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ElricEN wrote:

Not on a Hard difficulty skill check. Elder_basilisk assumes a +0 modifier on a weak skill at 1st level and at a DC of 15, that's your 30% chance right there

That's a... really weird assumption. First, I think it is a safe assumption that any build is going to have positive modifiers in at least 3 of the six stats? I can't think of any build that is going to have two stats of 18+, three 10s and an 8. just not going to happen. Personally, having at least +1 in four or five stats seems to be the norm, but let's say only three stats with pluses for the sake of discussion.

So, with three stats of at least +2 I can't think of ANY skill challenge where you will not have at least one untrained skill with a +2 bonus at 1st level. This also assumes that the majority of the time the players will have no relevant skills trained at all which is ridiculous.

I can't imagine a situation where a first level character MUST roll a skill challenge with less than a +2 bonus. It's possible that, for character or RP reasons they want to use a skill that happens to have a smaller bonus but that's a slightly different discussion.

ElricEN wrote:

Is this the method you're using for calculations of the odds of success on skill challenges throughout this thread? The odds are surely worse if you're rolling bad skills, but this method of approximation can mislead you greatly.

Consider 8 rolls (6 successes before 3 failures), with seven rolls at 100% and one roll at 0%. This formula suggests that we treat the overall outcome as the same as if all of the rolls had a 0% chance of success, yielding a chance to complete the skill challenge of 0%. However, the actual chance of success at the skill challenge is trivially 100%.

Your method is roughly correct when these probabilities of success on individual checks are close to the same. However, using the arithmetic mean (C1 + C2 + ... + Cn)/N is also roughly correct in this case and, whatever else its flaws, it can't mislead you into thinking the chance of success is 0 (or even close to 0, really) when it is actually 1.

I don't have any deep insight into a best method of approximation here, but the one you've chosen is problematic. Arithmetic mean would probably be better. Note that with 8 rolls, it probably isn't too hard to write a computer program that solves the problem by brute force by simply running through all (2^8) possible outcomes and calculating the probability of each.

Side note: Your example above is wrong because you have 9 rolls listed (1 + 1 +2 +5).

It is the method I have been using for calculating the odds of success where characters are rolling at different odds. Most of my discussion focused around the abstraction of everyone rolling at X% which does not depend upon that formula.

I don't think that examples using 100% and 0% are particularly instructive for evaluating its utility compared to the arithmetic mean. 0s especially screw things up pretty royally and 100%s also throw the calculations off. For instance, you are correct that the arithmetic mean won't lead you to believe the odds of success are zero when they are really one (in your 7 autosuccesses, one autofailure example), but they will lead you to believe the odds of success are non-zero when, in fact, they are zero. (Three autofailures followed by 5 autosuccesses would yield an arithmetic mean of a 62.5% chance of success on any given check--but three failures cause you to fail the skill challenge so the odds of success are actually zero). In fact, I think it is that kind of edge case that led me to reject the arithmetic mean (possibly in error).

Now, while 100% odds are not out of the question in skill challenges, 0% odds, on the other hand, are very hard to come up with (an 8 dex paladin wearing a heavy shield while rolling acrobatics and playing at he low end of the tier (we'll call it a +1 to the effective DC since he is two levels lower than the skill challenge) still beats the hard DC number if he rolls a 20. Maybe not if the skill challenge is designed to be higher level than the players, but that's still a bit worse than you can expect to see more often than once in a blue moon). In general, most odds will be in the range where neither method of aggregating the odds obviously fails.

(As an aside, it will probably yield more accurate results if you treat 100% attempts as simply reducing the complexity of the skill challenge rather than trying to figure them into aggregate odds. Thus a complexity two skill challenge with two 100% attempts has the same probability distribution as a complexity one skill challenge without the automatic successes. If there is a need to account for 0% attempts, it would probably be more accurate to the reduce the number of allowed failures than to attempt to figure them into the odds).

Comparing the results of the arithmetic mean approach to the method I was using, within ranges of 2-7 rolls at 80% and 1-6 rolls at 30%, I found that they are both in the same ballpark. The method that I have been using generally yeilds an aggregate probability that is 4-7% lower than the arithmetic mean--certainly noticeable, but not enough to change the broad conclusions I drew from the calculations. (If arithmetic mean is the correct way to do it, skill challenges are a little more forgiving than my previous posts indicated but they are still quite unforgiving of anyone who rolls at low odds). That said, I think you may be right and the arithmetic mean may be better than the method I was using, but I can't prove it right now--nor can I prove that the arithmetic mean is the correct method at the moment. Maybe I'll work on some equations during my lunch break tomorrow and see what I can come up with.

As for the brute force approach, I actually tried it (or, more precisely, I got my computer programmer brother to try it) and it's a lot harder than it looks--especially if you want to be able to expand the results to a complexity 5 skill challenge with its 12 required successes. We did end up brute forcing the complexity 2 and 5 skill challenges and used those results to check the formula for calculating the overall odds of success on the skill challenge given particular odds of success on an individual check. Consequently I have a lot more confidence in that formula than in the method I was using for aggregating the odds.

Telvin3d wrote:

That's a... really weird assumption. First, I think it is a safe assumption that any build is going to have positive modifiers in at least 3 of the six stats? I can't think of any build that is going to have two stats of 18+, three 10s and an 8. just not going to happen.

18/18/13/11/10/8 is probably the most common stat array out there.
20/14/13/10/10/8 is also common
as is 20/16/11/10/10/8 (I think that's an overly aggressive set of statistics, but I see a lot of rogues and swordmages with it)
18/16/14/13/10/8 is also quite common

There are obviously more possible arrays, but almost everyone is going to have at least one stat of 10-11 and at least one stat of 8. A 10 or 11 in a 3rd stat is probably the norm and the third lowest stat will rarely be higher than a 12 or 13. It will never be higher than 14.

Personally, having at least +1 in four or five stats seems to be the norm, but let's say only three stats with pluses for the sake of discussion.

So, with three stats of at least +2 I can't think of ANY skill challenge where you will not have at least one untrained skill with a +2 bonus at 1st level. This also assumes that the majority of the time the players will have no relevant skills trained at all which is ridiculous.

This assumes that all skills in the challenge are interchangeable. They're not; frequently LFR skill challenges seem to be written such that there is a maximum number of successes to be gained with skills X, Y, and Z, and the party needs to get at least one success with each skill.

I can't read the authors minds but I suspect that this is an attempt to avoid the "I autoaid the eladrin warlord and he rolls arcana 12 times at +18, can we move on now?" aspect of skill challenge strategy. It creates its own set of problems, however, as it is not uncommon for a party to lack even competency in one skill which forces the party to roll a low-probability check until they succeed at it--a difficulty that will sometimes cause a party to straight-up fail the skill challenge in the attempt (it is only slightly more likely that you will get at least one success against a hard DC out of three attempts with a weak skill (51%) than that you will fail three times in a row and end the skill challenge (49%)). It certainly was what caused my party to fail the skill challenge in Dragon Coast 1-3 and I don't think anything has led to more people posting that my examples of bad skill challenges are just DMs running skill challenges badly than inflexibility caused by the "and at least one success using bluff/etc" clause.

So, I can understand why authors do it, but it's still a bad idea.

I can't imagine a situation where a first level character MUST roll a skill challenge with less than a +2 bonus. It's possible that, for character or RP reasons they want to use a skill that happens to have a smaller bonus but that's a slightly different discussion.

It's actually pretty easy for me to imagine.

First let's work through the issue of someone having to roll a skill at +2
In LFR there are two basic kinds of skill challenges. There is the social skill challenge that usually has diplomacy, streetwise, and bluff as key skills (with intimidate as one or more automatic failures as often as not). And then there is the physical skill challenge that usually has athletics, endurance, and acrobatics as key skills. There are usually a few more skills involved--perception or insight usually give a +2 bonus here or there (kinda like aid other only harder), nature, religion, thievery, and arcana often find a way to figure into one kind of challenge or the other, but you usually need the basic skills too. And DMs who like to roleplay skill challenges will very frequently, say, "OK, you say that, now roll a bluff check." (Often prompting the conversation--"but I'm using diplomacy"/"That sounded like a bluff to me.")

Leaving the latter part for later, it's quite possible that an entire party might be lacking in one or more of the necessary skills.

Consider this party: Fighter, Tactical Warlord, Wizard, Warden, Ranger.
It's a fairly common kind of mix.
If it's a physical skill challenge, they are probably good unless it's one of those where everyone has to roll (in which case, the wizard should just mark off his healing surge now).
If it's a social skill challenge, on the other hand, they could be in trouble. If we assume that they each went to the trouble of getting some skills that could be useful, the wizard and fighter are probably competent to good at insight, the warlord is probably competent (but nothing more) in diplomacy, and the fighter may be competent at streetwise or intimidate (but probably not both). The skill that no-one is likely to have is bluff. Streetwise is also a good candidate for being absent.

So, if you have a skill challenge like Dragon Coast 1-3 where you need at least one bluff check to win, someone in the party will have to roll--probably at +0 (+1/2 lvl) against whatever kind of DC bluff happens to be.

Here's another example party--this time for the physical skill challenge.
artful dodger, laser cleric, warlock, charisma paladin, wizard.
If it's a social skill challenge, they probably have everything covered.
But if it's a physical skill challenge, they may be in deep doodoo. For the sake of argument, we'll assume that the paladin trained endurance (though with plate+shield penalties and a typically low starting con, he's probably still rolling at +2 or +3 (+1/2 level)). The rogue will almost certaily be good at acrobatics and could be competent at athletics (but may well not be). If the warlock uses constitution to attack, he may be semi-competent at endurance without training (though if he's a charisma warlock, he's pretty much screwed too). All told, only one or two characters even have a chance to be on the weak side of competent in endurance, only one has a chance to be competent in athletics (and may well not be) and while one is probably really good at acrobatics, none of the others will be (and the paladin is probably rolling at -3 (+1/2 level)).

Now neither party is typical, but they are the kinds of parties that frequently (perhaps 1/6-1/3) show up at LFR tables. And in either case, they will have to roll a check at +2 (if they're lucky) in any skill challenge of the "no more than 2 of X and at least 1 of Y" variety.

Now, why would a particular character have to roll at +2?

1. Because they're in a skill-unbalanced party like one of the ones above and no-one is good at it. And the module says that you need to get at least one success with the skill they don't have. (That was how my party ended up in the "roll bluff at +0 (+1/2 lvl) until you make it or fail the skill challenge" situation in Drag 1-3; we could have done diplomacy, or intimidate, and we were actually good at insight but our best bluff was untrained with a +0 charisma).

1.5 As to the argument that they will all aid other and pass anyway, that is a bit misleading. Due to the extremely constrained range of probabilities where skill challenges are not automatic successes, many DMs severely limit or do not allow aid other at all, inflict penalties to the primary check for a failed aid other attempt, or otherwise do their best to eliminate that option. The designers themselves have advocated any and all of those possibilities from time to time in the skill challenge articles and blogs. It is an understandable reaction to the "everyone aid the guy who's good at it and we'll automatically beat the skill challenge" strategy encouraged by the mechanics of the system, but it really screws people who have to succeed at a check they aren't good at. (Not that they necessarily don't deserve to be screwed if they are trying to use a skill they are terrible at to beat a skill challenge--I just maintain that they should be able to come up with a plan that avoids using that skill at all).

2. Because the DM makes every player roll something--either through the hard method advocated in the pre-errata DMG (I'm aware that there is errata, but a lot of people haven't really read it and just go off their memory of how the first skill challenges were run for them) or by a soft method that relies on social pressure and expectations. Rolling for initiative or going around the table and having each player explain what he is doing are the two most common kinds of soft-coercion I've seen. Theoretically, someone could say, "I sit in the corner, suck my thumb, and console myself by chanting 'at least I'm not failing, at least I'm not failing, at least I'm not failing'" but I've yet to see someone do it. Psychologically, it's a lot harder to avoid taking an action when DMs use the social forms used in other formats where taking an action is either mandatory (as it was pre-errata) or always good strategy (as it is in combat). Combine that with the anti-aid other pseudo house rules (how house rule is it if it comes from a WotC Dragon article on running skill challenges?) or the simple requirement that aid other be declared before the skill check it is aiding (ordinarily, this is a sensible rule, but if the DM is simply going clockwise or using initiative, the guy you want to aid has frequently already gone by the time your turn comes up) and you end up with people being pressured or forced into rolling checks they're not good at. This goes double if a previous character has already used up the one possible success with a skill the character IS good at. (For skill challenges that limit the maximum successes with each or with certain skills).

3. Because the DM is role-playing the skill challenge and he makes everyone who talks roll with the most obviously appropriate skill for the things they said.

I frequently here exchanges like this at the table:
Player: Surrender and we will have mercy upon you; resist and you will be utterly destroyed.
DM: OK, roll an intimidate check.
Player: I was going for a diplomacy check--I'm imploring them to surrender and emphasizing the carrot part of the ultimaitum rather than the stick.
DM: It sounds like intimidate to me.
Player: Oops.

Now that's not necessarily a terrible way to run a skill challenge (at least not more terrible than most other ways that use the terrible mechanics we're stuck with). But the net result is that unless your character is at least competent in the skill required for the situation, you need to shut up and give the DM with your best deer in the headlights look when he glances in your direction just to make sure you don't contribute a failure. Otherwise you end up rolling intimidate at -1 (+1/2 character level) and contributing a failure.

4. Because the skill challenge makes every character roll a something or a particular skill.

This is common in physical skill challenges like the "climb the chain" skill challenge in Spec 1-2 or the shipwreck skill challenge in Aglarond 1-2. And I actually like it in some cases. If everyone is marching through the blizzard, everyone should have to make an endurance check (or use the endure elements ritual) to avoid frostbite. It becomes problematic when it is over-used (yeah, here's this mod's surge tax for not having endurance/athletics/acrobatics) or where the skill challenge mechanics that limit the party to three failures are not discarded (the wizard failed his third endurance check so you're all lost in the woods).