Tag: probability

Categories
Dice

MathArtFun’s d120, Recast 2d6, and MultiDie

I love dice, so when MathArtFun‘s 120-sided Disdyakis Triacontahedron crossed my stream, I ordered one — along with a couple other oddities.

The big red one’s the d120, of course. To the right of it is their “Recast 2d6” pack (a version of Sicherman dice that uses a d12 and a d3), and below those are a d3 and a MultiDie.

(It took me a while to find the 120 face for that photo.)

d120

Weighing almost 3 ounces, the d120 is a hand-filling monster — about the size of a large lime or a small lemon. Like the Zocchihedron, stopping isn’t the d120’s forte — but for basically being a big ball, it actually stops fairly quickly.

Like the accompanying card says, it’s numerically balanced in the same way as most dice: all pairs of opposite faces add up to N+1, where N is the number of sides. It’s a nifty little beast.

MultiDie

The MultiDie is a d3 (unembellished numbers, on the faces), a d4 (numbers inside triangles, on vertices), and a d2 (circled numbers, also on vertices). After rolling, you read the top face or the number to either side of it; it works surprisingly well.

Recast 2d6

This one is quite clever: It’s a d3[1], in an interesting lozenge shape unlike all of my other d3s (but most like the even-more-lozenge-y Gamescience version), and a d12 numbered 1, 2, 3, 4, 4, 5, 5, 6, 6, 7, 8, 9.

Roll the pair of them, and you get the same spread of probabilities as an ordinary 2d6 roll. With all the PbtA games I’ve been playing lately, I figured these could be fun to add to my dice roster.

The paint job on most of the dice I received is below Chessex quality (my go-to for non-precision edge dice), but apart from that they’re nicely made. I dig the funkiness of the d120, and the Recast 2d6 set appeals to my inner probability geek. All in all, I’m glad I picked these up.

[1] I ordered a second d3 because I like my d3s to be a different shape than my d6s (it makes them easier to spot in the pile) . . . but I somehow missed that I’d be getting the same style of d3 in the Recast 2d6 set.

Out now: The Unlucky Isles

The Unlucky Isles [affiliate link], the first system-neutral guidebook for my Godsbarrow fantasy campaign setting, is now on DriveThruRPG.
Categories
Dice Tabletop RPGs

AnyDice: A handy game design tool

I love dice, I love fiddling with game design, and I love simple tools that make things easier.

At the nexus of those three things sits AnyDice.

Developed by Jasper Flick, AnyDice calculates the probability of each possible result for just about any die roll. (I say “just about,” but it’s never let me down.)

Need the probability curve for d8+d10, one of my favorite rolls for building random encounter tables? It can do that.

Funky dice for DCC RPG? Sure. Dice that don’t actually exist, like d67s? You bet!

AnyDice isn’t a die roller in the sense that it rolls dice and tells you what you got, like the Crawler’s Companion.[1] It’s all about the odds.

Although they wound up being percentile tables in the end, I used AnyDice extensively while I was designing my DCC RPG wilderness encounter tables. I used it to calculate the odds for Hexmancer rolls, to make sure the percentages lined up. Almost every post I’ve written involving math and dice, like comparing dungeon stocking in OD&D and Delving Deeper, was written with AnyDice open in another browser tab.

Writing this post made me realize just how often I use AnyDice without thinking about it, so I hit the “Please Donate!” button and made a contribution.

Math isn’t my strong suit, but AnyDice enables me to use math to do things I enjoy without beating my head against them. It’s a stellar tool for game design, and one I recommend bookmarking and using often.

[1] It has a die roller in the traditional sense built in, but it’s in beta and the functionality — unlike the core of AnyDice — is pretty limited.

Out now: The Unlucky Isles

The Unlucky Isles [affiliate link], the first system-neutral guidebook for my Godsbarrow fantasy campaign setting, is now on DriveThruRPG.
Categories
DCC RPG Old school Tabletop RPGs

DCC RPG wilderness encounter tables

I needed wilderness encounter tables for the DCC RPG (paid link) hexcrawl I’m running, but there aren’t any in the book. Jeff Rients created some excellent tables for wandering monsters by dungeon level (which also appear in Crawl! #5), but after searching high and low I couldn’t find any wilderness encounter tables online. So I created some.

They’re broken down by terrain type (for “fantasy western Europe”) and include number appearing for each monster. You can download them as a free PDF: DCC RPG Wilderness Encounter Tables. They’re also available as a plain text file so that you can fiddle with them to your heart’s content.

(2018 update: My tables, along with a shortened version of the design notes, appear in The Gongfarmer’s Almanac – Volume 3, 2018 (paid link), with excellent editing by Rob Brennan.)

There’s no scaling by PC level or party size in these tables, and they’re not “balanced” in any way. The world is the world, and what’s out there is what’s out there.

To use them, you’ll need a way of figuring out whether or not a random encounter takes place (I use the system from the B/X Expert Set [paid link]). That’s all!

I love design notes in gaming books, and a surprising amount of design goes into making wandering monster tables (these took me about 12 hours to make!), so the rest of this post is about my goals, process, assumptions, and the theory behind my tables.

Design goals

I went in with a few goals in mind:

  • Quick and dirty — when in doubt, make the choice that sounds the most fun, and do a lot with one roll
  • Showcase the flavor of DCC
  • Give each terrain type its own feel, which should be discernible to players after just a few encounters
  • Use only the monsters in the DCC core book, and use whatever they say (including rarity)
  • Don’t have too few monsters, because lack of variety is dull
  • But don’t have too many, either, because that dilutes each terrain type
  • Reflect “fantasy western Europe,” and a borderlands/wilderlands kind of region
  • Match the terrain types I used in Hexmancer, my system for procedurally generating hexcrawl terrain and features
  • Play nice with B/X D&D’s encounter chances by terrain type, since that’s what I use

The overuse of “men” in the monster names, while matching the feel of Appendix N, bugs me, but I figured changing it would make these tables less useful to others, so I left all of the monster names as-is.

Baseline

My baseline was always “What does the DCC rulebook say?”

If a monster entry listed terrain types, number appearing, relative rarity, or other details, I used those. If it didn’t, I looked at B/X and/or Jeff’s wandering monster list, and then came up with something that felt right to me.

I excluded monsters that are listed as underground-only, as well as the weird ones that seem like they’d work best as placed encounters, not random ones (extradimensional analogues, for example). I also left out things that only live in hot places or jungles (which aren’t in fantasy western Europe, or in Hexmancer).

Massage, dismantle, repeat

My first step was to list every DCC monster under all of the terrain types where it could appear. That gave me a picture of what a world created with this monster manual might look like, as well as some unique monster for specific terrain types and a host of critters that appear only in a couple places — both great starting points for flavor.

It’s not a short list, but it is short on specific things — normal animals, for example. And it’s a quirky list, which I like! Sure, the world likely does have animals in it the PCs could meet . . . but I didn’t worry about that.

I started out with d8+d10 tables, because that roll produces one of my favorite distributions for encounter tables. But I quickly found that I wanted more granularity, which led me to percentile tables. Those also have the added advantage of making the odds immediately discernible, which I like.

A few hours in, I hit on the idea of creating a template table based on the concept of using “brackets” of monsters to convey things about the world.

Broken out, those brackets look like this (in the order they occur on the table):

  • 10% (1-10) say a lot about the world (and the style of game I like to run), while being quite rare. Results 1-10 are on every table except Water, a big-picture statement about what kind of world feels like DCC to me.
  • 25% (11-35) emphasize the importance of humans and humanoids. Humans, humanoids, and subhumans (which are kind of like a mix of both), are on every table.[1] Humans are big in sword and sorcery fiction, and humanoids are big in D&D.
    • Taken in aggregate, the first 35% (1-35) also serve another purpose: Most of them are things that won’t always just try to eat you. Intelligent monsters, and encounters that aren’t always fights, are both good things in my book.
  • 20% (36-55) round out the flavor of the terrain type. These are often unique to the terrain type, but not always, and they’re indicative of what kind of place it is.
  • 45% (56-100) define the terrain type. You have a 45% chance of meeting each terrain type’s signature monsters. More than anything else on the table, these convey what that terrain is all about.

Seeing those odds in graph form also helped me decide that this was a fun distribution model (column height equals percentage chance of that encounter):

Having a template really sped up the process, too, because it made it feel less daunting. Instead of staring at long lists and not being sure quite where to start, I could just look at each terrain type and go, “Okay, which three say ‘forest’ best? Cool, now which four also look like good forest options?”

I ripped apart my draft tables a couple of times, but once I built them using these brackets they stayed pretty stable. My last couple iterations mostly involved comparing the lists, looking for ways to sneak in monsters I regretted not including (so many!), and — most importantly — making sure that the flavor of each terrain type came through clearly.

In B/X, some types of terrain are more dangerous than others by virtue of how likely it is you’ll have an encounter there: 1 in 6 on clear terrain (plains) vs. 3 in 6 in the mountains, for example. The way my lists shook out, some terrain types are also more dangerous because of what’s on them. For example, you’re 40% likely to meet some sort of giant in the mountains, which seems like fun to me.

Surprises and rolling your own

Two things surprised me about this process: how much work it was, and how personal it turned out to be. If two GMs sat down with the DCC book and designed wilderness encounter tables, I guarantee they’d look different — and probably not much like mine!

They’d use different die rolls, different breakdowns of monsters, and different philosophies about what a DCC world looks like. One would follow the B/X model of rolling once for terrain and then again on a sub-table for that terrain; another would compress things into one roll, like I did, but use 2d6 instead of d100. And since they’d both have to choose a subset of the overall monster list, they’d play favorites (just like I did!).

Chances are, if you’ve read this far, you can think of all sorts of things you’d do differently in building a set of DCC RPG wilderness encounter tables. I included my template in the plain text version, in case you like that baseline.

If you make your own tables, I’d love to see them. Post them somewhere and share them with the DCC community — the more the merrier!

[1] Except Water. Just add “except Water” to pretty much everything. Water is weird because there just aren’t that many water monsters in the DCC core book.

Out now: The Unlucky Isles

The Unlucky Isles [affiliate link], the first system-neutral guidebook for my Godsbarrow fantasy campaign setting, is now on DriveThruRPG.
Categories
D&D OD&D Old school Tabletop RPGs

Dungeon stocking in OD&D vs. Delving Deeper, plus The Strategic Review

My copy of Delving Deeper just came in the mail, and after a thorough skim I quite like it. I was after a retroclone that hews as closely as possible to OD&D[1] (paid link),  and at first blush DD seems to fit the bill.

But when I got to the section on dungeon stocking, it looked pretty different from OD&D. Let’s poke that bit and crunch the numbers, like I did with B/X D&D vs. Labyrinth Lord dungeon stocking.

OD&D vs. Delving Deeper

Both games assume that the GM is placing some things by hand before switching to random generation. In OD&D, that’s tricks, traps, and important treasures; in DD, it’s just important treasures (more on this later on!).

Here are the odds in OD&D:

  • Monster: 16.67%
  • Empty: 59.25%
  • Monster with treasure: 16.67%
  • Unguarded treasure: 7.41%

Here are the odds for dungeon stocking in DD:

  • Monster: 22.22%
  • Empty room: 44.45%
  • Treasure guarded by monster: 16.66%
  • Unguarded treasure: 8.34%
  • Treasure guarded by trap: 2.78%
  • Trick or trap: 5.56%

First, treasure: You’ve got a 24.08% chance that a given room contains treasure in OD&D, compared to a 27.78% chance in DD — basically the same. That’s awesome, because it indicates a similar balance of risk vs. reward, and a similar incentive to explore, in both games.

The first four categories in DD’s table correspond to the four categories in OD&D, so we can compare apples to apples in those cases — and they’re really close. The biggest difference is the chance of an empty room (without treasure), which is a whopping 14.8% higher in OD&D than in DD. That just about covers the increased chance of meeting a monster, finding a trap, or finding trapped treasure — the latter two of which aren’t options in OD&D’s chart.

And that’s the biggest difference, of course: DD’s two additional categories, which aren’t present at all in OD&D. Since Delving Deeper’s goal is “faithful emulation of the original 1974 edition,” where did those extra categories come from, and why are they there?

I have two guesses, one reasonable and one perhaps a bit more fun.

The reasonable one

My best guess as to the origin of those two categories is that DD’s authors wanted to provide a clarified take on OD&D’s system for random dungeon stocking, which entailed backing into the parts that OD&D doesn’t randomize.

OD&D includes a section called “Tricks and Traps,” and also notes “It is a good idea to thoughtfully place several of the most important treasures.” Those directives map pretty well to DD’s two “extra” categories.

It’s also significant that, unlike OD&D, DD only proposes that the GM place the “principal treasures” before rolling for the rest of the level — not tricks and traps. If you’re not going to stock those by hand, then they need to appear on the chart.

Legal “cover” may also come into play, too. By presenting stocking differently than OD&D, DD establishes a degree of variation between the two systems. At the same time, the percentages are mostly close enough that OD&D’s intent is preserved.

The Strategic Review

The fun guess involves pure speculation. When I was reading the DD section on dungeon stocking, the categories rang a bell — I thought I’d seen them in an early issue of The Strategic Review. Here’s the relevant chart from Gary Gygax’s article on random dungeon generation for solo play in issue #1:

Bingo! Those categories are almost identical to the ones in DD. The biggest difference is “Treasure guarded by trap” in DD vs. “Special or empty” in TSR; I’d argue those are pretty similar. (Crunching the percentages, they line up almost perfectly with OD&D, with a bit of fuzz factor in order to fit in the additional two categories. They don’t line up as perfectly with DD, but they’re still pretty close.)

I don’t know if Delving Deeper took that TSR article into account, but I do know that it encompasses the 1974 boxed set, Chainmail, and “some ‘zine commentary of the time (most particularly the FAQ that appeared in The Strategic Review and the unofficial untested thief as it appeared in The Great Plains Game Players Newsletter).” Given that the FAQ didn’t appear until issue #2 of TSR, contemplating an article in TSR #1 seems reasonable.[2]

Conclusions

Like B/X and Labyrinth Lord, Delving Deeper’s approach to dungeon stocking incentivizes the same play style as the system found in OD&D. Some treasure is unguarded, and about the same percentage of rooms in both games contain treasure.

Delving Deeper does a great job of breaking down the math used to stock an OD&D dungeon, and then matching it quite closely in the four categories that both games share. It then formalizes a part of the dungeon stocking process — tricks and traps — that OD&D leaves informal, and adjusts the percentages to make everything fit.

In a vacuum, that makes DD dungeon stocking look different from OD&D dungeon stocking — more traps, fewer empty rooms. But it’s not apples to apples, because DD expands the random generation system to encompass more dungeon elements.

It’s hard to directly compare OD&D’s combination of manual placement (tricks, traps, and principal treasures) and randomization to DD’s more fully randomized approach, which only involves manual placement of the big treasures. One GM might stick traps in 10% of her dungeon rooms, while another only traps 5% of chambers.

On the whole, it seems like it would have been easier to follow OD&D’s example exactly, sticking with four categories and matching the percentages more closely. But on balance I like that Delving Deeper attempts to fold the rest of the dungeon stocking process into one table, and that it does so by remaining faithful to OD&D’s intent — and, perhaps, to Gary’s take in The Strategic Review.

Update from Simon Bull

Over on G+, Simon Bull commented on writing this section of Delving Deeper:

DD V3-V4 were written, largely, mid 2013 to mid 2014–so a while back now–but being “legally different” to the original was an ever-present design consideration throughout.

I can remember spending a lot of time trying to get the dungeon stocking probabilities “just so”. I was aware that EGG’s expanded dungeon stocking article in the SR included the possibility of random traps and, although I don’t remember my precise rationale now, it probably helped me to “justify” adding traps to V4’s method of randomisation.

I can also remember being a bit dissatisfied with V4’s frequency of empty rooms, but I figured it was the least disruptive way I could add traps into the mix.

FWIW, I do consider the random dungeon stocking section–and particularly randomisation of monsters–a bit of a weakness in V4. However, I have done a lot a more thinking about it since then, and this element of game is presented far more cleanly in V5.

Thanks, Simon!

[1] “OD&D” can sometimes be a fuzzy term. Is it just the three original booklets? Those three plus Supplement I: Greyhawk (paid link)? All seven LBBs? What about the FAQ in The Strategic Review #2, or the prototype thief class that appeared in a fanzine before it was published in Greyhawk? I’m most interested in the three original booklets plus the FAQ, so that’s what I have in mind in this post.

[2] While I’m out on a limb, given that Gary published this article in 1975, just a year after OD&D came out, I wonder whether or not the percentages for “Special or empty” and “Trick/trap” in TSR #1 might not be pretty close to what he used in his home games when stocking a dungeon level. I have no way of knowing, but it’s fun to think about.

Out now: The Unlucky Isles

The Unlucky Isles [affiliate link], the first system-neutral guidebook for my Godsbarrow fantasy campaign setting, is now on DriveThruRPG.
Categories
B/X D&D D&D Labyrinth Lord Old school Tabletop RPGs

B/X D&D vs. Labyrinth Lord dungeon stocking

Wayne Rossi wrote an excellent post, Clones and Rules, Inside and Out, about the apparently subtle differences between some retroclones and their sources which, in fact, produce non-subtle differences in play. Here’s an excerpt, from his comparison of OD&D (paid link) dungeon stocking to Swords & Wizardry dungeon stocking:

An OD&D dungeon designed according to its guidelines is going to have “unguarded” treasure. According to the book it should be hidden and/or trapped. But a S&W dungeon isn’t going to have that, if the referee follows the guidelines in the S&W rule books. Over time the game is going to play differently, since the OD&D group is going to be looking for hidden treasure while the S&W group would be justified in looking for combat.

Wayne is one sharp dude, and he has a knack for noticing stuff, prying it apart, and being able to succinctly share what makes it tick. (His OD&D Setting PDF, which I blogged about here on Yore, is a marvelous example of this — and a great read.)

His comparison of S&W to OD&D got me thinking about my favorite flavor of D&D, Moldvay/Cook (B/X) (paid link), and its closest OSR analog, Labyrinth Lord. I wondered whether or not they differed in the area of dungeon stocking, and I realized I wasn’t sure — I’d just assumed they were pretty much identical.

But what if they weren’t? What if B/X and LL diverged in the same way as OD&D and S&W, or in a different subtle-but-significant way? Let’s take a peek.

Dungeon stocking

Both B/X and LL sum up dungeon stocking in one chart (plus a bit of explanatory text nearby), making them easy to compare. Here’s page X53’s chart from the Expert Set above page 124’s chart from LL.

They both use the same four categories: monster, trap, special (which LL calls “unique”), and empty. They also both employ two die rolls: d6 followed by d6 in B/X, and d% followed by d% in LL. LL’s chart is a bit cleaner, both because it uses percentages (which I find more intuitive to assess than fractions) and because of its layout.

Room contents

Broadly speaking, the percentages for room contents are about the same — except in one case:

  • Monster: 33.33% chance in B/X, 30% chance in LL
  • Trap: 16.67% in B/X, 15% in LL
  • Special/Unique: 16.67% in B/X, 25% in LL
  • Empty: 33.33% in B/X, 30% in LL

The chance of a room being empty or having a monster in it are close enough to identical to call them the same — about 30%. Ditto the chance of a trap, about 15%.

What’s different is the chance of a special/unique room, 1 in 6 for B/X vs. 1 in 4 for LL. That’s not a huge difference, but it’s a difference.

What about the chance of treasure?

Treasure

Here are the percentages for the chance of treasure being present in each system:

  • Monster: 50% chance in B/X, 50% chance in LL
  • Trap: 33.33% in B/X, 30% in LL
  • Special/Unique: Undefined in B/X, “Variable” in LL — essentially the same thing
  • Empty: 16.67% in B/X, 15% in LL

For all practical purposes, those percentages are identical.

Conclusions

B/X D&D and Labyrinth Lord are essentially the same game with respect to dungeon stocking, the chance for a given room to be empty or otherwise, and the chance for there to be treasure in the room.

The only meaningful difference is that you’re somewhat more likely to encounter a special/unique room in LL than you are in B/X (and, consequently, slightly less likely to have the other possible contents come up).

To me, this is evidence of a shared design goal: Give the players a meaningful choice when it comes to seeking out treasure. Which makes sense, because both systems share the same XP methodology: 1 XP for 1 GP, plus XP for monsters, with the bulk of your XP coming from gold.

Dungeon rooms with monsters in them are more likely to have treasure than any other types of room, but you have to deal with the monster (which is itself worth XP). Empty rooms have the lowest chance of yielding treasure, which makes searching them — and expending resources in the form of time, torches, and wandering monster checks — risky in and of itself, but if you’re lucky you find unguarded treasure.

LL incentivizes the same style of play as B/X, which is a testament to its clarity of purpose as a B/X retroclone.

I also like that the one real difference, special rooms, would give an LL-designed dungeon its own flavor when compared to a B/X-designed dungeon. The party would run into a couple more special rooms, and special rooms are neat. There’s a philosophical difference there, albeit a subtle one.

Out now: The Unlucky Isles

The Unlucky Isles [affiliate link], the first system-neutral guidebook for my Godsbarrow fantasy campaign setting, is now on DriveThruRPG.