Success chances for Skill Challenges

[sfedi]

Since the forum is in a fever of programming things to analyze the system, here's my 2 cents.

The basic question is this:

What's the chance of succeeding in a Skill Challenge of Complexity X if the individual chance of success of each skill check is Y?

Which is answered in this format:

Success chance for Skill Challenges complexity X

Individual chance Y: Z


Here are the results:

Success chance for Skill Challenges complexity 1 (3 successes, 3 failures)

Individual chance 30%: 16%
Individual chance 35%: 24%
Individual chance 40%: 32%
Individual chance 45%: 41%
Individual chance 50%: 50%
Individual chance 55%: 59%
Individual chance 60%: 68%
Individual chance 65%: 76%
Individual chance 70%: 84%
Individual chance 75%: 90%
Individual chance 80%: 94%
Individual chance 85%: 97%
Individual chance 90%: 99%


Success chance for Skill Challenges complexity 2 (6 successes, 3 failures)

Individual chance 30%: 1%
Individual chance 35%: 3%
Individual chance 40%: 5%
Individual chance 45%: 9%
Individual chance 50%: 14%
Individual chance 55%: 22%
Individual chance 60%: 32%
Individual chance 65%: 43%
Individual chance 70%: 55%
Individual chance 75%: 68%
Individual chance 80%: 80%
Individual chance 85%: 89%
Individual chance 90%: 96%


Success chance for Skill Challenges complexity 3 (9 successes, 3 failures)

Individual chance 30%: 0%
Individual chance 35%: 0%
Individual chance 40%: 1%
Individual chance 45%: 1%
Individual chance 50%: 3%
Individual chance 55%: 7%
Individual chance 60%: 12%
Individual chance 65%: 20%
Individual chance 70%: 31%
Individual chance 75%: 46%
Individual chance 80%: 62%
Individual chance 85%: 78%
Individual chance 90%: 91%


Success chance for Skill Challenges complexity 4 (12 successes, 3 failures)

Individual chance 30%: 0%
Individual chance 35%: 0%
Individual chance 40%: 0%
Individual chance 45%: 0%
Individual chance 50%: 1%
Individual chance 55%: 2%
Individual chance 60%: 4%
Individual chance 65%: 8%
Individual chance 70%: 16%
Individual chance 75%: 28%
Individual chance 80%: 45%
Individual chance 85%: 65%
Individual chance 90%: 84%


Success chance for Skill Challenges complexity 5 (15 successes, 3 failures)

Individual chance 30%: 0%
Individual chance 35%: 0%
Individual chance 40%: 0%
Individual chance 45%: 0%
Individual chance 50%: 0%
Individual chance 55%: 0%
Individual chance 60%: 1%
Individual chance 65%: 3%
Individual chance 70%: 8%
Individual chance 75%: 16%
Individual chance 80%: 31%
Individual chance 85%: 52%
Individual chance 90%: 76%

The code for doing this is in Dolphin Smalltalk, if anyone wants to take a look at it.
It's not easily postable because it is object oriented.

 

[ricardo440]

that is really interesting. Need to persuade my GM to change to one of the alternative systems.

 

[AbdulAlhazred]

Yeah, there have been various iterations of these probabilities posted in different combinations. Stalker0 did a bunch of them right after 4e came out and then there have been a few updates.

You are using the errataed SCs? Some of the higher complexity numbers look a bit low when you go with the SC errata where all complexities have 3 failures.

 

[sfedi]

I think the errata only changes the DCs of the Skill Challenges.

I only work with the probability of each check and the total number of succeses (3 x Complexity) and the number of failures (always 3).

The probability of each check is the result of the combination between the DC and the skill bonus used for it.

 

[Infiniti2000]

The errata changes the complexities. That will totally change your results.

"It's not easily postable because it is object oriented."

Non sequitur! Are you telling me C++, Java, etc. are not easily postable? Or, that only Smalltalk is OO?

 

[msherman]

Non sequitur! Are you telling me C++, Java, etc. are not easily postable? Or, that only Smalltalk is OO?

He's not talking about the language, but the actual programming environment. Smalltalk doesn't have "source files", per se:
Smalltalk - Wikipedia, the free encyclopedia

 

[keterys]

It's 2 + 2*C, not 3*C successes needed. But the errata is what made it 3 failures max, so you at least had that already.

 

[Elric]

When characters have different chances of success on skill challenges, these probabilities become more complex. On the WotC boards, Elder Basilisk used an approximation based on the geometric average of each party member's chance to succeed on a roll (Skill challenges).

I'm pretty convinced that this systematically underestimates the chance to succeed on the skill challenge as a whole (my reasons here), while using the arithmetic mean would lead to results that could be above or below the true probability. That said, his basic points hold up fine:

Characters with weak skills should never try to roll them on a skill challenge; the best strategy is to declare you're using your best skill, giving some possibly ridiculous explanation why it's relevant, or else to avoid participating at all for fear of being called on to use a weak skill (since participating is typically optional). Characters should also use Aid Another as much as possible, which combined with the other suggestions could make skill challenges trivial. A naive strategy of "rolling for it" without using "Aid Another" works on easy challenges, but is unlikely to work on tough ones.

A sophisticated programmer could probably find a good way to "brute force" these calculations; simply running 100,000 simulations for each set of values is also a valid approach.

 

[AbdulAlhazred]

Well, you can do it for a given skill challenge fairly easily. Its just a simple sum of probabilities really. If everyone has to participate and discounting Aid Another its not hard at all. Aid Another is also not really ever mentioned as an option in SCs except for "group checks". So personally I maintain AA doesn't apply to normal SC rolls and nothing WotC has ever published AFAIK is contrary to that. The very existence of secondary skills kind of indicates its not really supposed to be possible since AA would be equivalent to a DC10 secondary skill use and for most SCs that would be easier than any secondary (which often have difficult level DCs).

As for the option to "do nothing", its certainly not excluded by the core SC mechanics, but no DM should write an SC that allows that. Every character who is present and participating at all should have to make some kind of die roll. Otherwise you might as well just have the guy with the super high skill bonus in one primary skill sit there are roll a bunch of dice.

The trick is to be able to calculate any kind of odds with various possible secondary skills, failure canceling rolls, one-time skill uses, etc. It can be done, but much like the issue with modeling combat you just never know what people will actually decide to do. Assuming they max their probability of success is logical but it would be nice to be able to compare options and see what happens when you change your SC design a bit.

 

[FireLance]

At the risk of sounding like a broken record, I would like to reiterate that I think the "three failures" model and the "failed skill check results in a failure" condition is a very poor setup for skill challenges in general.