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4 years ago ::
Jul 02, 2009 - 12:20AM
#161
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Date Joined:
Apr 29, 2009
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That's exactly right. We used the binomial formula. And most of the difficulty we had coming up with the formula resulted from overthinking it and trying to account for possibilities that were already accounted for by the formula.
One more point that I should have remembered to make already. The arithmetic mean of a set of (not all-equal) numbers is always higher than the geometric mean. So the arithmetic mean method numbers that you get will always be higher than the geometric mean method numbers (and indeed, that's what you indicated you found). The problem is that you don't know where the true value lies relative to these two numbers.
I suspect that the geometric mean approximation tends to underestimate the party's chance of success compared to the true value. For theoretical "skill challenges" that last a maximum of 2 rolls (2 successes before 1 failure, or vice versa), the geometric mean approximation gives an answer that is sometimes lower than the true value, and never higher than the true value.
The arithmetic mean approximation can be either above or below the true answer, as the examples so far have demonstrated.
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4 years ago ::
Jul 02, 2009 - 10:13AM
#162
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Huh. None of my characters have any of the arrays mentioned--in fact, I don't think any of them have an 18. Certainly, none of them have an 8 or 9. I haven't come up with any backstory that justifies either extreme.
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4 years ago ::
Jul 02, 2009 - 10:55AM
#163
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- Senior Volunteer Community Lead
Date Joined:
Aug 19, 2007
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I like using the 8 as a place to hook something wacky. One character's Tick & Capt. Hammer-like qualities, another's frank gullibility, etc.
I think all of my characters have one 18, though, or two in the case of the dragonborn. Only takes a 16 before the bump.
Then again, I don't actually consider an 18 or an 8 actually extreme unless you don't get a racial stat bump in the 18.
Keith Richmond
Living Forgotten Realms Epic Writing Director
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4 years ago ::
Jul 02, 2009 - 11:26AM
#164
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Date Joined:
Aug 19, 2007
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My most common array, pre-racial bumps, is 17, 14, 14, 10, 10, 8
This lets you get a good primary, a pretty good secondary, and still a +2 in the "off" defense.
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4 years ago ::
Jul 30, 2009 - 9:45PM
#165
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Date Joined:
Apr 29, 2009
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I suspect that the geometric mean approximation tends to underestimate the party's chance of success compared to the true value. For theoretical "skill challenges" that last a maximum of 2 rolls (2 successes before 1 failure, or vice versa), the geometric mean approximation gives an answer that is sometimes lower than the true value, and never higher than the true value.
The arithmetic mean approximation can be either above or below the true answer, as the examples so far have demonstrated.
I've become pretty convinced that using the geometric mean approximation (see here) (weakly) underestimates the true probability of succeeding at the skill challenge: the answer you get with the geometric mean approximation can never be higher than the true answer, and will usually be lower.
In addition to being able to prove this for "skill challenges" of a max of 2 rolls, I tried a number of calculations using random numbers for the chance of success per roll for challenges with a max of 3 rolls, and it was always true. In the 3 roll case, an optimization package trying to minimize the quantity (true value [from brute force calculation] - geometric mean approximation's value) could never get it to go below 0. That's enough for me to conclude by heuristic proof that this is probably true for skill challenges of any number of rolls 
Now, that doesn't mean that the geometric mean method is less accurate than the arithmetic mean method in all cases. When the arithmetic mean method overestimates the true probability, then even though the geometric mean underestimates the true probability, it might still be closer to the true value.
Still, this cautions against using the geometric mean approximation method to determine the chance of success on skill challenges, unless you are trying to establish that the chance of success on a skill challenge is at least as high as a particular value.
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4 years ago ::
Aug 03, 2009 - 6:58AM
#166
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Date Joined:
Aug 18, 2007
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This was exactly Elder_basilisk's point. See here: http://forums.gleemax.com/showpost.php? … count=100. If character with a bad skill modifier on a relevant skill tries to use it, he seriously hurts the party's chances at a hard skill challenge. The best strategy on a skill challenge is to avoid doing anything that would lead you to make a skill check that's not a good skill for you, and to Aid the PCs with good modifiers as much as you can get away with.
Here is a curious thing - if in your life you were presented with a real complex problem and there were 5 or 6 people present each with a different array of strengths what would you do?
The answer is typically (in an effective group) play to the strengths of the team members and have the others help them where relevant. Strategic groups are often built with this in mind as it maximises the effectiveness of the group.
Seems like a reasonable way to approach skill challenges to me.
(Oh and as a side note the DRAG1-3 "Get Past the Obstacle" skill challenge made me want to punch someone.... I must read it myself one day and see what the issue was when we played it)
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4 years ago ::
Aug 03, 2009 - 9:26PM
#167
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Date Joined:
Dec 16, 2005
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Here is a curious thing - if in your life you were presented with a real complex problem and there were 5 or 6 people present each with a different array of strengths what would you do?
Look at a concrete problem and apply our skills to that problem rather than creating a problem in order to justify the use of our best skills.
Examine our party's weaknesses as it pertains to that problem and try to find ways to mitigate them rather than assuming that someone who is good will roll that skill and therefore I won't have to. (For example, the rogue rolls stealth in the Core 1-1 or Drag 1-3 skill challenge, therefore the paladin does not have to roll stealth to sneak by the guards--it doesn't make sense in narrative terms but it's the smart thing to do in a skill challenge).
Create a plan to interact with the problem rather than coming up with a justification for everyone to use their best skills.
The answer is typically (in an effective group) play to the strengths of the team members and have the others help them where relevant. Strategic groups are often built with this in mind as it maximises the effectiveness of the group.
Seems like a reasonable way to approach skill challenges to me.
Except that it is viewed with disfavor by the powers that be. In the original DMG version of skill challenges, everyone was required to roll a check, whether or not they were good at it. The errata (fortunately) removed that portion, but the idea that everyone is supposed to do something is still very strong as evidenced by the podcast discussing skill challenges and the various suggestions to limit or punish the use of aid other and other things characters might do in order to avoid making a check.
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4 years ago ::
Aug 04, 2009 - 1:23AM
#168
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(For example, the rogue rolls stealth in the Core 1-1 or Drag 1-3 skill challenge, therefore the paladin does not have to roll stealth to sneak by the guards--it doesn't make sense in narrative terms but it's the smart thing to do in a skill challenge).
Which is not exactly how the skill challenge should be run. You are making a narrative assumption, which you yourself already concludes is wrong. It could have been made clearer, but the assumption is that if just the stealthy PC makes that Stealth check the PC is doing something that removes the need for others to be stealthy. In case for CORE1-1, the rogue could be on watch alert for patrols or in another way direct the group to follow a particular route that is particular well hidden and correctly timed. In case of DRAG1-3 the idea is that the rogue scouts ahead directing the rest of the group away from any locals. I should have added a comment along the lines that if the group as a whole tries to be sneaky, everybody in the group should make a Stealth check and depending on the circumstances it would be the average result (if PCs can potentially remove failures since their is time to aid their fellows) or the lowest roll.
Discussions like these made this potential thinking error by DMs clearer, hence the change in CORE1-8 where this has been made much clearer. The only time I actually allow one PC to make a Stealth check for the group as a whole while close together is during something like a wilderness trip where the stealthy character is in charge of determining the route of the group and the Stealth check is not as much directly opposed by a present observer but about the chance of meeting patrols in the region.
In the end, the author has a responsibility to makes the intent of the skill challenge clear. I know I failed in that regards in the past. It does not remove the need for the DM to use his own common sense either. The fact that a skill challenge describes the possibility of using Athletics when the PCs take a particular route, does NOT suddenly put the PCs on that path when the players decide to use Athletics. The players still need to come up with a plan of action and then follow that plan using the skills most logical for that plan.
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