Yet Another Damn Skill System

A few days ago, I got into a small discussion--barely a chitchat, really--with +Paolo Greco about our mutual love for diminishing returns in dice systems.  (He has a elegant example over at his blog.)

I've come to realize that there are a lot of ways to generate different trends with dice.  This is because I think about dice a lot.  I walk around with a couple in my pocket.  I fall asleep with dice in my bed.  Once I drank too much at a party and vomited, and that was like, 30-40% dice.  I think I rolled a 23.

Anyway, here's a diminishing return system for skills.

The S System

Roll two dice and subtract the smaller number from the bigger number.  If this resultant number is equal to or smaller than the skill/stat/whatever, the attempt succeeds.

The shorthand for this is sX, where X is the die size.  (Like d6 . . . s6, s8, etc)

Here's a couple examples of an s6 roll against a Pick Pocket skill of 1.

Rolled: 3, 4
3 - 4 = 1
1 is equal to (Pick Pocket) 1, so the attempt succeeds.

Rolled: 6, 3
6 - 3 = 3
3 is greater than (Pick Pocket) 1, so the attempt fails.

There are two huge advantages here:

1. Untrained (Score of 0) still has a chance to succeed (if both dice show the same number).  With a d6, this is about a 17% chance.

2. There are diminishing returns as you invest points into this skill.  That is, each point you put into the skill causes the % of success to increase by a smaller amount.  But since reproducibility and confidence are so important, players will still want to invest in skills, even at higher ranks.

Let's look at some probabilities.

 s6 Probabilities

Rank	% Exact Roll	% Success
0	17%	17%
1	28%	45%
2	22%	67%
3	17%	84%
4	11%	95%
5	5%	100%

So you can see, that even if a player has NO ranks in a skill, they still have a 17% chance to successfully attempt a skill (assuming you let them).  But that first point increases their chance of success to a whopping 45%!  Every point after the first one gives diminishing returns.

Is 17% too high for you?  Do you want a finer graduation between Unskilled and Masterful?  Use a bigger die.  Rolling s8, s10, or s12 will all give you more discrete steps, while preserving a simple mechanic and giving diminishing returns.

In practice (and I have been practicing) this is dang fast.

And if you want to adjust difficulty, you can modulate the ranks by +/- 1 or 2.

Just for fun, here's the table for an s10 roll.

 s10 Probabilities

Rank	% Exact Roll	% Success
0	10%	10%
1	18%	28%
2	16%	44%
3	14%	58%
4	12%	70%
5	10%	80%
6	8%	88%
7	6%	94%
8	4%	98%
9	2%	100%

Ain't it cute?

Critical Failures and Success

If you roll the worst possible result (like a 1 and a 6 on a s6 roll), something bad happens.  This is pretty rare.

If you roll doubles, and the number shown is equal-to-or-less-than your skill rating, you get a critical success, and good things happen.  So if you have Skill 4 and roll double 3s, thats a critical success.  Obviously, this means that you can never get a critical success if you have no skill in something.

The advantage of this is that critical failures will always be a threat no matter how skilled you are, while critical successes become more likely as you become more skilled.

And. . .

Here are the s6 and s10 curves on anydice.com:
http://anydice.com/program/2d7b

I can think of a couple of ways to rejigger it to apply to stat checks, too.