hsi379
Topic Author
Posts: 33
Joined: Fri 10 Sep 2021, 19:24

Council Skill Endeavor math odds success rate

Tue 19 Oct 2021, 22:36

Starting a new post because Councils seem to be getting a bunch of posts lately and I think I figured out how to do more complete tables of Odds. Odds of dice pools come from Anydice. Figuring out X successes in Y rolls of a dice pool from Python simulation.

I encourage anyone to try to replicate this and/or verify so we know that it’s correct. I am not 100% sure but think it’s close.

Here’s the results I got for TN14-16 and 2S-4S dice pools. Resistance is across the top. +1 means an extra roll (from good introduction, etc.). So 6+1 means chance of getting 6 successes in 7 rolls.

TN16
        3	3+1	3+2	6	6+1	6+2	9	9+1	9+2
2S	17	27	37	7	12	17	0.03	5	8
3S	52	70	82	48	62	73	45	56	67
4S	83	94	98	88	95	98	92	96	98

TN15
	3	3+1	3+2	6	6+1	6+2	9	9+1	9+2
2S	23	36	48	12	19	27	7	11	5
3S	61	79	89	59	73	83	59	71	80
4S	88	97	99	93	98	99	96	98	99

TN14
	3	3+1	3+2	6	6+1	6+2	9	9+1	9+2
2S	31	46	60	20	29	40	13	20	27
3S	69	86	94	70	83	91	72	82	90
4S	92	98	99.7	96	99	99.7	98	99	99.8

So roughly (because the shifts are not completely symmetric and things get wonky at 4S+ and where the probability is very high):
• Change in TN = ~5-10%
• Extra round = ~10-20%
• Change in # die (on every roll) = ~30-40%
• Change in “difficulty” (reasonable to bold request) = +/- 3 total tries with adjusted success target = wonky. With 3S+ dice it is negligible or actually easier to do longer challenges.

Some thoughts:
• Because of bonus successes from Tengwars, shift in dice pool is a lot more important than TNs
• Shifting from a 3 resistance to a 9 resistance challenge doesn’t really track to the description (reasonable vs. outrageous request) as it can be harder but not massively so. And as you get higher dice pools, it may actually be easier to do an Outrageous Request than a Reasonable Request (more chances for extra success for 9 rolls and less chance of failure per roll)! Clearly not intended
• Success rates are so low for 2S pools, you need to get that extra dice somehow (use hope on a lot of rolls, friendly audience) for any reasonable chance of success
• While 3S pools look like decent odds at first, if the Party gets a good introduction (often likely) and/or uses resources (hope) they can move the odds up to almost guaranteed (4S results) success unless they are penalized a dice
• 4S pools become trivial unless penalized a dice, and even that can return to trivial by using resources. 5S+ seem to be auto success unless penalized multiple dice

Overall, this is a little disappointing as the “sweet spot” of results seem fairly narrow, and the official tools to tweak are not very granular. Likely, I will house rule this heavily before use.

Prove me wrong (I wouldn’t mind)! Discuss!
 
TryhardLM
Posts: 12
Joined: Sat 25 Sep 2021, 14:01

Re: Council Skill Endeavor math odds success rate

Wed 20 Oct 2021, 04:44

Thank you for sharing this and breaking down the implications!
 
gyrovague
Posts: 591
Joined: Tue 28 Apr 2020, 16:52

Re: Council Skill Endeavor math odds success rate

Wed 20 Oct 2021, 07:05

This makes me realize something about Councils that I've been circling around but hasn't fully formed into a coherent thought.

First, although this is well done, the reality is a bit more complicated because different characters will participate, who all have different skill ranks and TNs. Still, it's possible to reduce the whole Council to a single probability, because if you know the characters participating you can, step-by-step, determine which skill each should use on their turn. That is, your company's best strategy can be laid out in it's entirely before you start.

And that's because...and here's the key point...nothing that happens during a Council will alter that optimal strategy. In the algorithm for Councils, there is no feedback: the results of the dice rolls are not used as inputs back into that algorithm.

That is the essence of what has been bothering me about Councils.
 
fahrgast
Posts: 37
Joined: Sat 03 Jul 2021, 16:20

Re: Council Skill Endeavor math odds success rate

Wed 20 Oct 2021, 09:28

In the algorithm for Councils, there is no feedback: the results of the dice rolls are not used as inputs back into that algorithm.

I would say this is not entirely true. During the Interaction phase "the Lore­master chooses whether the audience of the Player-­heroes is Reluctant, Open, or Friendly". Nothing prevents that a roll during this phase can change attitude of the audience, making easier or harder subsequent rolls.
 
Dunheved
Posts: 494
Joined: Wed 11 Mar 2020, 02:07
Location: UK

Re: Council Skill Endeavor math odds success rate

Wed 20 Oct 2021, 09:52

Big thanks to OP for doing the numbers too. I was at a complete loss how to think about even setting up any sort of numerical analysis for something with so many successive steps. And this would be well beyond me.
 
a2le
Posts: 23
Joined: Fri 03 Jul 2020, 19:11

Re: Council Skill Endeavor math odds success rate

Wed 20 Oct 2021, 14:13

First of all thanks a lot for sharing it and trying to clarify this thorny subject!
Assuming that the odds are correct, I think that the main theme here is the counterintuitive behaviour of the "resistance", I mean: higher resistance might involve a lesser hope expenditure, and an easier task for a character with skill greater than 2.
BTW, I think that the longer the skill endeavour is in terms of numbers of skill rolls, the higher is the risk that it becomes a mechanical, thus boring task.
Somehow, as it has already been said elsewhere, it seems to me that the new council mechanic doesn't solve the problems of the Encounters of the 1st ed, but, on the contrary, it adds to them a new one: that mentioned above.
 
fahrgast
Posts: 37
Joined: Sat 03 Jul 2021, 16:20

Re: Council Skill Endeavor math odds success rate

Wed 20 Oct 2021, 15:16

hsi379, please, could you explain your math?

According to https://anydice.com/program/2186c, as an example, the success probability with 3S and TN14 is 0.6948. Then, if you need to get n successes with n rolls, your overall probability of success would be:
n             |  3     |   6    |    9
---------------------------------------
% of success: | 33.54% | 11.25% | 3.77%

Edit: I have written a simple python script to help simulate the math: https://gist.github.com/jantoniomartin/ ... 20cbe95e83

Edit: Using this script with 10.000 iterations, these are the results I get for TN14:

	3	3+1	3+2	6	6+1	6+2	9	9+1	9+2
2S	7,20 %	19,85 %	35,45 %	0,63 %	2,70 %	5,97 %	0,04 %	0,23 %	0,79 %
3S	34,05 %	63,99 %	82,99 %	11,02 %	31,96 %	54,21 %	3,69 %	13,67 %	30,05 %
4S	70,58 %	93,33 %	98,57 %	48,56 %	81,73 %	94,41 %	33,72 %	67,82 %	87,72 %

Edit: By mistake, I hadn't taken into account that "as seen on page 18, each rolled success icon counts as an additional success." I have edited the script above to include this rule and ran 1,000,000 iterations for each case, and these are the results:

    3        3+1      3+2      6        6+1      6+2      9        9+1      9+2
2S  22,83 %  35,42 %  47,30 %  11,97 %  18,53 %  26,04 %  6,61 %   10,27 %  14,85 %
3S  59,68 %  77,41 %  87,99 %  57,42 %  71,60 %  82,08 %  56,28 %  68,56 %  78,36 %
4S  84,14 %  94,93 %  98,52 %  88,86 %  95,55 %  98,38 %  92,11 %  96,55 %  98,60 %

As hsi379 pointed out, it seems that this rule is broken. For example, if you have 4 skill ranks, you have a higher chance of success in a longer, more difficult council, which makes no sense. It seems that the main cause of distortion is counting success icons as additional successes in councils.
Last edited by fahrgast on Wed 20 Oct 2021, 17:40, edited 1 time in total.
 
gyrovague
Posts: 591
Joined: Tue 28 Apr 2020, 16:52

Re: Council Skill Endeavor math odds success rate

Wed 20 Oct 2021, 16:22

In the algorithm for Councils, there is no feedback: the results of the dice rolls are not used as inputs back into that algorithm.

I would say this is not entirely true. During the Interaction phase "the Lore­master chooses whether the audience of the Player-­heroes is Reluctant, Open, or Friendly". Nothing prevents that a roll during this phase can change attitude of the audience, making easier or harder subsequent rolls.
I don't think so. If all skill rolls are modified up or down simultaneously, then your optimal skill choice remains your optimal skill choice.
 
fahrgast
Posts: 37
Joined: Sat 03 Jul 2021, 16:20

Re: Council Skill Endeavor math odds success rate

Wed 20 Oct 2021, 16:33

In the algorithm for Councils, there is no feedback: the results of the dice rolls are not used as inputs back into that algorithm.

I would say this is not entirely true. During the Interaction phase "the Lore­master chooses whether the audience of the Player-­heroes is Reluctant, Open, or Friendly". Nothing prevents that a roll during this phase can change attitude of the audience, making easier or harder subsequent rolls.
I don't think so. If all skill rolls are modified up or down simultaneously, then your optimal skill choice remains your optimal skill choice.

Sorry, I had misunderstood you. The rules for the phase of interactions say "The players choose their own course of action as they see fit." However, I'm not sure that this means that players can plan ahead a series of rolls. I think that choosing the skill for each subsequent roll should depend on the dialog between the heroes and the npcs. Otherwise, a council would be a silly and boring mechanic if a company could choose to roll always the same skill.
 
fahrgast
Posts: 37
Joined: Sat 03 Jul 2021, 16:20

Re: Council Skill Endeavor math odds success rate

Wed 20 Oct 2021, 17:49

I have fixed my post above and, as hsi379 pointed out, it seems that this rule is broken. For example, if you have 4 skill ranks, you have a higher chance of success in a longer, more difficult council, which makes no sense. It seems that the main cause of distortion is counting success icons as additional successes in councils.

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