Target Number Theory

[shehee]

First I'd like to explain how I understand target numbers for challenges, then I'd like to ask a question about target numbers and probability.

As I understand it, the difficulty of something is a vague expression, like moderately difficult. You take that expression an, using a chart, compare it to a number, which you then roll one or many dice for.

The roll itself is a factor used to describe randomness. To describe a characters skill, there's either a modifier, like +3, for a single die, or if multiple dice are used, the number of dice represents skill.

Now, OK, I realize this is only one way to do it, but does this sound right?

Also, looking at a couple of systems, 50% of the time somebody should be able to do something moderately difficult. The question is, is 50% of the time a reasonable way to do things if all of the above is accepted.

Thanks for any help,
Ryan
(Still new, be kind)

[Rob Carriere]

Ryan,
Right or wrong, reasonable or not, all of that depends on your design goals.

The first question shouldn't be, `do I use X die roll system?', or even `is Y% chance of success right for difficulty Z?'.

The first question should be: `What do I want to get out of those die rolls?'

High chance of success means that people (players and probably characters) will be confident, sure of their ability. Lower the chance of success and that certainty erodes as people start to sweat it.

Similarly, high range of results means a feeling of gambling, small range of results means that you pretty much know what you can and cannot do.

Taking the ubiquitous D20 as an example, at low levels my character might have a skill modifier of +6 or so. The d20 adds between 1 and 20 to that. That is, the random element is almost 4 times larger than the skill element. Play at such levels feels like gambling.

Now flip that around, and consider a character that has a 20 skill and adds a d6 to that. Compare the possible results: 7-26 for the D20 guy and 21-26 for the D6 guy. Obviously the D6 guy has a much better idea of whether he'll be able to succeed or not.

Which is better? What do you want? Gambling can be a great source of excitement, and so can knowing that you will fail if you are forced to rely on skill X under the present circumstances.

Same thing for the success chance. Do you want a lot of failed skill attempts in a session, or do you want the characters to succeed most of the time?

Once you've got those questions answered, once you have a clear vision of what you want from your dice mechanic, then we'll be able help you hash out a system that achieves those goals in no time flat. But we do have to know what you want first.

Hope that helps,
SR
--
EDITED to add a missing word in an annoying place.

[Akamaru]

Somehow I've always felt it to be sort of silly that a "moderate" difficulty is always 50% chance of success.
If I imagine myself trying to do some task I have some skill in and I fail half the time, I'd call it a lot more than moderately difficult. I think a 75% success rate sounds more moderate. I mean you're statistically still failing every fourth try. Even that is a lot if you think about it.

[Rob Carriere]

Akamaru,
That's a design tool that you have your hands on there. Consider two kinds of moderate difficulty (and two kinds of hard, two kinds of easy, etc).

The first kind of moderate difficulty is the difficulty that crops up  most often in play.

The second kind of moderate difficulty is the kind that is labeled `moderate' in the rules.

(and the third choice is what the actual probability is that you attach to the descriptor)

These need not be the same at all! You can run a game where the most frequently used difficulty is `superhumanly tough'. In fact, a lot of people run such games, Champions, GURPS Supers, whatever.

The label you put on the difficulty is Color and as the supers games show, you can use that to manipulate how the game feels. Is the most common difficulty `superhumanly tough' and the PC succeed 90% of time? Supers. Is the most common difficulty `moderate' and the PCs fail half the time? Anti-hero story. And so on.

Going back to your example, if you're playing competent PCs and they muck up at moderate difficulty half the time, then Something Is Wrong, as you say. Depending on what the designer wants, either the probabilties need adjusting, like you did in your last paragraph, or the difficulties need to be re-labeled. If I take your rule book and change `moderate difficulty' into `requires expertise', then suddenly the 50% sounds a lot less silly.

SR
--

[Tim C Koppang]

Going along with a lot of what has already been said, you might consider what kind of failure/success rate you want from an ends point of view.  First, consider what failure means in your game and likewise success.  Then determine how often or how important each event is to the overall play experience.  Adjust probabilities as required.

In all honesty, I'm coming at this problem from a Narativist point of view.  In my mind, failure as it relates to a premise, can lead to important character development and the like.  But then so can success.  How will weighting outcomes towards either result affect the Nar experience?  Perhaps I think each is equally important, and so I'm going to design my game with that balance in mind.

So really, I propose that it's important for the game designer to consider when tests are called for and what success or failure means exactly.  When you figure that out, then you can look at your dice mechanics with a goal in mind.

Also important to remember: tests don't necessarily have to be 100% success or failure.  Lots of games employ a gradient of success.  But again, the same principle applies.  What does 60% success mean in relation to a 95% success?  How can I design the mechanics, i.e. probabilities in this case, to facilitate the type of play I'm after?