Characteristic Saves

I use CHAR (characteristic) saves a lot in my games; I like to get as much mileage out of the characters' stats as possible. For success, I require that the player roll below their relevant stat score — for example, if you have an INT of 15, for a successful (unmodified) INT save you'd have to roll 14 or less.

Where success in a situation is a matter of luck, or the grace (or anger) of the gods, I use the standard level-based character save mechanism with a d20, but where it's a matter of the character's own physical or mental abilities, a CHAR save is more appropriate.

I've vacillated between using 3d6 and 1d20, but I've decided to stick permanently with 3d6 from now on. The graph shown here (which, as usual, you can clickupon to bloatify) describes the result curves for each.

The d20 curve is perfectly straight. You're as likely to roll a 1 or 20 as you are to roll any other number. It's simple, but that's about all it has going for it, and it doesn't reflect the distribution of stat scores as rolled. Compared with the 3d6 curve, it markedly benefits those with very low stats, and markedly penalizes those with very high stats.

With 3d6, on the other hand, your chance of success in a simple, unmodified CHAR save better reflects the rarity of exceptional (or pathetic) stat scores, and positive or negative modifiers can become significant much faster than in the linear d20 scale — for example, if you have an INT of 9 and you make a CHAR save at +2, on d20 that gives you +10% chance of success, while on 3d6 it means +25%. If you're making the save at -2 on the other hand, while on the d20 scale it's just -10%, on the 3d6 curve it's actually -16.6%, and those penalties or benefits flatten out a lot at either end of the curve.

What I haven't quite figured out just yet is how to accommodate CHAR scores beyond the 3-18 range, especially in CHAR-vs-CHAR contests. I have an idea or two, but I think I need to do some more maths to see whether they'll work as I hope they will.

Anyway, BELL CURVES RULE! LINEAR SCALES DROOL! YEAH!

Addendum:

Difficulty No. of dice Range Average Roll
Very easy 1d6 1-6 3.5
Easy 2d6 2-12 7
Average 3d6 3-18 10.5
Difficult 4d6 4-24 14
Heroic 5d6 5-30 17.5
Superheroic 6d6 6-36 21
Legendary 7d6 7-42 24.5
Mythic 8d6 8-48 28
As mentioned in the comments, those with stats over 18 could be assumed to automatically pass any unmodified CHAR save, and very difficult unopposed tests could just require more dice — 4, 5, 6 or more d6, with the players (or monsters) still required to roll below their relevant stat. All that would be required on my part would be to formulate a rational scale of difficulty, probably a FUDGE-like descriptive scale would be most useful, methinks.

As far as opposed CHAR-vs-CHAR rolls go, I'm tending towards a dice-pool system in which you get 1d6 for every 3 points in the relevant stat, and then do a roll-off. The opponent who rolls the highest score wins the contest.

Yet Another Hill

 I got a cheap 30-watt foam-cutting hot wand from China a few days ago, and tried it out by carving up a foam off-cut into another hill. ...