:10 scale, you need a hero to be at least 10th level in order to appear on the table as an independent figure (and even counts as only getting 1 hit before going down).

Michael's idea was to allow "PC Party" units -- all of whom might be 3rd-7th level or some-such, acting as a single, combined figure. Such a great solution; I never bothered to allow heterogeneous units in this way because I thought it would be too much trouble. But Michael's done a great job of basically averaging out all the armor, moves, combat abilities, and magical powers you might encounter. He even has an expanded spells section for use at that level. I'm completely flattered that he spent enough time to deeply understand Book of War as he clearly does, and I think it's a real step forward for the game. Check out his rules expansion on Google Docs, I highly recommend it!




Monday, February 2, 2015

Back to Posting

Okay, we've been off for about a month here at the Hotspot, so we should probably get back to posting, eh? Thanks so much for all the kind words and support for the Book of Spells, 2nd Edition (a stripped-down, open-game-content, digest of spells for Original D&D and related games; see the last post). For the moment I'll be taking a bit more laid-back attitude towards posting, since I have a number of obligations with my new full-time math lecturer position at CUNY. Maybe once a week unless there's a burst of things I need to get off my chest?

Here's some possibilities of what might be coming up on the blog this year. I hesitate to even say this, because I always feel like a loser if I wind up not following through (partly why I'm unlikely to ever "Kickstarter" anything). So this is very tentative and just really spit-balling here. But if any of these interest you more than another, please chime in and let me know.
  • More Book of War stuff (simple mass-warfare with miniatures, statistically strongly aligned with D&D; see the sidebar). Possibly more gameplay, some rules revisions that have their way into our games in the last few years. Maybe a 2nd or expanded edition? Any time you see a dig into old combat rules it's probably coming from a what-works-for-BOW context.
  • Possibly some steps in the direction of campaign/domain-based play with Book of War?
  • Hopefully pretty soon some posts on play or materials I had when I was a young person.
  • Maybe some work on wilderness adventures. 
  • And, I've got the glimmer to possibly keep going with Spells Through the Ages until I've got an essay on the history and evolution of magic-user spell in the original rules. Right now I'm what, one-third or one-half done? We'll see how that goes, maybe a nice thing to collect when complete.
Any other ideas?