Nazgûl and Denizen of the Dark

[Michebugio]

I must say that your number are wrong. You have not taken into account that you need to score a Tengwar to succeed.

You don't need a Tengwar to succeed against Thing of Terror. You need a Tengwar to stop rolling every round for it, which is different

And, by the way, zedturtle's results are exactly the same as the ones I posted...

I'm not sure a binomial equation is any more reliable than my getting close and fudging it a bit. How were you accounting for the Gandalf rune? Obviously rolling a G rune and a tengwar is an auto success but rolling a G rune and no Tengwar is not a success. How are you accounting for that result? Rolling an Eye means no possibility of success even with two 6s on the success dice.
Are you saying that you plugged the numbers in to an equation without understanding how the equation deals with the numbers?

No, I understand the equation well, I meant that I wasn't able to understand your method.

By the way, the calculations I made are the following:

The probability distribution of the results of 2 dices is:

2: 2,78%
3: 5,56%
4: 8,33%
5: 11,11%
6: 13,89%
7: 16,67%
8: 13,89%
9: 11,11%
10: 8,33%
11: 5,56%
12: 2,78%

The Action dice (D12) is taken into account by saying: how do I reach, say, TN 18 with every one of the probabilities shown above by adding to them the roll of a D12?

Well, with results from 2 (2.78%) to 7 (16.67%), your only possibility is to roll a Gandalf (automatic success), which is 8.33% (1/12). With a result of 8, you have to roll Gandalf or 10 (16.67%, or 2/12). With a result of 9, you have to roll G, 10, or 9 (25%, or 3/12)... and so on.

So the probability of obtaining 18 is P = 8.33% x (2.78% + 5.56% + 8.33% + 11.11% +13.89% + 16.67%) + 16.67% x (13.89%) + 25% x (11.11%) + ... = 16.44%

So you don't need to think about the mean values (Gandalf results cannot be taken into account to calculate mean values), you just use the probabilities of success, which are perfectly accurate.

Put this in a spreadsheet and you can quickly calculate the probability of success for every TN, and for every number of dices.

BTW I wasn't offended by your abruptness as I recognise that English is not many peoples first language here and make allowances for incorrect or uncertain phrasing.

It sounded more rough as I intended it to be, and I'm sorry for that. So thanks for your understanding, I really didn't want to offend and I'm glad this wasn't the case.

[zedturtle]

It is no particular trouble. Just will take a little while to get to the computer, extend the range and the watch it work. (It's a brute force Monte Carlo program, I think it does 10 million rolls for each permutation; I know for sure it takes a bit of time to run.)

[Glorelendil]

The other thing that needs to be borne in mind is the consequences of failure. Saying, "You have an 80% chance of success!" sounds good, but "You have a 20% chance of X" isn't so great if X = Death.

[Indur Dawndeath]

Michebugio
By the way, the calculations I made are the following:

That looks correct, but at some point you need that Tengwar, otherwise you need to roll every round and that greatly reduces your chance of success.

[Glorelendil]

Michebugio
By the way, the calculations I made are the following:

That looks correct, but at some point you need that Tengwar, otherwise you need to roll every round and that greatly reduces your chance of success.

Yes I think this is a totally fair point.

My math skills break down at this level so I can't derive the probability, but I could write a few lines of code to generate an approximation by dice and rounds. I.e., "with 3 dice after 4 rounds your chances are...." Will see if I can do that later tonight.

[Michebugio]

That looks correct, but at some point you need that Tengwar, otherwise you need to roll every round and that greatly reduces your chance of success.

Actually the chance of success is always the same each round (no matter how many successful rolls you already scored), unless your statement is "before any roll is made, you have less chances to succeed X times in a row than just one time", which would be correct... but this isn't the place for a probability dissertation, I guess

My problem with doubling the attribute is that in Rivendell it is made pretty clear that the TN for all Fear tests against the Witch King is TN18. If you double that, then the free people are facing TN34 when all Nazgûl are together. TN26 for the Witch King +8 for all the rest.
Try to beat that Aragorn on weathertop... Or perhaps that was not all nine

Well, the only consequence would have been that he couldn't spend Hope for that combat scene, which shouldn't be a terrible hindrance for such an experienced Ranger, except in the most dire circumstances.

[Indur Dawndeath]

The other thing that needs to be borne in mind is the consequences of failure. Saying, "You have an 80% chance of success!" sounds good, but "You have a 20% chance of X" isn't so great if X = Death.

The result is not instant death, but it is pretty bad. 1 Hate and you are Weary, and after that I (a Nazgûl) would hit you with Black breath every round

[Glorelendil]

That looks correct, but at some point you need that Tengwar, otherwise you need to roll every round and that greatly reduces your chance of success.

Actually the chance of success is always the same each round (no matter how many successful rolls you already scored), unless your statement is "before any roll is made, you have less chances to succeed X times in a row than just one time", which would be correct... but this isn't the place for a probability dissertation, I guess

I think his point was that the odds on any one round stay the same, but the cumulative odds change.

[Indur Dawndeath]

That looks correct, but at some point you need that Tengwar, otherwise you need to roll every round and that greatly reduces your chance of success.

Actually the chance of success is always the same each round (no matter how many successful rolls you already scored), unless your statement is "before any roll is made, you have less chances to succeed X times in a row than just one time", which would be correct... but this isn't the place for a probability dissertation, I guess

I think his point was that the odds on any one round stay the same, but the cumulative odds change.

Thank you very much Glorelendil.
I think it is relevant to have an idea how difficult it is to avoid being Daunted, because once you fail, you will become Weary the next round. Any Piercing blow at TN18 without any Hope is a difficult task, especially for a Ranger with 2d armour. That is only a 14.59% success chance...

[zedturtle]

Alright, as requested:

Code: Select all

DICE       TN 20     TN 22     TN 24     TN 26     TN 28     TN 30     TN 32     TN 34
0          -  -  -  -  -  -  -  -  -  -  -  - 8.33 % (GANDALF) -  -  -  -  -  -  -  -  -

1          -  -  -  -  -  -  -  -  -  -  -  - 8.33 % (GANDALF) -  -  -  -  -  -  -  -  -

2          10.64%    8.55% -  -  -  -  -  -  - 8.33 % (GANDALF) -  -  -  -  -  -  
WEARY                                           (same as above)

3          25.66%    16.32%    11.03%    8.90%     8.36% -  - - 8.33 % (GANDALF) -  - -
WEARY      18.05%     12.85%   10.45%             (same as above)

4          50.42%    36.22%    24.39%    16.06%    11.28%    9.15%    8.46%    8.33% 
WEARY      29.69%    21.66%    16.21%    12.09%     9.97%    8.99%    8.46%    8.33%

5          74.37%    61.17%    47.14%    34.00%    23.29%   15.78%   11.40%    9.32% 
WEARY      43.20%    33.52%    25.53%    18.81%    14.42%   11.52%    9.70%    8.90%

6          89.81%    81.53%    70.46%    57.52%    44.17%   32.03%   22.28%   15.50% 
WEARY      56.37%    46.39%    37.06%    28.52%    21.94%   16.81%   13.13%   10.91%