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The normal rules for Aid Another are that you have to pick who is leading in a skill before rolling. The person Aiding gives either a +2 or +4 to the skill check on a Success or Critical Success.
I have seen a variant in multiple adventures for PF1 and Starfinder where everyone rolls, the highest result is the skill roll and you treat the others as Aid actions.
I like this method a lot better since it uses the most favorable roll. If you have two characters as the table both good at a skill, it tends to promote a friendly rivalry (let’s see who finds it first!) and doesn’t make someone who rolled really well feel like their roll was wasted because they chose to Aid rather than roll for the skill.
I know this would give a higher result than the current method, but is that really that bad? I would like to suggest this be the default Aid. I wouldn’t mind if the bonus from the Aid were reduced to +1/+2 because of the higher chances of success.
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I have performed similar probability calculations before, but the resulting probability polynomials are very hard to interpret. If you want a sample, peek at my paper A posteriori probability decoding through the discrete Fourier transform and the dual code, by Erin Schram (my real name) in Codes and Designs, editted by Arasu and Seress, published de Gruyer, 2002.
But instead I can give a situation with a very similar probability.
Imagine that Alice, Bob, Charles, and Diane are all playing characters that must make a knowledge roll to solve a puzzle. One successful check means success for the entire party. First, Alice rolls her check with Bob, Charles, and Diane rolling to aid. Second, if Alice failed, Bob rolls his check with Alice, Charles, and Diane rolling to aid. Third, if Alice and Bob failed, Charles rolls his check with Alice, Bob, and Diane rolling to aid. Fourth, if Alice, Bob, and Charles failed, then Diane rolls her check with Alice, Bob, and Charles rolling to aid.
That has very close to the same probablity of success as Alice, Bob, Charles, and Diane all rolling once each, the highest result selected as the check and the other three rolls selected as attempts to aid.
A rough explaination of why the probabilities are very close is imagine in the first case with the four separate rolls, each individual happened to roll the same number four times in a row. That is identical to re-interpreting the single set of rolls in the second case four times: once as if Alice were checking and the others aiding, once as if Bob were checking and the others aiding, once as if Charles were checking and the others were aiding, and once as if Diane were checking and the others were aiding. Selecting the best case is just selecting the best of the four ways to interpret a single set of dice rolls.
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Mathmuse, I think we're less focused on the exact math and more focused on making Aid Another a more attractive option.
And I agree with the concept that where Aiding Another is possible, that we shouldn't need to decide who is performing the action. You simply take the highest roll and add the bonus for aiding.
With the understanding that not all task can be aided or the number of people that can attempt to assist can be limited.
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The amusing aspect of BretI's question is that I used her system.
Two characters in my party, Seoni and Aust, had +8 in Arcana. Thus, they could decipher an emblem on a roll of 17 or higher without aid, and 15 or higher with aid. I set the Aid DC to 20. At first, I let Aust make his check, aided by Seoni, then Seoni make her check, aided by Aust. If neither succeeded, they had to study the emblem for another hour and try this again.
This grew boring. Waiting an hour in-game was no problem: the barbarian in the party was using the time to heal via her Superstition totem and to pile rocks in front of the secret door by which the Night Heralds would arrive. But making the same rolls over and over again hoping for better results was dull.
So for the final emblem my players suggested BretI's method. I let them switch to it for variety and to cut the number of rolls in half. By coincidence, it worked immediately.
The non-spoiler summary is that my Playtest players asked to use BretI's "everyone rolls once and use the highest" method after a long series of repetitive rolls where everyone checked while the others aided. Repeating the same dice roll over and over again waiting for good-enough results is boring, even when the party is on a deadline so that the tension should be rising.
I did not calculate how much it changed the probabilities until I saw BretI's question, and I was surprised that the odds were the same.
Mathmuse, I think we're less focused on the exact math and more focused on making Aid Another a more attractive option.
And I agree with the concept that where Aiding Another is possible, that we shouldn't need to decide who is performing the action. You simply take the highest roll and add the bonus for aiding.
With the understanding that not all task can be aided or the number of people that can attempt to assist can be limited.
True, the math only needs to be in the right ballpark, unless you have players who would rather perform a long, boring process than a short one because the long process gives slightly better odds. I have played with old-school players who believe a good turn is, "I move 5 feet down the hallway and check for traps."
The real advantages of BretI's method are:
1) Fewer dice rolls are required.
2) It gives a realistic sense of group activity rather than splitting a group activity into a bunch of individual activities.
That it gives the same odds is just icing on the cake. We GMs don't have to worry about changing the odds.
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Thank you for your in-depth summary!
I guess, the only real question I have that lingers, is how do things like Treat Wounds, that have a Crit-Fail/Bolster mechanic, interact with using the proposed streamlined rolling, and using the others as assists?
I'll admit to allowing the above in home games for 1E on more than a couple occasions, and knowing that all it does was make things less ... tedious at times, is a relief.
If worst case, running things with Bolster/Crit Fail options as RAW, and everything else this way, is still a compromise that I think is for the better, math permitting.
Hmm... I'm on the fence with the idea. For certain checks.
Most of these checks were given the "Secret" tag in PFPT. Things like Perception, Recall Knowledge/Lore, etc. In the Playtest I prefer these as secret, as it dissuades player rerolling and makes them need to act on what the GM gives them, not the Meta-knowledge of the dice coming up as a 1.
In 1e and Starfinder though I think, again, things like Perception and Knowledge would do better with this system. FOMO (Fear Of Missing Out) causes most parties to stop dead when they get a low Perception to search the room. More often and not, they all roll individually for the highest chance someone will succeed. Turning that into, "Everyone who passed the DC adds +2 to the highest roll" would be good. Maybe I'll suggest it as a homebrew rule next Starfinder session.
Treat Wounds and things like Disable Device though, I don't think would do well with the system. If you do have multiples capable of Treat Wounds, you get the benefit of healing more than x-people at a time, and not botching them all on a critical failure.
You also do have the GM able to say "no more than X people can aid this check", so that plays into it as well to prevent just everyone rolling to hope for success. Or have failures on the Aid subtract 2 from the best result, and critical failures subtract 4. Make the table need to think about it.
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Most of these checks were given the "Secret" tag in PFPT. Things like Perception, Recall Knowledge/Lore, etc. In the Playtest I prefer these as secret, as it dissuades player rerolling and makes them need to act on what the GM gives them, not the Meta-knowledge of the dice coming up as a 1.
I rejected secret rolls in my games. It removes the fun of the players rolling for themselves and adds a burden on the GM.
I can trust my players to keep the metagame knowledge about a poor roll out of their roleplaying. My wife's character in The Lost Star had Dubious Knowledge, which gives both true and false information on a regular failure of a Recall Knowledge check, and she faithfully roleplayed believing both pieces.
You also do have the GM able to say "no more than X people can aid this check", so that plays into it as well to prevent just everyone rolling to hope for success. Or have failures on the Aid subtract 2 from the best result, and critical failures subtract 4. Make the table need to think about it.
In PF2, Aid gives a +2 circumstance bonus, so multiple Aid bonuses don't stack. All that Aid from many helpers does is increase the chance that at least one helper succeeded at aiding and increase the slim chance of a +4 circumstance bonus from a critical success. In BretI's method, the player who rolled well enough for a critical success on Aid would also be the highest roll, so he or she would have the check roll rather than an aid roll, so that reduces fishing for critically successful Aid.
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Or have failures on the Aid subtract 2 from the best result, and critical failures subtract 4. Make the table need to think about it.
Please, not that!
It will make people less involved when it isn’t a skill they are good at. I want people to feel like they are contributing to the adventure.
On the secret rolls, they would have to know that they are making the checks in order to Aid Another. Many Perception checks are made as a reaction, so those would not allow for Aiding. If they are searching, I see no reason to not allow it. It makes for less dice rolling for the GM.
Personally, I feel they went a little too far with the secret rolls.
I would have to look again at Treat Wounds, but I’m really not sure that is so bad. I would limit how many could help on that just because there is a point where there isn’t room for everyone to help.
As for Disable Device, given my experiences with the playtest it might allow people to finally succeed! They currently require three or more rolls to pick a lock. In the adventures I ran, every single lock caused at least one breakage. The Disable Device has the same multiple rolls required mechanic where the chances of critical failure are pretty good.
Another thought would be to say if there are any critical failures, you must have more successes than critical failures or the critical failure happens. Taking the example of a trap, if you had three people attempting to neutralize it and one got a critical failure, if neither of the other got some sort of successs (normal or critical) then the trap goes off.
The normal rules for Aid Another are that you have to pick who is leading in a skill before rolling. The person Aiding gives either a +2 or +4 to the skill check on a Success or Critical Success.
I have seen a variant in multiple adventures for PF1 and Starfinder where everyone rolls, the highest result is the skill roll and you treat the others as Aid actions.
I like this method a lot better since it uses the most favorable roll. If you have two characters as the table both good at a skill, it tends to promote a friendly rivalry (let’s see who finds it first!) and doesn’t make someone who rolled really well feel like their roll was wasted because they chose to Aid rather than roll for the skill.
I know this would give a higher result than the current method, but is that really that bad? I would like to suggest this be the default Aid. I wouldn’t mind if the bonus from the Aid were reduced to +1/+2 because of the higher chances of success.
This largely disincentivizes specializing in any skill, especially since the player making the main roll is, more often than not, the one with the most investment.
When that investment becomes trivialized because someone has a lucky rolling streak, that player begins to question the point of his investment when his ability to succeed is diminished by the sheer number of dice rolling.
I would probably allow multiple people to try aiding, since the bonuses or penalties it grants don't stack (and their results determine the overall modifier), but the players are still only going to get one actual roll.
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This largely disincentivizes specializing in any skill, especially since the player making the main roll is, more often than not, the one with the most investment.
When that investment becomes trivialized because someone has a lucky rolling streak, that player begins to question the point of his investment when his ability to succeed is diminished by the sheer number of dice rolling.
I would probably allow multiple people to try aiding, since the bonuses or penalties it grants don't stack (and their results determine the overall modifier), but the players are still only going to get one actual roll.
Disincentives? No, not really. Let's go over the mathematics and the algorithm involved.
1. Identify a Magic Item
Suppose the party finds a magic item with DC 25 to identify and DC 15 to Aid in identifying. The wizard has a +9 in Arcana, the druid has a +8 in Nature, the bard has a +7 in Occultism, and the paladin has a +4 in Religion. They each spend 10 minutes studying the item, then pool their skills and make their rolls. If they were still in Exploration mode, they would each send an action and a reaction as if they were Aiding.
The wizard rolls 4 for a result of 13. The druid rolls 16 for a result of 24. The bard rolls 7 for a result of 14. The paladin rolls 11 for a total of 15. Both the druid and paladin successfully Aided, so everyone gains an +2 circumstance bonus. No-one critically failed the Aid, so no-one has a circumstance penalty.
Then we interpret the results in 4 ways. The wizard's check is 15, regular failure, so he cannot identify the magic item and can't try again for 1 day. The druid's check is 26, so he figures out the general features of the item, including how to activate it. The bard's check is 16, another regular failure. The paladin's check is 17, a third regular failure. Since the succeeded, the party learns what the magic item can do.
If all we cared about was a success, we would immediately look at the druid's unaided result of 24, also see that the paladin's unaided result of 17 is enough to Aid the druid, and see that no-one had a critical failure to aid. Thus, the druid's final check is 26, enough to successfully identify. Using the best interpretation rather than the 4-way interpretation is BretI's original method, but if critical failures matter, we ought to take the 4-way interpretation.
In the current PF2 system, we would have multiple rolls. First, the wizard would study the item for 10 minutes and everyone else would prepare to Aid. The wizard rolls a 4, the druid and bard roll successfully to Aid, but that is still only a 15, a regular failure. Second, the party spends another 10 minutes with the druid studying the item and everyone else preparing to Aid. The druid rolls a 16 and the wizard rolls a 17 for a critical Aid, and the paladin rolls a regular Aid. This, the druid's check is 28, so he succeeded at the identify. Nevertheless, the wizard is disappointed that he did not roll that 17 when he was trying to identify, and the paladin is disappointed that the wizard upstaged his Aid. And the party took 20 minutes rather than 10 minutes.
2. Group Stealth
The 4-way interpretation also adapts to checks that really ought to be taken as a group, such as sneaking together.
The party has to sneak past an open doorway with a guard on the far side. The guard's Perception DC is 18 and the GM decides that Aiding sneak in this case is difficult, so DC 15. The wizard has +7 Stealth, the druid +9, the bard +8, and the paladin +4.
The wizard rolls 7 for a result of 15, the druid rolls 19 for a result of 28, the bard rolls 4 for a result of 12, and the palading rolls 10 for a result of 14.
Interpreting 4 ways, the wizard is critically aided by the druid, so his Stealth check is 19 and he successfully sneaks. The druid gains only a regular aid from the wizard, so the druid's check is 30, a critical success of the Sneak action had a critical success, which it doesn't. The bard and paladin are critically aided by the druid, so their checks are 16 and 18 respectively. Alas, 17 is a failure, so the guard spots the party and calls the alarm.
3. Lockpicking
The 4-way interpretation does not adapt to situations where one character is undoubtedly doing the work and the others can only aid. For example, if the party bard picks a lock, then only the bard is using the thieves' tools and only he can succeed at the lockpicking.
I guess, the only real question I have that lingers, is how do things like Treat Wounds, that have a Crit-Fail/Bolster mechanic, interact with using the proposed streamlined rolling, and using the others as assists?
Treat Wounds has a clause, "A given creature can be subject to only one Treat Wounds attempt per 10-minute period, so two characters can’t treat the same target’s wounds simultaneously." The 4-way interpretation really amounts to everyone trying simultaneously while also aiding simultaneously, so it cannot be used with Treat Wounds.
For anything else that is bolstered against, either automatically or on a failure, just check each individual case. If failure means cannot try again but success does not, then those people who individually failed are bolstered against and those who individually succeeded can try again.
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In my previous post, I gave the procedure for the 4-way interpretation of a group skill check, but I had promised the mathematics. I expect most of you will skip this.
Let's look at a simple case. Player 1's character has a p1 chance of succeeding at the check unaided, player 2's character has p2 chance, the chance of aiding is q easier than the chance of success, and the chance of success while aided is 0.1 easier than the chance of success.
Player 1's chance of success with player 2 rolling to aid is handled as two cases: player 1 succeeds without needing the +2 circumsance bonus from aid, which has probability p1, or player 1 succeeds only from the +2 bonus, which has probability (0.1)(p2+q) where 0.1 is the chance of succeeding via the +2 bonus and p2+q is the chance of player 2 successfully aiding. These two outcomes are mutually exclusive, which means I can sum the probabilities to gain the overall chance of success: p1 + (0.1)p2 + (0.1)q.
Player 2's chance of success with player 1 rolling to aid has a similar calculation and gives a (0.1)p1 + p2 + (0.1)q chance of success.
To figure out the chance that at least one of those two checks succeeds, I divide the successful outcomes into three mutually exclusive cases: both players succeed, player 1 succeeds while player 2 fails, or player 1 fails while player 2 succeeds. Those probabilities are (p1 + (0.1)p2 + (0.1)q)*((0.1)p1 + p2 + (0.1)q) and (p1 + (0.1)p2 + (0.1)q)*(1 - (0.1)p1 - p2 - (0.1)q) and (1 - p1 - (0.1)p2 - (0.1)q)*((0.1)p1 + p2 + (0.1)q). The sum of those probabilities is (1.1)p1 + (1.1)p2 + (0.2)q - (0.1)p1^2 - (1.1)p1p2 - (0.1)p2^2 - (0.11)p1q - (0.11)p2q - (0.01)q^2.
Clear as mud, right? When probabilities become quadratic polynomials with some negative terms, telling what factors make it larger or smaller becomes difficult. If I had used four players, the polynomial would be quartic (4th degree).
Next, let's look at the 2-way interpretation of a single die roll by each player. Player 1's d20 roll can be divided into three mutually exclusive outcomes: (a) failure, (b) successfully aids but cannot succeed at the primary check, (c) could succeed at the primary check with a +2 bonus, and (d) succeeds at the primary check without aid. For player 1, the probabilities of those cases are (a) 1 - p1 - q, (b) q - 0.1, (c) 0.1, and (d) p1. For player 2, substitute p2 for p1. If player 1 has a failure (a), the for success player 2 has to succeed without aid (d). If player 1 successfully aids but not successfully checks (b), then player 2 has to succeed with or without aid (c) and (d). If player 1 could succeed with aid, the player 2 has to aid or succeed with or without aid (b), (c), or (d). If player 2 succeeds without aid, it doesn't matter what player 2's result is. The probabilities of those cases add up to (1 - p1 - q)(p2) + (q - 0.1)(p2 + 0.1) + (0.1)(p2 + q) + p1 = p1 + p2 + (0.2)q - p1p2 - 0.01.
The difference between the two-checks probability and the 2-way-interpretation probability is D = (1.1)p1 + (1.1)p2 + (0.2)q - (0.1)p1^2 - (1.1)p1p2 - (0.1)p2^2 - (0.11)p1q - (0.11)p2q - (0.01)q^2 - p1 - p2 - (0.2)q + p1p2 + 0.01 = (0.1)p1 + (0.1)p2 - (0.1)p1^2 - (0.1)p1p2 - (0.1)p2^2 - (0.11)p1q - (0.11)p2q - (0.01)q^2 + 0.01. Given that p1, p2, and q are greater than or equal to 0, less than 1, and multiples of 1/20, the maximum value of D is 0.043, and the minimum value is -0.081, so the two probabilities are close to each other.
For example, suppose player 1 and player 2 both have a +7 to the check and the check DC is 20 and the Aid DC is 15. Ignoring critical successes and failures, player 1's chance of succeeding at the check with player 2 rolling to Aid is 8/20 + (0.1)(13/20) = 0.465. Player 2's chance of succeeding at the check with player 1 rolling to Aid is also 0.465. The chance of at least one success is 0.714. If both roll and the results are interpreted 2 ways, the chance of success is 8/20 + 8/20 + (0.2)(5/20) - (8/20)(8/20) + 0.01 = 0.700. The difference is 0.014, which disappears in rounding error when we round to the nearest 1/20.
Interesting that the results align closely.
I think a benefit of "best roll of group" approach is that it avoids obscuring the actually optimal approach from player,
i.e. whether Aiding or not Aiding is more likely to result in (Crit) Success or avoid (Crit) Failure.
Which IMHO is now not at all clear to many players, who can complain about results even while ignoring potentially optimal approach.
If the check is optimally attempted with Aid, it seems reasonable for this to just be part of default mechanic.
I am also curious what impact would follow from Aid being mutually exclusive with making own check (for checks that disallow retries).
And what 'best roll of group' mechanic might potentially closely match that (also given DCs matched to mechanic, see below).
I think tangential to this is how game accomodates for checks with multiple characters.
AFAIK right now Difficulty tiers are set on single character basis, despite being openly acknowledged
that certain types of checks may only need 1 character's success, or others may need ALL characters' success.
Rather than 'actual Difficulty' being obscured, it seems desirable for those types of checks
to simply have their own DC tables (columns) which accurately account for the check dynamics.
Which seems beneficial to both GMs and Paizo's own adventure design...
And also makes particular nuances in independent Aid vs "best of" approaches less relevant,
since the DCs would be set for desired over-all Difficulty, although shape of curve is particular to chosen mechanics.
EDIT: I am curious how 5 or 6 character rolls affect the math, which can also occur via Familiar/AnimalCompanion (or even above 6 rolls).
It seems advisable for adjustments for 5 or 6 players to strictly account for multi-char checks whatever the specific mechanic.
I think tangential to this is how game accomodates for checks with multiple characters.
AFAIK right now Difficulty tiers are set on single character basis, despite being openly acknowledged
that certain types of checks may only need 1 character's success, or others may need ALL characters' success.
I'm not certain which update to the rules included it, but this text is part of Update 1.6
The DC numbers on this table are to determine whether a single character can succeed or fail at a task. Sometimes, you'll have a check that the entire party can roll against, with no real complications that would happen on a critical failure, and where only one person really needs to succeed (such as a Perception check when everyone is searching the same area.) If you want the whole party to face the same degree of difficulty in a case like this, simply increase the DC by 4.
I'm not certain they did the math on that rule, nor what their assumed party size was. I think that the DCs through the playtest were high enough that increasing them by another four means the party is pretty much fishing for a natural 20. I don't know about your groups, but for us that really isn't a lot of fun. Good way to make the whole group feel incompetent.
I think tangential to this is how game accomodates for checks with multiple characters.
AFAIK right now Difficulty tiers are set on single character basis, despite being openly acknowledged
that certain types of checks may only need 1 character's success, or others may need ALL characters' success.I'm not certain which update to the rules included it, but this text is part of Update 1.6
The DC numbers on this table are to determine whether a single character can succeed or fail at a task. Sometimes, you'll have a check that the entire party can roll against, with no real complications that would happen on a critical failure, and where only one person really needs to succeed (such as a Perception check when everyone is searching the same area.) If you want the whole party to face the same degree of difficulty in a case like this, simply increase the DC by 4.I'm not certain they did the math on that rule, nor what their assumed party size was. I think that the DCs through the playtest were high enough that increasing them by another four means the party is pretty much fishing for a natural 20. I don't know about your groups, but for us that really isn't a lot of fun. Good way to make the whole group feel incompetent.
They already updated the DC's to count this +4
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I really like this option. We ran into this issue recently, where we wanted to aid our best person searching for stuff but it quickly became apparent that fishing for Nat 20s was a better idea. That's thematically a lot less interesting, since instead of a party working together as a group, you have five individuals all hoping someone gets lucky and nobody else's roll will count for anything if they do.
We should want to keep players engaged and working together.
(As for secret rolls, we almost never use them. Making the DM roll 5 rolls instead of letting each player roll 1 both slows down the game and makes the players feel more like they're being told a story than being active participants. Opposed rolls are when we do, as your NPC opposition will roll in secret typically.)
Adjusting the Chance of Success
When creating challenges at the PCs’ level, use the following guidelines to determine what degree of difficulty is a good fit. Then consult Table 10–2: Skill DCs by Level and Difficulty to determine the appropriate DC. The table’s Level column indicates the task level, while the subsequent columns present DCs for each difficulty. You’ll most often use the hard DC, but various environmental and situational circumstances can adjust the DC to a higher or lower category, as described later.The DC numbers on this table are to determine whether a single character can succeed or fail at a task. Sometimes, you’ll have a check that the entire party can roll against, with no real complications that would happen on a critical failure, and where only one person really needs to succeed (such as a Perception check when everyone is searching the same area). If you want the whole party to face the same degree of difficulty in a case like this, simply increase the DC by 4.
I believe that this is bad advice. I can prove that the last sentence is bad mathematics.
For simplification, let's assume that every party member has the same chance of succeeding at the roll, and label that chance p. Given that a single individual success means success for the party, the chance of a party success is 1-(1-p)^n where n is the number of party members making the check.
Let's throw in some numbers for examples. Suppose an individual character in a four-member party has a 10% chance of success, p = 0.1. Then 1 - (1-p)^n = 1 - (1-0.1)^4 = 1 - 0.9^4 = 1 - 0.6561 = 0.3439, which I round to a 35% chance of success for the party.
In the opposite direction, suppose we want the four-member party to have a 15% chance of success. Then we have to perform algebra: 1 - (1-p)^4 = 0.15. Therefore, (1-p)^4 = 0.85 and 1-p = 4th root of 0.85 = 0.96018.... The gives p = 1 - 0.960 = 0.04, which I must round to 0.05, AKA 5%, to convert into a d20 roll. Note that in this example, the individual check has a +2 penalty beyond the desired group DC.
I looked at some more cases to see how that penalty changes, and then I did some calculus, and then I figured out how to explain what is going on without the calculus. Let me create a table of p versus f(p) = 1-(1-p)^2 for the values of p from 0/20, 1/20, ... 20/20.
f(0%) = 0%, f(5%) = 18.5%, f(10%) = 34.4%, f(15%) = 47.8%, f(20%) = 59.0%,
f(25%) = 68.4%, f(30%) = 76.0%, f(35%) = 82.1%, f(40%) = 87.0%, f(45%) = 90.8%,
f(50%) = 93.7%, f(55%) = 95.9%, f(60%) = 97.4%, f(65%) = 98.5%, f(70%) = 99.2%,
f(75%) = 99.6%, f(80%) = 99.8%, f(85%) = 99.9%, f(90% and higher) = 100.0%
Then we invert the function f to create g, which turns group probabilities into individual probablilies. For example, to find g(90%) we look through the f table and see that f(45%) = 90.8% is the closest to 90%, so g(90%) = 45%.
g(0%) = 0%, g(5%) impossible, g(10%) impossible, g(15%) = g(20%) = 5%,
g(25%) impossible, g(30%) = g(35%) = 10%, g(40%) impossible,
g(45%) = g(50%) = 15%, g(55%) = g(60%) = 20%, g(65%) = g(70%) = 25%,
g(75%) = 30%, g(80%) = 35%, g(85%) = 40%, g(90%) = 45%, g(95%) = 55%, g(100%) = 100%
Let's look at the meaning of the g table. If the GM wants a group success rate of 75%, he needs an individual success rate of 30%. That is a difference of -45%, a -9 penalty. Let's convert g to h, which gives the penalty for the differences, that is h(x) = 20*(g(x)-x).
h(0%) = +0, h(15%) = -2, h(20%) = -3, h(30%) = -4, h(35%) = -5, h(45%) = -6,
h(50%) = -7, h(55%) = -7, h(60%) = -8, h(65%) = -8, h(70%) = -9,
h(75%) = -9, h(80%) = -9, h(85%) = -9, h(90%) = -9, h(95%) = -8, h(100%) = -0
The suggested penalty, -4, shows up in only one case, or maybe two cases if we decided to fill in the gap at 25% with h(25%) = -4.
Let's see how this works in practice. The party has escaped the underground complex by a route different than they entered. They are now in the forest and want to head back to town. They need the Sense Direction action, which requires a Survival check, to find their way back without getting lost. If they fail, they will have to camp without gear and will be attacked by wolves during the night, because the GM likes rub in how incompetent they are, I mean, likes to have reasonable consequences for failure. All Sense Direction says about the DC is, "The GM determines the DC and how long this activity takes."
The GM checks Table 10-2 for 3rd level, since they just escaped from a 3rd-level dungeon. He considers the essence of the challenge: the party is only 10 miles for town, they might stumble across a trade road from town, if they find a large clearing then they might spot familiar mountains on the horizon, and the sun is setting so the direction west is fairly obvious. The difficulty is Easy. Table 10-2 says DC 10. The GM upgrades that to DC 14 as per the group directions, and asks the party to roll for Survival to find their way to town.
By coincidence, all 4 members of the party have +4 to Survival (3rd-level trained +3, wis +1). A party member has to roll a 10 or higher to succeed, 55% chance of success. The f table tells us that the group has a 95.9% chance of success. In contrast, one person rolling against DC 10 has a 75% chance of success.
For the advice to work as intended, the DC should have been 19, because h(75%) = -9.
Unfortunately, for the level adjustment to work, you need to use the h table. To use the h table, you need to know the chance of success. Thus, the GM needs to check his copies of the character sheets, see the Survival +4, subtract the +4 from DC 10 to get 6, convert 6 to 75% chance of success (though we could build this step into the table), and look up the penalty of -9. That is too much work. I argued in another thread that looking up values in a table for leveling up is not difficult, but I have a different opionion about looking up values in a table in the middle of a game. That is annoyingly time consuming, especially if I forget which page has the table.
A much easier method would be for the GM indulge in creative excuse-making, "I know the DC for a single person to roll to find town after looking for clues about the direction to town. The Survival check reflects the chance of finding a clue after wandering randomly and having enough Survival knowledge to recognize the clue. If you each rolled individually, that means you split the party to wander in different directions. Do you want to do that?" The players will say no, and agree to one Survival check by the best survivalist at DC 10, with the rest of the party rolling to aid at DC 15. Yes, this would be a weird case where the Aid DC is higher than the Check DC. Given the Surival +4, with the party rogue selected as the checker, the chance of him succeeding on his own would be 75%, and the chance of him succeeding only with aid and receiving that aid would be 9%, for a total of 84%.
As for how Paizo get a -4 penalty, let's look at the 21 cases, filling in the gaps with a smooth increase: +0, +0, -1, -2, -3, -4, -4, -5, -5, -6, -7, -7, -8, -8, -9, -9, -9, -9, -9, -9, +0. The average is -5.4, which I would round to -5. Hm, that is not -4. Maybe they calculated the 3-member case instead. Or maybe they guessed.
The average is -5.4, which I would round to -5. Hm, that is not -4. Maybe they calculated the 3-member case instead. Or maybe they guessed.
It seems plausible to consider in 4-member party, 1 member may not be eligible to make a check, which may be gated by proficiency tier. That is kind of adjacent to issue of all 4 characters likely not having equal score albeit the latter is probably more hand-wavable than former. Also, they presumably are less interested in the group:single relationship across ALL spectrum, but only ones within difficulties the game considers notable and viable challenges.
I'm not certain which update to the rules included it, but this text is part of Update 1.6I think tangential to this is how game accomodates for checks with multiple characters.
AFAIK right now Difficulty tiers are set on single character basis, despite being openly acknowledged
that certain types of checks may only need 1 character's success, or others may need ALL characters' success.The DC numbers on this table are to determine whether a single character can succeed or fail at a task. Sometimes, you'll have a check that the entire party can roll against, with no real complications that would happen on a critical failure, and where only one person really needs to succeed (such as a Perception check when everyone is searching the same area.) If you want the whole party to face the same degree of difficulty in a case like this, simply increase the DC by 4.
I'd still be interested in another column for difficulty requiring ALL 4 characters to pass. Or considering other types or approaches to checks... Could there not be checks where HOW MANY characters pass is translatable to degree of success/failure of the challenge? e.g. collapsing bridge trap dumping party into water forcing Swim checks... the Difficulty should probably be calibrated around HOW MANY character pass/fail that, with expected amount of failure (or partial failure as group).
An interesting dynamic for some 'tests' for some situations, such as your collapsing bridge scenario might be cool to define that all the players make a check. All successful members are allowed to make a free check as an Aid Other to someone who isn't passing their check to attempt to assist them.
That would certainly be in line with many heroic narratives, where someone tosses their hand out and helps someone who almost didn't make it. You could have them roll an Aid roll, or it could be that a standard practice for tasks defined that way would allow them to use their personal roll to act as the aid roll (thereby anyone succeeding the roll can give a bonus to someone who didn't). The idea being to naturally give the weaker party members a chance to get a boost, and help the party get across.
Oh, another potential mechanic... just like Locks can require 'so many successes' to overcome. Some failures might only kick in after more than one tier of failure. [which might include a critical failure dropping you two tiers, of course]
So one failed check may not be enough to alert the guards, instead it takes at least two failed stealth checks/tiers. Critical successes might be able to offset a failure, as well, creating a distraction that the guards follow up rather than the noise that their ally made.
The average is -5.4, which I would round to -5. Hm, that is not -4. Maybe they calculated the 3-member case instead. Or maybe they guessed.It seems plausible to consider in 4-member party, 1 member may not be eligible to make a check, which may be gated by proficiency tier. That is kind of adjacent to issue of all 4 characters likely not having equal score albeit the latter is probably more hand-wavable than former. Also, they presumably are less interested in the group:single relationship across ALL spectrum, but only ones within difficulties the game considers notable and viable challenges.
Let's check this by calculating the 3-member case. f3 = 1 - (1-p)^3, g3 is the inverse of f3, and h3 is g3 converted to a penalty, h3(p) = 20*(g3(p)-p).
f3(0%) = 0%, f3(5%) = 14.3%, f3(10%) = 27.1%, f3(15%) = 38.6%, f3(20%) = 48.8%,
f3(25%) = 57.8%, f3(30%) = 65.7%, f3(35%) = 72.5%, f3(40%) = 78.4%, f3(45%) = 83.4%,
f3(50%) = 87.5%, f3(55%) = 90.8%, f3(60%) = 93.6%, f3(65%) = 95.7%, f3(70%) = 97.3%,
f3(75%) = 98.4%, f3(80%) = 99.2%, f3(85%) = 99.7%, f3(90%) = 99.9%, f3(95%) = f3(100%) = 100.0%
g3(0%) = 0%, g3(5%) impossible, g3(10%) = g3(15%) = 5%, g3(20%) impossible,
g3(25%) = g3(30%) = 10%, g3(35%) = g3(40%) = 15%, g3(45%) = g3(50%) = 20%,
g3(55%) = g3(60%) = 25%, g3(65%) = 30%, g3(70%) = 35%, g3(75%) = 40%,
g3(80%) = 45%, g3(85%) = 50%, g3(90%) = 55%, g3(95%) = 65%, g3(100%) = 100%
h3(0%) = +0, h3(5%) = +0*, h3(10%) = -1, h3(15%) = -2, h3(20%) = -2*,
h3(25%) = -3, h3(30%) = -4, h3(35%) = -4, h3(40%) = -5, h3(45%) = -5,
h3(50%) = -6, h3(55%) = -6, h3(60%) = -7, h3(65%) = -7, h3(70%) = -7,
h3(75%) = -7, h3(80%) = -7, h3(85%) = -7, h3(90%) = -7, h3(95%) = -6, h3(100%) = +0
* this number placed in gap by interpolation.
Average value of h3 is -4.4, which rounds to -4. Okay, that works.
I'd still be interested in another column for difficulty requiring ALL 4 characters to pass. Or considering other types or approaches to checks... Could there not be checks where HOW MANY characters pass is translatable to degree of success/failure of the challenge? e.g. collapsing bridge trap dumping party into water forcing Swim checks... the Difficulty should probably be calibrated around HOW MANY character pass/fail that, with expected amount of failure (or partial failure as group).
One failure means the whole group fails is just the mirror image of one success means the whole group succeeds. We simply need to switch the success and failure probabilities and turn penalties into bonuses. So, the i4 table below is the h table above reconfigured for the one failure means the whole group fails, so what bonus do we give the individuals to set the group chance of success to the individual chance of success?
i4(0%) = +0, i4(5%) = +8, i4(10%) = +9, i4(15%) = +9, i4(20%) = +9,
i4(25%) = +9, i4(30%) = +9, i4(35%) = +8, i4(40%) = +8, i4(45%) = +7,
i4(50%) = +7, i4(55%) = +6, i4(60%) = +5*, i4(65%) = +5, i4(70%) = +4,
i4(75%) = +3*, i4(80%) = +3, i4(85%) = +2, i4(90%) = +1, i4(95%) = i4(100%) = +0
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An interesting dynamic for some 'tests' for some situations, such as your collapsing bridge scenario might be cool to define that all the players make a check. All successful members are allowed to make a free check as an Aid Other to someone who isn't passing their check to attempt to assist them.
That would certainly be in line with many heroic narratives, where someone tosses their hand out and helps someone who almost didn't make it. You could have them roll an Aid roll, or it could be that a standard practice for tasks defined that way would allow them to use their personal roll to act as the aid roll (thereby anyone succeeding the roll can give a bonus to someone who didn't). The idea being to naturally give the weaker party members a chance to get a boost, and help the party get across.
(I am mostly cutting-and-pasting this from a thread on skill gating.)
My wife made a climbing-expert barbarians for In Pale Mountain's Shadow and insisted that I provide climber belaying rules where climbers keep their teammates from falling. Expert Climber Aiding Trained Climbers
And later, I generalized the ability to belay climbers to an expert-only action, Save Other.
[[R]] SAVE OTHER
Trigger An ally has critically failed a skill check or saving throw and the consequences have not yet occurred.
Requirements The ally is willing to accept your aid, and you have prepared to help (see below). You must also have expert or better proficiency in the skill or save, or trained proficiency and a Lore that directly relates to the skill check or saving throw.
You intervene in an ally's activity to prevent the consequences of a major failure. To use this reaction, you must first prepare to intervene, usually by using an action during your turn. You must explain to the GM exactly how you could intervene, and she determines whether you can prevent the consequences.
When you use your Save Other reaction, attempt a skill check or saving throw of the same type and DC as the ally's failed check. During the preparation, the GM may have chosen a different skill check for the intervention check, if intervening with the other skill is more feasible, such as an Acrobatics skill check to intervene on a Reflex save.
Success You convert your ally's critical failure into a failure.
Critical Success You grant your ally a chance to reroll the skill check or saving throw. A critical failure on the reroll becomes a failure.
Critical Failure You suffer the same consequences as the ally.
I have several motives in inventing Save Other:
1) Some of these actions, such as belaying a fellow climber, exist in the real world.2) I like teamwork, and Save Other provides a stronger method of preventing catastrophic failures in group activities than Aid.
3) We need a set of actions that expert proficiency opens up, and Save Other is fairly universal. For example, it could be used with Recall Knowledge: "That big, red flying reptile that breathes fire is a fruit bat." "Idiot, bats aren't reptiles." "Oh, right. I don't know what it is."
Oh, another potential mechanic... just like Locks can require 'so many successes' to overcome. Some failures might only kick in after more than one tier of failure. [which might include a critical failure dropping you two tiers, of course]
So one failed check may not be enough to alert the guards, instead it takes at least two failed stealth checks/tiers. Critical successes might be able to offset a failure, as well, creating a distraction that the guards follow up rather than the noise that their ally made.
I found that multiple rolls when not under a time limit is boring. I would rather take a single ten-minute action that requires one roll than a series of one-minute actions that require two successes to actually succeed. A warning system for failure would not be as bad, because the character is trying to minimize warnings.
I have performed similar probability calculations before, but the resulting probability polynomials are very hard to interpret. If you want a sample, peek at my paper A posteriori probability decoding through the discrete Fourier transform and the dual code, by Erin Schram (my real name) in Codes and Designs, editted by Arasu and Seress, published de Gruyer, 2002.
But instead I can give a situation with a very similar probability.
Imagine that Alice, Bob, Charles, and Diane are all playing characters that must make a knowledge roll to solve a puzzle. One successful check means success for the entire party. First, Alice rolls her check with Bob, Charles, and Diane rolling to aid. Second, if Alice failed, Bob rolls his check with Alice, Charles, and Diane rolling to aid. Third, if Alice and Bob failed, Charles rolls his check with Alice, Bob, and Diane rolling to aid. Fourth, if Alice, Bob, and Charles failed, then Diane rolls her check with Alice, Bob, and Charles rolling to aid.
That has very close to the same probablity of success as Alice, Bob, Charles, and Diane all rolling once each, the highest result selected as the check and the other three rolls selected as attempts to aid.
A rough explaination of why the probabilities are very close is imagine in the first case with the four separate rolls, each individual happened to roll the same number four times in a row. That is identical to re-interpreting the single set of rolls in the second case four times: once as if Alice were checking and the others aiding, once as if Bob were checking and the others aiding, once as if Charles were checking and the others were aiding, and once as if Diane were...
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