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There is a lot of effort and thought going into these ideas, and they are great to read through and to consider.
Though (as I mentioned before) I have no great skill in designing/implementing statistical approaches I can see the time and concern people have put in, so thanks for that.

I really see the point made about having more than a few rolls to garner success in a Council. And even in 1e, I didn't enjoy prolonged sets of rolls to 'win' an Encounter. Stubbazubba makes the point about " interesting and fresh" and the point is valid. Often less is more, and more tense too.

So, still aiming for simplicity. How about this?

1. All Councils need 3 Winning rolls to pass.
2. The Time Limit is 3 for all Councils.
3. For Easy Councils, any level of Success works and counts as a Winning roll.
4. For Standard (medium) Councils only a roll that includes at least one Tengwar counts as a Winning roll.
5. For Hard Councils, only a roll with at least 2 Tengwars counts as a Winning roll.
6. For all councils, if a roll produces more Tengwar than needed, all the surplus counts as + 1 Success.
7. Introduction Success roll gives + 1 Time to the Time Limit; but Success is as difficult as steps 3, 4 or 5 above


Example for hard council with skill 3 TN = 15

Introduction: rolls 9 + (4 + 6 + 2). Beats TN, but only with 1 Tengwar, so Time limit stays at 3
Roll 1 (spends Inspired Hope to get 5d6): rolls 0 + (6 + 1 + 6) + (3 + 3). Beats TN with 2 Tengwar therefore FIRST success
Roll 2 (spends Hope on new skill, for 4d6): rolls 2 + (2 + 1 + 3 ) + (1 + 6). Beats TN but with only one Tengwar, so NOT a Success
Roll 3 ( spends Inspired Hope on Favoured roll for 2d12 and 5d6): rolls [3 + 8] + (6 + 4 +2) + (3 + 6), total 29. Beats TN and with two tengwar this is the SECOND success. Had yet another Tengwar been rolled, then it would be both a SECOND and a THIRD success

The LM this would either rule a Failure, or some sort of serious complication, Success with Hard Woe.
But three rolls plus an introduction.

Suggestion:

Resistance levels as normal. Base time limit is 1 if the audience is reluctant, 2 for open and 3 for friendly. A success on the introduction roll increases the time limit by 1, plus 1 per t.

On interaction rolls, t’s can be spent on one of the following effects, depending on the type of skill used.

Emphatic words - any skill
Counts as an additional success

Introduce argument - Heart or Wits skill
Increase the time limit by 1

Seek favour - Strength or Wits skill
If the council ends in a success, improve the outcome in some way (to be agreed with the Loremaster)

Sway crowd - Strength or Heart skill
Improve the attitude of the crowd by one level (reluctant -> open -> friendly) for the remainder of the council

The purpose of this is to mark harder councils actually harder, and also turn them into a little mini game, rather than just rolling a load of skill checks in a row. Inspiration is obviously taken from the combat system, so hopefully it should be familiar enough to be engaging rather than confusing. I like having a variable time limit to make the council feel a little more natural, and increase the tension throughout. This makes the very easy councils actually a bit easier and the harder ones much harder. Outrageous/reluctant (9 successes in ~2 rolls) looks impossible (as it should do), but by chaining Introduce Argument, a skilful/lucky company might pull it off. I'd be slightly worried about Seek Favour allowing players to upgrade a reasonable request to bold or outrageous with very little cost, so the LM must be careful about what he allows. Open to suggestions for other effects, particularly to replace this one.

The other issue I have/see with Councils is the prospect of 9+ skill checks with little to no guidance on how to keep those checks fresh or interesting. From the outset, there are easily optimized solutions to a static game where the Resistance and all the TNs are known in advance. Disallowing/penalizing repeated checks might nominally increase the diversity of skills used, but it doesn't make it much more interesting, it just means you have to calculate the next best choice, as well. There just has to be some hidden information, or at least something that delays or changes the optimal approach and ways to discover it in the game's abstraction.

This is an issue with most extended skill check systems (D&D 4e skill challenges, etc.). The book could use better guidance for the LM. As other have said, I've found the key is to engage the fiction and have some new piece of fiction introduced after every roll or 2-- for councils this can be all kinds of things, like another NPC speaking up with a different personality that they now have to engage with, the scene moving from the throne room to a the banquet table, letting slip a otherwise unknown detail, etc.

But to your other point -- the "game" part of it is not so great. It's just a series of skill checks, and there is every incentive to try to shoehorn in your best skills. In TOR2e you can decide on whether to spend hope or not, but not much other decision making.

I think there are 2 options.

1) Just acknowledge that this is not much of a "game" but rather more of a background resolution system to traditional freeform roleplaying. The real purpose is having a non-arbitrary resolution over multiple dice rolls and have non combat scenes that incentivize the whole party acting. (at least in the versions where every PC gets 1 roll per 'round'). Have a table agreement to just engage the fiction and not worry about which skills you are using and adjust the difficulty to account for the fact that not everyone will have a top skill for every situation. Yes, the solution is optimized/set but at least it's not dependent on 1 roll and isn't just "whenever the DM decides it's over", and there can be some fun in the how it gets resolved as well since you get story out of each of the success and failed roles.

2) Try to figure out ways to make the "game" portion better and more strategic. Things like modifiers to certain skills could work like you have. The only really interesting set up like this I have seen is in FATE Diaspora. They use a map, factions or people represented as pawns, and countdown to add more strategic elements to social conflict. So the objective is not just counting successes but rather something like "moving the 3 factions onto the space that represents supporting your position before the other side moves it onto the space representing their position". Now there is active opposition and there are more "game moves" such as moving to get closer to the faction before you can influence it, setting up barriers, trying to take out the opposition directly vs. influencing the 3rd party factions toward your position, etc. It's very abstract in concept but adds some game moves that are usually reserved for physical combat like positioning. There is also usually not just success / failure. In this example, if the time runs out and no one has influenced the factions enough then there is another end state where no gets exactly what they want.

Forgive me if others have already thought of these ideas...

It seems to me that the main problem/complaint is that the Time Limit is equal to Resistance (with possible modification if the Introduction goes well), meaning that the more outrageous the request, the more time is allowed at the council. So, even though the required number of successes is increased, the player-heroes can make more rolls, which kind of defeats the purpose of Resistance, especially for more skilled Companies.

I can think of a couple solutions:

1. Divorce the Time Limit from Resistance and set it at a standard 3-5 rolls for a short (3), medium (4), or long council (5) based on the narrative. The Time Limit may still be modified by the Introduction roll as written.

2. Keep Resistance but eliminate Time Limit altogether and go back to a Tolerance rating that indicates the number of failures allowed before the Interaction portion of the council ends based on the disposition of the audience: Friendly = 3 failures, Open = 2 failures, Reluctant = 1 failure. Tolerance is set and then modified by the quality of the Introduction roll (+1 for every Tengwar rolled). If the Introduction roll is failed, Tolerance is unmodified but if the Council fails, it ends in a Disaster. Note: Tolerance may provide more drama in some ways when compared to Time Limit as the council can abruptly end due to a failed roll. Tolerance is also a cleaner mechanic. Time Limit can get messy because poor rolls may create a situation where it becomes impossible to pass even if time remains, meaning the Loremaster will need to pay close attention to what's possible or dice rolls will be made in vain.

Suggestion for either solution: Players may spend Tengwars to apply the Gain Insight or Widening Influence options, shown on the Skill Special Success Table (p. 19), to gain special (secret) information or to increase the Time Limit or Tolerance (depending on the solution) by +1 respectively.

Besides all this, I think Councils could still use slightly more guidance when it comes to setting them up. For instance, the following could be added to the USEFUL SKILLS section after the sentence: "The Skills listed below can be used to various effects during Interaction": When setting up a council, choose a number of key Skills important to the Company's goal or audience. Then, determine what kind of information can be learned or what responses are provoked should the player-heroes use them successfully.

2. Keep Resistance but eliminate Time Limit altogether and go back to a Tolerance rating that indicates the number of failures allowed before the Interaction portion of the council ends based on the disposition of the audience: Friendly = 3 failures, Open = 2 failures, Reluctant = 1 failure. Tolerance is set and then modified by the quality of the Introduction roll (+1 for every Tengwar rolled). If the Introduction roll is failed, Tolerance is unmodified but if the Council fails, it ends in a Disaster. Note: Tolerance may provide more drama in some ways when compared to Time Limit as the council can abruptly end due to a failed roll. Tolerance is also a cleaner mechanic. Time Limit can get messy because poor rolls may create a situation where it becomes impossible to pass even if time remains, meaning the Loremaster will need to pay close attention to what's possible or dice rolls will be made in vain.

The downside to Tolerance is that it means the best move for a player without a strong Skill is to not play, to let others with higher Skills just make every roll because a failure has such negative consequences for everyone. That is still somewhat true in RAW, where a party is better off letting only those with 3+ in low-TN appropriate Skills roll, but it's not as severe.

As hsi379 has pointed out, the way to actually incentivize everyone to participate in this mechanic is to give everyone a roll per round, and then limit the numbers of rounds and base the number of successes required on that dynamic. That way you haven't made everyone else worse off if your check fails. But that, I fear, becomes unwieldy quickly. Either the fiction lurches frequently to keep things interesting for 12 rolls to accomplish one objective, or you're having a lot of folks just roll the same thing to do the same thing lots of times over with cosmetic changes in the fiction if any.

The more I chase my tail on this, the more I think your 1. is a "good enough" solution that's actually hard to improve upon: 3/4/5 for easy/medium/hard, + intro tengwars for councils, that requires 3/6/9 successes, and the LM just has to have a twist or two in there to keep it interesting.

Many thanks to the ideas that keep on coming and the analysis that follows it.

Its a brave decision to say that the attempt to streamline and integrate TOR1e Encounters into the new TOR2e Councils has come up with broken maths. And it would be a blunt and harsh verdict to say RAW TOR2e Councils is a failed mechanism. But that is the way it seems.
Each time I see some new posts in this thread, I get another angle to consider.
I have to say that the suggestion with the smallest change needed from published rules might be the most straightforward to implement.
Reading James's ideas has provoked another version to me. (And I am uncertain which might be the most effective*)

HERE'S THE IDEA

It might be simplest to reverse the RAW numbers. Hard Council: 3 Successes in 3 Rolls / Open Council: 6 Successes in 6 Rolls / Easy Council: 9 Successes in 9 rolls. Logically, this makes Easy the most attainable, and Hard the least attainable.

*On the other hand, perhaps it is time to go back to the very beginning and decide "What is Council?" What rules will get this realised, rather than tweaking what we have, or what we used to have . Use a clean slate and rewrite the whole thing..

There are definitely some good ideas here. For my part, I‘d like to keep dice rolling in social interactions a bit shorter than in raw and some of the suggestions here. With playing online, a resistance of 9 and a time limit of say 10 would be too much for my group.

I‘d go with a flat resistance 4 and a time limit of 4 for an easy council, 3 for an open and 2 for a hard. I‘d grant extra successes for good roleplaying as well. A good introduction gives a bonus to the time limit as usual.

On one of my earlier posts (#7 in this thread) I offered an idea where Councils were broken down into one two or three Stages depending on difficulty/Resistance. But I did no Maths to help. I have done a bit now, I think.

Original idea: Organise every Council into Stages. A stage is completed with three Successes. Easy Councils are only 1 Stage; Standard Councils take two Stages; and Hard Councils are three Stages. Tengwars in one stage cannot be transferred into any other stage.

I think that the maths for OPTION C here is not so hard as I thought.
If the percentage probability of a Company passing an Easy Council (i.e. 3 Success in 3 Time) is P%, then each separate Stage is the same difficulty (because it is also 3 Success in 3 Time, it will be also be P%.) To get the combined percentage chance of Success for two stages or for three stages I think you just multiply the probabilities together each time.

So an Easy Council is P%; one stage
A Medium/Open Council is P% multiplied by P% for overall success; two stages - you multiply probabilities if both events are to succeed
A Hard Council is P% multiplied by P% multiplied by P%; three stages - you multiply all three probabilities together if all events are to succeed

e.g. hsi379 posted earlier that a group with 3S skill levels has 65% or 0.65 chance of Success with Easy Councils
which means that the same group has 0.65 x 0.65 = 0.42 or 42% chance with a medium Council overall,
and 0.65 x 0.65 x 0.65 = 0.27 or 27% chance of success with hard Councils overall.

Which does make Easy the most likely to pass and Hard the least likely.

The downside to Tolerance is that it means the best move for a player without a strong Skill is to not play, to let others with higher Skills just make every roll because a failure has such negative consequences for everyone. That is still somewhat true in RAW, where a party is better off letting only those with 3+ in low-TN appropriate Skills roll, but it's not as severe.

Isn't it true to character though that those with low social skills would likely be afraid to speak? I don't see this as a problem. The fun is when those who aren't good speakers want to speak up regardless of the consequences. Others might try to stop them (because they chance blowing it for everyone), but this is all part of the drama and makes for a great time.

For the record, I like the idea of a Time Limit better than Tolerance. So, I am going to try my first option above (setting the Time Limit at 3 for a short council, 4 for a medium council, and 5 for a long council, modified by Introduction roll) to see how that goes, but I might add a sub-rule that when someone fails on an Eye (a gaffe), it counts as 2 rolls. This builds in the idea of the host losing patience (the spirit of a Tolerance rating). Also, I will need to pay attention to the total successes, because when it becomes impossible to reach the Resistance, the council should end prematurely. To keep the council going, the condition must be: (1 + highest skill rating among companions) =/> (Resistance − total successes).

While I agree and can plainly see that the math for council time limits is biased towards success the longer a Council goes on, it appears to be true primarily when disregarding the entropy of the narrative context of a council, as others have pointed out in prior posts. When considering a council scene, if all we see is a series of dice rolls used to build up a pile of successes before a timer expires then there may be no manner of mechanical fix sufficient enough to overcome that in a satisfying way. Mechanizing roleplay has always been a tricky thing to do. The key is leveraging the narrative context to the fullest extent possible, and using it to inform the mechanics of the scene.

The narrative context of a council can be impacted by any number of factors: who is talking (is the audience wary of dwarves?), what they are saying and how they are saying it (the context for skill application - not all Persuade skill rolls are alike), overusing the same skills again and again (Awe me once shame on me, Awe me twice shame on you), using the same skills back-to-back (audience less affected by a repetitive argument), audience Attitude (RAW), audience predisposition for certain methods of argument presentation (which skills and/or Attributes are they most/least likely to respond to?), etc. The list goes on.

Even with longer council timers statistically weighted in favor of success, these longer councils should typically result in the introduction of more contextual entropy than shorter councils, with the net effect being a reduction in the chance of success when compared to a shorter council. I view councils like a knock-down, drag-out battle of wills, with all the trimmings of any other battle one might run at the table. The Player-heros are asking for results their audience does not want to provide, at least initially. This is not fundamentally different from any other combat. There are two sides in direct opposition, regardless of their attitudes towards one another. Even best friends don’t agree 100% of the time. This is social combat, yes, but it's still combat, and even if narratively it comes off as generally pleasant in its execution, under the hood it is a vicious battle to get what you want from those that aren’t immediately predisposed to provide it.

So I generally operate my councils using a few guidelines, keeping in mind this is all-out war in the most pleasant context possible. I think some version of this would have been helpful to include in the section of the core rulebook to teach LMs how to run decent councils.

• Always consider the audience’s Attitude (Reluctant/Open/Friendly). Easiest to do as this is directly addressed in the core rules.

• Consider the Distinctive Features of those primarily addressed by each skill check. Another easy one as this is also RAW, but sometimes overlooked.

• Consider that skills (generally) may become less effective the more they are used, particularly when using the same skill in the same general context it's already been used. If used in a different context a penalty may be avoided or less severe. Using the same skill back-to-back without a significant context change is particularly egregious.

• If one Player-hero is doing all the talking/convincing, the audience may become wary as this intimate group of travelers isn’t acting together in a convincing manner.
  “Why does your dwarf companion have nothing to say? Has he no voice of his own in these matters? Speak now, with haste dwarf, lest I eject you from my halls!”

• Consider which skills, or even group of skills under certain Attributes, are more or less likely to have an effect on this particular audience. Factor it in if it makes sense.

• Consider that no two skill checks are alike, even if it’s the same skill. Take the context of the skill activation into consideration. As a broad example, a Persuade skill check can be activated in different contexts. How does the audience respond to that context?

• Apply Risk Levels to each skill check as appropriate. Use context to set consequences. Maybe the failure (or success with Woe) of a skill check makes the next few checks harder as the audience negatively reacts!

• Apply Endurance reductions along with the use of Risk Levels. A longer council can get exhausting, resulting in Weary participants.

• Finally, consider any other complications/advantages inherent to the scene or scenes that make up the council. Apply these as appropriate.

The thing I try to keep in the forefront during a council is that the roleplay should be more important than, and feed into, the skill rolls, not the other way around. Most importantly, not all audiences will react the same to the same application of methods. This IMO is the key to unlocking interesting councils. It’s really all about keeping narrative context at the forefront and using that to inform the skill checks. And of course the mini-game of discovering how best to approach a particular audience can be a fun game to play if done correctly.

As an aside, this same general logic can be applied to Skill Endeavors, which “suffer” from the same mathematical predisposition for success with longer time limits when reduced merely to a handful of dice rolls with no situational context applied.