d20 versus 3d6

Alright, so say you want to design a mechanic similar to "3rd edition" D&D where you have to "beat" a target number set by the referee to succeed at a certain task. If you have a d20 handy, you get something like this:

Target	Success?
1	100%
2	95%
3	90%
4	85%
5	80%
6	75%
7	70%
8	65%
9	60%
10	55%
11	50%
12	45%
13	40%
14	35%
15	30%
16	25%
17	20%
18	15%
19	10%
20	5%
21	0%

Sound good? Pretty good! And you are probably all more than familiar with it anyway... Now what if instead of a d20 all you have is a d6? The only way to stay in roughly the same range for target numbers is to use 3d6 since that'll cover 3 to 18. If you go that route, here is (roughly) what you get:

Target	Success?
1	100%
2	100%
3	100%
4	99.5%
5	98.2%
6	95.4%
7	90.7%
8	83.8%
9	74.1%
10	62.5%
11	50%
12	37.5%
13	25.9%
14	16.2%
15	9.3%
16	4.6%
17	1.9%
18	0.5%
19	0%
20	0%
21	0%

Sound good? What? Oh you're still thinking about it! Well, it's good as far as the numbers go, they are pretty close to the actual chances of beating these targets. What you're probably trying to figure out is if there's a method to this madness. There is indeed, but we don't really need to go there. What should be perfectly obvious is that this is very different from the "adding +1 to the roll means adding +5% to your chance of success" simplicity of using a d20.

Also note how the chances for success and failure are really "scrunched together" at the ends with 3d6. If we call anything >90% "virtually certain" and anything <10% "virtually impossible" then we have 7 numbers for the former (1-7) and 7 numbers for the latter (15-21) leaving only 7 numbers (8-14) for everything in between. (Of course we could simply "lose" 1, 2, 20, and 21 since they do not represent distinct chances of success anyway.)

Inside the 8-14 range we have of course 11 which regardless of d20 or 3d6 stands for a "50/50" chance of success. Between 11 and 12 (or 10) we lose (gain) 12.5%; between 11 and 13 (or 9) we lose (gain) 24.1%; between 11 and 14 (or 8) we lose (gain) 33.8%; and that exhausts the "in between" range. What's curious about this is that rolling d8 or d12 over a suitably adjusted range of target numbers actually gives rather similar percentages. Here's the d8 for example (I'll leave the d12 as homework):

Target	Success?
1	100%
2	87.5%
3	75%
4	62.5%
5	50%
6	37.5%
7	25%
8	12.5%
9	0%

Here's a rough graphical comparison (go by the percentage chances when you compare 3d6 to d8, not by the range of numbers covered):

Do I have a point with all this? I do indeed: Rolling 3d6 against a target number in the 1-21 range is silly! Why?

1. You're messing up a perfectly fine and intuitive linear progression that allows players to judge the impact of a bonus or penalty in a straightforward way.
2. You're not getting anything more interesting out of your 3d6 roll that you couldn't get out of a suitably adjusted d8 or d12 roll, and those would in turn again be more transparent in terms of bonuses and penalties.
3. You're making people roll a bunch of dice where one would suffice, thus endangering the miniatures on my table and making us get up to pick dice off the floor more often.

If you like the 1-21 range of target numbers, then please roll the appropriate and well-understood die for it.

Now I hear some of you say "But I like rolling 3d6, it feels so cool!" and of course I cannot help you with that: Taste can neither be legislated nor rationally understood. So keep on rolling 3d6 despite knowing better, it's your game!