# NaBloPoMo 2014 – Entry 18 – Why D20s Suck… Finally

Posted by docryder

Random item: I saw a young woman today who made me think “Damn, I wish was physically 18 again.” And I reminded myself that my maturity level isn’t in line with my age, so no adjustment there is necessary.

So, I’m starting early in the evening, so I think I’m going to finally write the infamous “Why D20s Suck” post.

I’m going to start with the admission that I suck at math, but I do get the ideas behind probabilities and statistics. So, a lot of this is going to be a little vague, but should get the point across.

Back in the day (c. 1979), we rarely used d20s alone. Old d20s were marked with only single digits on all the faces. I still have a few or those I use regularly for d10s, and it scares the shit out of the kids at the *LFR* table when I roll out a crit with my new bard character and his *piercing songblade* (which does a d10 per plus). I’ve always got to remind them I’m rolling d10s, not d20s.

Anyway, in those days, all our dice were precision dice, with sharp edges on the faces. The way we got a “20-sided die” result was often to roll two dice, a d6 and a “d10,” with the d6 acting as a coin flip that determines whether or not you add 10 to the digit on the d10. Usually, we used the results of 1, 2, and 3 for reading the d10 straight, and 4, 5, and 6 for adding 10. For example, if your d6 came up 2, and your d10 came up 7, you got a seven. If your d6 instead came up 5, then the d10 would be read as 17. In this way, the d20 had a bit of a bell curve. Not much of one, but a bell curve all the same.

Sometimes, we would use different colors to label the numbers. Half might be in white, the others in black, and then you’d call which color was high, again adding 10 if the number rolled was the color called high.

And therein lies the problem. Theoretically, each surface of a normal d20 has a 5% chance of coming up. In practice the numbers are a little different, but not significantly so. You can check out this article on Gnome Stew to get more info. It boils down to this, d20s have no bell curve. A d20 is a flat die. Of course, all single-die rolls are, assuming all the surfaces are built correctly and carry the same area.

So, rolling a result of 20 has the same percentage as rolling a 1. Most games assign a significance to those numbers, the higher being a critical hit, the lower being a fumble. The **Cypher System** adds significance to 18 and 19, too. This is an artifact of imagination. They really aren’t special as they all have the same chance of coming up as any other number.

Monte Cook has mentioned in a couple of places that he thought about using a 2d10 roll for **Cypher**, but he felt that the d20 was a “visceral” artifact he wanted to maintain. And I get that, but lately, I’ve seen that the reality is that the d20 is a grossly flawed die to base your resolution system on. Any single die system is going to have this problem.

Now that I’ve spent all this time on explaining the basic problem, I’m going to repeat some of the examples of the problems I’ve experienced.

One of the most prominent is what happened with my characters in the *LFR* game. **4e’s** way of creating challenge is by setting difficulty numbers about 15 points above the level of the PCs, at least as far as AC is concerned. Other Defenses work similarly. So, in order to maintain viability, a player needs to 1) focus his character on one stat, to maximize it’s functionality, and 2) purchase the right feats, that improve the character’s accuracy. My previous character was divided between two stats, and a lot of feats had been spent to give the character his multi-class powers, so they couldn’t be spent on accuracy feats. The current character is exactly the opposite: all of his powers key off one stat, and he’s got the feats to improve his accuracy.

Another example of the flaw is my prior campaign, especially towards the end. The ranger in the party could not be surprised without a lot of DM fiat, as the build had such a high Perception skill that even high level sneaks could not roll high enough to surpass the character’s skill, much less his total roll. I came up with similar problems with the bard, whose social skills were off the chain as well. I’m seeing some of that with my current character in *LFR*: The skills the bard is focused on are based on the same stat his powers are focused on. Some classes have that synergy built into them.

We saw similar results in our **3/3.5e** games. Worse, if characters are built the right way, they become invulnerable. We had a character who could stand on the event horizon of a black hole (basically, as that was what we determined a sphere of annihilation was), because the character in question, a fighter, had a high enough Fort Save that she couldn’t be drawn in. I had a fighter that couldn’t be hit, as eventually we arranged for an AC so high monster couldn’t hit my character. In both cases, I’m referring to Epic level characters, but the idea persists throughout the system. My LFR experiences are showing that.

It’s simply a flaw with using a single die, and attempting to fix the system with bonuses to make the flat rolls “balance.”

**5e** is trying to fix this with a “bounded accuracy” system. I haven’t looked at this as deeply as I should, but this is how I understand it: By limiting the the bonuses, the hope is that challenging the dice can be achieved. Note that I said “challenging the dice.” That’s because the player can only make decisions what his character does, not what the die roll is, or really what the difficulty is (excepting the effort rules in **Cypher**). **5e** difficulties are limited to 5/10/15, and bonuses are limited to 6 at 20th. Even if it’s difficult to get a score above 18, since the **3/3.5/4e** attribute bonus math is in place, that means a +10 at 20th level, without other bonuses (and we know that other bonuses are available, just maybe more difficult to acquire). So, at 20th level, a character will still beat a difficult action 80% of the time, assuming a match-or-beat system (a +10 versus a 15 difficulty means a 5 or better on the die wins the challenge). Even a first level character will likely beat a difficult action 45% of the time, provided it’s with his strong stat. At low levels, the die is more important, but eventually that switches and the character’s skill overwhelms the die.

Again, the linearity makes the game flawed.

This is why I want to return to a bell curve based system like **Fate**. The system is built for the skill of the character to be paramount, and the die roll, being a bell curve, tends to settle towards the middle of the curve, and not swing the game in crazy directions like a d20 does. Like percentile-based games, and others that use multiple, accumulative dice, the Fate system leans to the center and becomes more predictable, not only for the players, it’s also for GM, which d20-based systems fail at.

So, there you go. That’s my problem with the d20 summed up, and maybe beaten to glue. I hope you’ve managed to stick with me here, and get some insight into what I’ve been blogging about for a while.

Working tomorrow, so I need to go. Later.

## About docryder

I'm an experienced table top gamer with an open mind to new game systems. I'm looking to explore ideas I've got. Some are pretty meta, some are pretty mundane. Welcome to my world.Posted on November 19, 2014, in D&D 4e, Metagaming, NaBloPoMo. Bookmark the permalink. 3 Comments.

Thanks for writing this up. I really agree regarding the d20 and that has been a big reason for me investigating other games that don’t rely on it like Fate and Savage Worlds.

Hey, followed you home from your link to my article. Here are a few tidbits you might enjoy:

-Rolling a d20 by rolling a d6 for the 10s place and a d10 for the 1s place creates (in theory) the exact same distribution as a normal d20 in the same way as one d10 for the 10s and another for the 1s gives you a uniform number between 1 and 100. There’s no bell curve.

You can see a graph here: http://anydice.com/program/4c0b

However it may well have seemed like it did because even though all those dice started as sharp edged precision dice they weren’t made of high impact plastic so they suffered from wear and tear fairly quickly. (as opposed to our modern dice which start out in poor condition and stay that way) Also, because you were rolling two dice, you had two dice’s damage to alter the probabilities involved. Also, since damage to dice tends to effect two opposite sides of the die, a die with a long 1-20 axis will indeed seem to roll bell-curved.

-You mentioned the 5e system. I crunched the numbers on that one. You may find it useful:

http://www.gnomestew.com/specific-rpgs/disadvantage-vs-2/

-Multiple dice don’t give a true bell shaped curve (because their results aren’t smooth) but with as few as 3 dice their curve approximates a normal curve (the standard bell curve) fairly well. As such, the 68, 95, 99.7 rule applies fairly well too (and sort of well to sets of 2 dice). This rule says that 68% of your rolls will be within one standard deviation of the average roll of your dice, 95% will be within 2 standard deviations of your average, and 99.7% will be within 3.

So for example, 3d6, with it’s average roll of 10.5 and it’s standard deviation of 2.96 rolls between 7.5 and 13.5 about 68% of the time, between 4.6 and 16.4 about 95% of the time and 1.6 and 19.4 about 99.7% of the time. (You can see how it’s an APPROXIMATE bell curve, not an exact one).

Of course the average roll on a collection of dice is easy. The formula for standard deviation of a single die is sqrt(([n^2]-1)/12) where n is the number of faces (so a d20 has standard deviation of sqrt(399/12) which is ~5.77. For more than one die, multiply by the square root of the number of dice, so 2d10 has a standard deviation of sqrt(2) * sqrt(99/12) which is ~4.06. 5d4 has standard deviation of sqrt(5) * sqrt(15/12) = 2.5.

The 4 fudge dice (treat them like d3s) have standard deviation of sqrt(4) * sqrt(8/12) which is ~1.63

Um, yeah. Like I said, I’m bad at math, but I get the ideas behind it. This is math. I am bad at it. 🙂 However, I think outside of the correction of the two-die d20, I think you’re otherwise saying I’m correct.

Thanks for the input. I’m sure someone out there follows it. 🙂