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jthurn
Posts: 165
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Re: TN16: A in depth computer simulation. How Miserable and Weary affect probability

Fri 23 Jul 2021, 18:58

He's not sending a satellite to Mars, after all...
MIDDLE EARTH IS MORE IMPORTANT THAN MARS!
Someone had to say it.
 
Elenath
Posts: 31
Joined: Sun 18 Jul 2021, 00:22

Re: TN16: A in depth computer simulation. How Miserable and Weary affect probability

Sat 24 Jul 2021, 01:41

Dorjcal, I what to say thank you again. Your posts are more that good enough for my needs.
 
hsi379
Posts: 8
Joined: Fri 10 Sep 2021, 19:24

Re: TN16: A in depth computer simulation. How Miserable and Weary affect probability

Mon 13 Sep 2021, 08:51


Let me know what do you think about of this probabilities, and you are welcome to request other tables!
Since this seems to be the math thread -- I have a request.

Has anyone ran a 3, 6, and 9 resistance skill endeavor / council? I believe it works -- at least 3 succeses in 3 rolls, 6 success in 6 rolls, etc. Gandalf is auto success and each Tengwar adds an extra success.

Would love to see the charts for TN 14 and 16?

How does it change if you add a roll (e.g., from introduction)? So say 6 succeses in 7 rolls at TN 14?

Thanks!
 
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eternalsage
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Re: TN16: A in depth computer simulation. How Miserable and Weary affect probability

Tue 14 Sep 2021, 01:02

That would be good info, I think. Either methodology is fine by me, but I don't want to reignite a flame war over it.
“It is useless to meet revenge with revenge; it will heal nothing.” - Frodo Baggins, Return of the King
 
hsi379
Posts: 8
Joined: Fri 10 Sep 2021, 19:24

Re: TN16: A in depth computer simulation. How Miserable and Weary affect probability

Wed 15 Sep 2021, 02:05

Ok, since no one has taken me up on it yet, I went ahead and learned some python.

Big alert – I am not a coder and did this with 1 hr of python knowledge so I may have screwed it up! It would be great if someone could confirm or deny.
I used aramis’ and Dorjcal’s percentages for a single roll of a dice pool so I was limited in what I could do.

For 3S and TN16 I get a chance of success of (>= the resistance):
3 resistance = 52.3%
6 resistance = 47.7%
9 resistance = 44.6%

For 4S and TN16 I get:
3 resistance = 83.3%
6 resistance = 88.1%
9 resistance = 91.5%

And finally TN13 at 2S dice from Dorjcal post:
3 resistance = 37%
6 resistance = 26%
9 resistance = 19%

IF, and a big IF these are correct there are a number of very interesting implications:
• Because of bonus success from Tengwars, dice pool seems way more important than TN
• As you get higher dice pools, it may actually be easier to do a 9 resistance challenge than a 3 resistance challenge (more chances for extra success)!
• in general, success rates are very low for 2S pools and very high for 4S +.

Again – I am not 100% confident this is correct. I am hoping this gives someone the impetus to check my work or do it themselves.

Thanks.

Python code below:

Here’s the code for 9 resistance, using the weights from aramis’s post for 3S dice and TN 16 since it goes beyond 2 Tengwars:
***
import random
count=0
for i in range (1000000):
numberList = [0, 1, 2, 3, 4]
mylist= (random.choices(numberList, weights=(45.833, 24.306, 23.148 , 6.25, 0.463), k=9))
if sum(mylist) > 8:
count = count +1
print (count/1000000)

***

4S and TN16
****
import random
count=0
for i in range (1000000):
numberList = [0, 1, 2, 3, 4, 5]
mylist= (random.choices(numberList, weights=(21.599, 31.797, 33.565 , 11.42, 1.543, 0.077), k=9))
if sum(mylist) > 8:
count = count +1
print (count/1000000)


2s and TN 13 using Dorjacal numbers:
***
Import random
count=0
for i in range (1000000):
numberList = [0, 1, 2, 3]
mylist= (random.choices(numberList, weights=(50.04, 31.3, 16.16 , 2.5), k=9))
if sum(mylist) > 8:
count = count +1
print (count/1000000)

**
 
Dunheved
Posts: 164
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Location: UK

Re: TN16: A in depth computer simulation. How Miserable and Weary affect probability

Wed 15 Sep 2021, 09:26

I know absolutely ZERO about such coding, and am going to sound pathetically ignorant here ("Not for the last time!"). However, am I right in thinking that your mini program runs the odds many times - a millon? - and reports the % of Successes, and so your numbers might fractionally change if they were run again? Assuming that is broadly what it means, then it is an interesting set of numbers and with the numbers used, your conclusions seem valid. Well done & Thanks.

Implication: So, if each PC gets one relevant Council related skill up to level 4, such events should be easy to do almost every time (80 to 90% or so).

Q. I presume that if you had one or two elves in the mix you can always throw in a couple of magical successes if it looks like things are going to go awry? In this case, any elf can of course get away with even having a Zero skill level! I don't know how difficult it would be to model the effect of having a free Elf Success whenever you needed it, as you would only use the magical result after other rolls that had already failed: adding in a Magical Result would NOT be a random choice. Already I can see a can of worms opening....
 
hsi379
Posts: 8
Joined: Fri 10 Sep 2021, 19:24

Re: TN16: A in depth computer simulation. How Miserable and Weary affect probability

Wed 15 Sep 2021, 20:06

I know absolutely ZERO about such coding, and am going to sound pathetically ignorant here ("Not for the last time!"). However, am I right in thinking that your mini program runs the odds many times - a millon? - and reports the % of Successes, and so your numbers might fractionally change if they were run again? Assuming that is broadly what it means, then it is an interesting set of numbers and with the numbers used, your conclusions seem valid. Well done & Thanks.

Implication: So, if each PC gets one relevant Council related skill up to level 4, such events should be easy to do almost every time (80 to 90% or so).

Q. I presume that if you had one or two elves in the mix you can always throw in a couple of magical successes if it looks like things are going to go awry?
Yes, it is a simulation so it is not exact. I don't think it should be off by more than a few tenths of a percent however (if the code is correct).

You are also correct in that it does not take into consideration ways to improve your situation:
1) favored, hope, inspirations -- note hope and inspiration hope can be huge in this case because of the potential for extra successes
2) for councils, successful introductions can easily add 1-2 additional rolls (more for higher die pools)
3) other virtues and such
4) in councils -- whether the audience is reluctant, open, and friendly -- getting an extra die on EACH roll or losing a die on each roll can be huge. This is a chance at a little strategy -- appealing to the right people, if different people in a group have different attitudes

This seems to make the lower percentage for say 3S at TN16 seem not too bad, since the party can swing things in their favor by a good introduction and hope use. I do worry at the higher end 4S+ that they might be way too easy. Not sure about the 2S end -- you have to spend hope on every roll I think to get to decent numbers. Hard to fully make conclusions without a full set of tables which I don't think I'm proficient to do.

Here's some odds for success with 3S TN16 and a good introduction roll:

For 3S and TN16 I get a chance of success of (>= the resistance), with tries = resistance (failure on introduction -- happens 46% of the time)
3 resistance = 52.3%
6 resistance = 47.7%
9 resistance = 44.6%

For 3S and TN16 with +1 to length (so 3 succeses in 4 tries, 6 successes in 7 tries, etc.) - happens 24% of the time
3 resistance = 69.9%
6 resistance = 61.5%
9 resistance = 56.4%

For 3S and TN16 with +2 to length -- happens 23% of the time
3 resistance = 81.8%
6 resistance = 72.9%
9 resistance = 66.9%

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