Dorjcal
Topic Author
Posts: 81
Joined: Sun 11 Jul 2021, 10:22

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

Tue 20 Jul 2021, 22:19

I was curious to calculate the probabilities of a roll with TN = 16, and to understand how Weary and Miserable affect the result.

To get some insight I wrote some simple code and run 100k simulations for each roll. This means that the results are close to the actual probability, even though there is still some fluctuation. 12 was counted as automatic success.
(I could have calculated the probability, but I like more a brute force approach to avoid errors)

Regular success table for a TN = 16
Image

Now if a character is Weary, only 4,5,6 are counted on a success die.
Image

As expected Weary starts to have an effect only when 2 or more dice are rolled, and the effect is greater than rolling one die less in regular conditions

Now, let´s have a look on how Miserable affect the results:
Image

If we compare it to the Regular success table, Miserable has a negligible effect, and only when 4 or more dice are rolled

Finally, let´s see how Weary AND Miserable affect the results together:
Image

The effect of Miserable is again almost negligible, unless you are rolling more than 6 dice.

Let me know what do you think about of this probabilities, and you are welcome to request other tables!
 
Mythicos
Posts: 124
Joined: Tue 16 Jun 2020, 03:46

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

Wed 21 Jul 2021, 02:32

Very interesting.

If you're up for it, I'd be curious to see the same tables for TN = 13 and TN = 18, the best and worst case scenarios; that would give us a great feel of how the math works out across the spectrum.
 
Elenath
Posts: 31
Joined: Sun 18 Jul 2021, 00:22

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

Wed 21 Jul 2021, 04:16

Very interesting.

If you're up for it, I'd be curious to see the same tables for TN = 13 and TN = 18, the best and worst case scenarios; that would give us a great feel of how the math works out across the spectrum.
Ditto
 
Themadviolinist
Posts: 57
Joined: Sat 10 Jul 2021, 16:01

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

Wed 21 Jul 2021, 05:06

Isn't the best case TN 11: ranger's Kings of men, a +1 stat, plus prowess a -1tn applied to the strength stat?
 
gyrovague
Posts: 396
Joined: Tue 28 Apr 2020, 16:52

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

Wed 21 Jul 2021, 07:27

Very interesting.

If you're up for it, I'd be curious to see the same tables for TN = 13 and TN = 18, the best and worst case scenarios; that would give us a great feel of how the math works out across the spectrum.
I threw this together for you:
https://codeasart.com/tor/simulator/tor_odds.html

Doesn't count tengwars, though (mostly because the result wouldn't have been very pretty.)

It's "only" doing 50,000 iterations per TN/Dice combo, so you might see some small anomalies in the data.
 
Dorjcal
Topic Author
Posts: 81
Joined: Sun 11 Jul 2021, 10:22

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

Wed 21 Jul 2021, 08:37

Very interesting.

If you're up for it, I'd be curious to see the same tables for TN = 13 and TN = 18, the best and worst case scenarios; that would give us a great feel of how the math works out across the spectrum.

Here it is!

Image
 
Asgo
Posts: 60
Joined: Tue 29 Jun 2021, 12:18

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

Wed 21 Jul 2021, 09:09

interesting
first thanks for running the numbers :)

I think the TN13 case is the most telling actually. While the miss rates on something like TN18/17 might have caused the immediate reaction, I think you just have to look at the *success* rates for TN13 as reason for the chosen scaling.
Basically all skill levels above 3 are just backups in case of complications that deduct dice.
Or to formulate the other way round, with the TN calculation scheme reducing the base TN further makes skill ranks almost pointless for strong attributes.
So being potentially too punishing for early game low stat tests just is a consequence of the chosen TN range, the "change" resolution via dice and the wish to give characters notable progress when investing skill points.
 
baldrick0712
Posts: 291
Joined: Fri 28 May 2021, 12:29

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

Wed 21 Jul 2021, 12:38

It's interesting, if unsurprising, that the "Miserable" condition has such a paltry impact on chance of success. So, gaining Shadow is not such a big deal until it reaches your maximum Hope score (when all rolls become ill-favoured). I suppose being miserable can be played up for its roleplaying aspects though, even if the actual impact is hardly noticeable.

[EDIT] Interestingly again, in 1e, when you were Miserable you suffered a Bout of Madness if you rolled Eye of Sauron on any test. That is significantly more impactful than being Miserable in 2e.
 
Mythicos
Posts: 124
Joined: Tue 16 Jun 2020, 03:46

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

Wed 21 Jul 2021, 14:14

Thank you to both Dorjcal and gyrovague!

interesting
first thanks for running the numbers :)

I think the TN13 case is the most telling actually. While the miss rates on something like TN18/17 might have caused the immediate reaction, I think you just have to look at the *success* rates for TN13 as reason for the chosen scaling.
Basically all skill levels above 3 are just backups in case of complications that deduct dice.
Or to formulate the other way round, with the TN calculation scheme reducing the base TN further makes skill ranks almost pointless for strong attributes.
So being potentially too punishing for early game low stat tests just is a consequence of the chosen TN range, the "change" resolution via dice and the wish to give characters notable progress when investing skill points.

That's been my analysis as well.

With your permission Dorjcal, this is a table that sums up the success % for regular dice rolls (no weary/miserable status):

Success dice % Success (no negative status)
TN 13 TN 16 TN 18
0 8.33 8.28 8.33
1 22.06 9.86 8.32
2 49.96 27.31 16.65
3 76.5 54.22 38.92
4 92.21 78.4 65.16
5 98.25 92.5 84.93
6 99.74 98.05 95.11

People are worrried about beginning characters and their failure rate... And they have a point: most PCs will have a hard time to breach the 50% success threshold unless having very favourable factors (Useful Item, Skill 2-3, Favourable roll...).

Seeing the numbers makes me a little worried about the Success rate at the other end of the spectrum, when PCs have had the time to invest multiple XPs. Keeping things challenging in combat, for example, will mean dropping huge numbers of enemies or fighting very powerful ones.
 
Elenath
Posts: 31
Joined: Sun 18 Jul 2021, 00:22

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

Thu 22 Jul 2021, 04:48

Thank you to both Dorjcal and gyrovague!
Indeed

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