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.

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