Wednesday, December 6, 2017

Alternative to the d20 System

Early D&D used to be a mishmash of various different rules. Roll this die for this, that die for that, look on a table for this other thing. Thieves rolled a percentile die (two d10s with one treated as the "tens" place) and compared to a table on thieves skills; fighters rolled a d20 and looked up their result on a table organized by their level and the targets AC; later fighters rolled a d20 and compared THAC0 and AC to the result; some traps you rolled a d6 and found it on a 1, some doors you rolled a d8 and forced it open on a 1, some checks you rolled a d20 and tried to get under your ability score like STR.

It was kind of a crazy, scattered mess.

They started fixing this with the mentioned THAC0 system, which took the look-up tables for striking an enemy and condensed them down to a simple equation based on your roll on a d20. This simplifcation inspired centering the entirety of the rolls on a similar mechanic: roll a d20, add some modifiers, compare to a target number. Rather than tons of crazy rules and tables and different dice for everything, any time you wanted to check if you character succeeds at an event you had one basic mechanic you could turn do:
 d20 + Modifiers >= DC, 
where DC is "difficulty class", a target number meant to encapsulate how hard a task it. This is the d20 mechanic, and is usually listed in quick start and players guides as "the most important rule," or the "core mechanic."

It was such a powerful simplification that most D&D clones use it now. Even RPGs attempting to emulate the original 0E rules of D&D still rely on the d20 system, rather than duplicating the To-Hit tables and Thieves percentile tables.  So systems like DCC or OSRIC or Basic Fantasy all use the d20 core mechanic, despite being "old school" games trying to emulate an older version of the rules.

The d20 mechanic is still a table, though; just a very simple, linear table that can be written as an equation. It is a table where each entry differs from its nearest neighbors by 5%. A +1 sword means a sword that has an additional 5% chance to hit. An additional 2 to your (ascending) AC means the chance to hit you decreased by an amount of 10%. A lock with a DC of 15 and a lock with a DC of 10 differ by a step of 25% in the chance to pick them (that is New Chance = Old Chance + 25%).

The simple equation for your chances of succes is :
 Chance success = (21 - DC + Mods)*5% = (21-DC+Mods)/20
In tabular form, the DC system would look like this:
Mod -3 -2 -1 0 +1 +2 +3
DC 9 45% 50% 55% 60% 65% 70% 75%
DC 10 40% 45% 50% 55% 60% 65% 70%
DC 11 35% 40% 45% 50% 55% 60% 65%
DC 12 30% 35% 40% 45% 50% 55% 60%
which is such a boring and simple table that you've probably never seen anyone bother to write it out. It's just down 5% for higher DC, up 5% for higher mod, constant steps of 5%. A DC of 10 is considered "baseline," and an average character has a 55% of success, higher or lower from there. 

The d20 system is a really good, simple system. There are alternatives out there. Understandably, most alternative systems try to use six-sided dice, because those are the only dice most normal people know of. Apocalypse dice is one alternative, which uses 2d6. Tunnels and Trolls runs on d6s. The Hypereon systems use d6s.

 I recently discovered an alternative system that sort of goes in the opposite direction. I saw it first proposed on the Goodman Games forum by the author of the blog PeopleThemWithMonsters (described in the linked post, somewhat expanded here).  It's a bit of a crazier system, though it produces probability tables very similar to those for the d20 system. It has some benefits to the standard d20 system and resolves some problems, and overall gives games a more wild "feel", even while sticking pretty close to the original d20 chances of success.

I'm going to call this the Target Dice Chain system. It is not prefaced on a single die, but on a long list of dice. Several games use this list of dice, calling it the "dice chain." It is as follows:
You may be thinking, "Hold on now, there's no such thing as a d3 or a d48," but you are wrong.  Most of these odd dice can still be simulated using "normal" polyhedra, as I detailed somewhat in a previous post.  You may be thinking "What even is a d0 or a d1?" You aren't likely to find them in your friendly local game shop, but you can simulate them by taking a blank d6 and marking every face with a "0" for d0 or "1" for d1.

 In each check, there are two dice that get rolled: a target die and a check die.

The GM rolls the target die. Increased difficulty corresponds to moving to a die higher up the dice chain, starting at d6.

The player rolls the check die. Modifiers correspond to one step up (or down) the dice chain, starting at d6.

In checks, the smaller die is always rolled first. This helps maintain the tension and makes sure both parties roll.

Your baseline check for an average character corresponds to rolling one d6 for the GM, one for the player, and player wins if his die meets or beats the GM's. This corresponds to a check with a DC 10. 

If the character has a +2 to his check, then roll a d6 for the GM and a d8 for the player (two steps up the chain), and player wins if his die meets of beats the GM's. This corresponds to a  DC of 10 and a +2 bonus.

If the check is actually fairly difficult, and the player has a -2 to this check, then you roll a d12 for the GM and a d4 for the player, and the player wins if his die meets of beats the GM's. This corresponds to a DC of 15 with a -2 bogus.

The underlying mechanic works like this:

The GM picks a target die (TD) according to the difficulty of the task. The player rolls a check die corresponding to his ability, starting at 6 and doing up or down one step in the dice chain for each point of modifier. You then make an opposed roll with the check die against the TD, and tie goes to player.

You can express the die roll symbolically as:
 d6 + (MOD)d >= TD
 where +d is a way of saying "up one step in the dice chain", and +3d means "up 3 steps in the dice chain", and +(MOD)d means "up (MOD) number of steps in the dice chain."

The TD can be chosen sort of arbitrarily, but should correspond to the difficulty. A d6 is the baseline TD (TD 6), and corresponds to a DC 10. A TD 12 (that is, a d12 as target die) is a fairly difficult TD, and corresponds to a DC 15. For even more difficult checks, doubling seems to work, with a TD 24 being close to a DC 20 and a TD 48 being close to a DC 25 (though the correspondence weakens at higher DC). A TD 3 is pretty close to a DC 5. Use dice in between for DCs in between. Maybe a TD 8 for a DC 12, or a TD 20 for a DC 18.

But why would anyone use this system, anyway?

This system is a bit "swingier" than the usual d20 system. In d20, certain DCs are simply impossible unless you have a bonus for that check: so, even with a +3 bonus, a DC of 25 is simply impossible. You will never succeed. In the TD system, there is always a chance for success. Even for a TD 48 check, with a -4d, there is still a chance for success. Contrariwise, in the d20 system, you can reach a point where failure is impossible. If you have +10 to a skill, then you always succeed on a DC 10 check. In the TD system, failure is also always possible. Even the best mess up and fail, even the most difficult task can be bested by a stroke of luck. The whole system sort of spreads probability around, leading to more unpredicted outcomes.

Here is a chart for comparison, showing the probabilities of success for different mods to a check for different DCs and the corresponding DC.

Normal dice chain, d6+(MOD)d to beat target
MOD -3 -2 -1 0 +1 +2 +3
DIE d3 d4 d5 d6 d7 d8 d10
DC5 65% 70% 75% 80% 85% 90% 95%
TD3 67% 75% 80% 83% 86% 88% 90%
DC10 40% 45% 50% 55% 60% 65% 70%
TD6 33% 42% 50% 58% 64% 69% 75%
DC15 15% 20% 25% 30% 35% 40% 45%
TD12 17% 21% 25% 29% 33% 38% 46%
DC20 0% 0% 0% 5% 10% 15% 20%
TD24 8% 10% 12% 15% 17% 19% 23%
DC25 0% 0% 0% 0% 0% 0% 0%
TD48 4% 5% 6% 7% 8% 9% 11%

As you can see, it actually sticks pretty close to the usual d20 results.

One major issue this resolves is the opposed check mechanic. Sometimes in D&D, you may find yourself grappling with an orc. In the simplest resolution of this, you'd just make an opposed STR check; you roll a d20 and the orc rolls a d20, add the modifiers to the respective rolls, meet or beat the orc's roll. While this maybe has the feel of a battle of strength, it's actually identical to a base DC of 10 (proven mathematically here), plus your mods and minus the orc's mods, in terms of probability. If you are at +2 on your STR and the orc is at +3, then it's just
 d20 + 2 - 3 >= 10. 
It turns all opposed rolls into static DCs. You could replace opposed rolling with a constant DC and get the same statistical results.

In the TD system, roll a die corresponding to where you are in the dice chain. In the example of a player at +2 and orc at +3, you roll a d8 and the orc a d10, meet or beat the orc. Here an opposed roll is central to the mechanic, and you get a more immediate feel for the power mismatch between the player and the orc in terms of the physical dice being rolled. Imagine then a dragon rolling a d30 vs an average human's d6, or an advanced player rolling a d12 against a d4 mook.

Another major advantage is that it tracks so well with the d20 system. In any game using the d20 system, you can just slide the target die system right in the d20 system's place without a lot of difficulty. If you use the TD system and want to have some particular check be a DC check instead, just slide that in there, keeping the same bonus. It converts almost instantly.

But there are a few major drawbacks to the target dice system.

One, you have to get all those dice. And they aren't very cheap. If you use a computer dice roller like Roll20 then this isn't even an issue: typing 1d48 will work just fine. But if you like the feeling of physically rolling, you'll have to buy more weird dice. I don't know if a GM should be opposed to owning more dice (who doesn't like newer, weirder dice?), but the availability is an issue, as is the money. Luckily, you can find the "off" dice in the dice chain (d3, d5, d7, 14, d16, d24, d30) from several sets offered by Koplow or Impact! miniatures intended for games like DCC RPG which use the dice chain already, usually for around $8 or $12 -- which is still expensive compared to the standards, but about the same as an adventure module.

Two, is that there is no way to make something impossible. Even if you had the ridiculous TD 120, with a d1 check die, there's a chance of success 1 in 120 times. I reported this earlier as a benefit, but maybe in some instances it's a drawback. Maybe you want that lock to be impossible to pick. Maybe you want that armor to be impossible to hit. There's also no way to make something guaranteed. Even if your PC rolls the ridiculous d120 against a TD2, you can fail 1 in 120 times. The swinginess of the system can be a cool and exciting way to mix things up, or it could topple tough challenges through sheer stupid luck of the draw.

Tuesday, December 5, 2017

Advanced Berenst#in Bears Theory - Complex Euclidean Space

I wrote a blog post several years ago about the Berenst#in Bears that, somehow, against all odds, managed to get picked up on the internet.  It's been posted on Reddit and other outlets several times, and accounts for about 95% of all traffic to my blog.

The post is of course intended to be silly, but part of the silliness is that hidden inside this ridiculous proposition of universes merging over children book names is a very mathematically complicated thesis about the nature of space and time.

I don't think I did a very good job explaining what that thesis is, because I often see my blog being referenced as claiming either time travel, the many-worlds hypothesis, or something else about quantum mechanics are responsible for us finding ourselves in this piteous state of being in the wrong universe with the wrong cartoon bears.

In this post, my goal is to outline what exactly it is that I was "claiming," so that if the story gets picked up again (unlikely now that more major outlets have picked it up), maybe people can actually at least summarize what I'm saying correctly.

TL;DR the theory is about changing the geometry of spacetime by allowing all four dimensions to be general complex numbers.

Let me start with what the theory is not.

Saturday, November 4, 2017

A Rule for Shields from Descending Armor Class, Applied to Ascending Armor Class

I've been playing 'D&D 'ever since I was a young boy and found my dad's Dungeon Master's Guide on his bookshelf (the original, by Gygax).  I was still too young to understand a lot of it (Gygax opens with a discussion of uniform vs binomial probability distributions...), but I spent hours of days flipping through the pages, looking at the pictures and reading the descriptions of a fantastic world.  It inspired me to make my own games about exploring through planned dungeons with friends and having them use ability scores to get through.

By the time I was old enough to try to really figure out the rules, version 3.0 was out, which made a lot of changes.  One of the biggest was replacing the original Descending AC and THAC0 system with the slightly more intuitive Ascending AC system.  This system always just made sense to me, whereas DAC and THAC0 always seemed weird and complicated.  I never understood how DAC worked, and never really saw a good explanation of it, and so just never used it.  It was only recently, when getting into old school tabletop RPGs, that I decided to look up an explanation of how DAC and THAC0 used to work.

Wednesday, October 25, 2017


test for commenting

Update: I think I figured it out.  Comments should work better now.

From my phone I can comment.  From my computer, I'm only able to  comment if I use a separate page for  comments.

Sunday, September 24, 2017

The Baker and the Beast

I have an idea for a movie.  It's a moving tale of passion and vocation.  I've pitched it to my wife and a few friends, and all agree, it's pretty brilliant.

Since it infringes on all kinds of Disney copyright, and since the premise is kind of ridiculous, it will never actually be made into a movie.  So I figured I'd just pitch it here.

The genesis.

So, I hate pop music.

I am very susceptible to having songs stuck on my head.  And I absolutely hate it. For this reason, I despise pop music with the burning fury of a thousand suns.  I will not enter stores playing pop music, because then I'll have these obnoxious jingles stuck in my head for months.  Solid months.

So I developed a coping mechanism.  When a song gets stuck in my head, I gradually deform the lyrics to make the song stupider and stupider, until it more accurately reflects the worthless string of noises it so truly is.

It's kind of childish, but it makes me feel better.  If I have to be infected with these memetic viruses from every store corner and coffee shop, at least I can mock the virus.  I'd mock the flu too, if I could.

Back to the movie idea.

I went to see Beauty and the Beast a few months ago when it came out.  They repeat the animated Disney version with the classic soundtrack, but in live action and with some slight tweaks to the story.  They seem to have attempted to answer some of the fan speculation questions that Cracked reposts every four months, like why the enchantress cursed all the servants for what the prince did, and they added a lyric here or there, but mostly the same story and same songs from my childhood.

One of the songs from the film got stuck in my head.  The opening song, "Bonjour," where Belle is walking through the village openly dsparaging the simple townsfolke as "provencial" for having to actually work for a living to support their families, instead of getting to read books all day and refuse to do chores.

The song isn't really as dumb or obnoxious as pop music, but it was in my head, nonstop for weeks.  And when I have an earworm eating my brain I start getting a tad resentful.  So I started changing the words to the song.

But by changing those words, I changed more than just the intro song.  I actually changed the direction of the entire plot, which lead to a completely different movie.  A movie called:

The Baker and the Beast

Monday, September 18, 2017

Replies not working

I just want to apologize to people who have commented and I haven't replied.  For some reason, Blogger is eating my reply comments, so that after I hit "submit" the reply doesn't get saved to the server.

A similar problem also happens to people trying to comment on older posts with lots of comments.  I can't complain about Blogger, it being free and all, but I will need to look into my server situation and perhaps go with a different hosting platform.

UPDATE: I think the problem is my computer's browser (safari).  I tried updating all of my computer's software, but it still doesn't work very well with Blogger.  I have tried responding to some comments three or four times now, and this is really frustrating.

Sunday, September 17, 2017

I am a monotheist about Zeus

Growing up in the time I did, I have had plenty of chances to hear atheists -- on talk shows, PBS documentaries, classrooms, debates, YouTube videos, internet forums -- present their arguments, and I've heard almost all of them by now.  There are especially some arguments that get brought up rather frequently, and then keep getting repeated for years later.

There's one in particular I want to address, the "One God Further" argument.  I believe the argument originates with Richard Dawkins, but I have certainly heard Christopher Hitchens and others make similar arguments on stage.  This argument is that we are all atheists about most of the gods anyone has ever claimed to believe in.  I'm an atheist about Zeus, Hercules, Mithras, Minerva or any of these other figures.  Dawkins simply goes one god further than I do.

And so, to clarify this issue once and for all, let me just resolutely state that I am not an atheist about Zeus.

I'm really not.

I am a monotheist about Zeus.

My issue with Zeus isn't that he's clearly ridiculous and there's no evidence for him.  I mean, yeah, Zeus is pretty ridiculous and there's no evidence for him.  But that isn't really my objection to Zeus worship.

My objection to Zeus worship is that Zeus isn't the kind of thing that should be rightly called a god, or the kind of thing that should be worshipped.