What does The Precarious World thought (Researched) actually do?

[WingedDog]

The question is in the topic. :)

[Ash//Fox]

Basically whenever you have a skill check in this game, the outcome is decided by your skills, things that can alter the situation, temporary stat boosts, clothes, etc. and then a 2d6 dice roll.

So for example say you want to quick pull Kim into a hug faster than he can paralyze you with his authority (made up example). The game has decided that this is an Espirte De Corps check and you have a skill level of +3. You're also wearing your Cop Jacket which gives a skill boost of +2. You're also also wearing a friendship bracelet which gives +1. You took some psycidelics so that's a boost of +1. You earlier told the racist lorry driver to ♥♥♥♥ off and backed up Kim so that's +2. The game has given this a difficulty of 30 (impossible)

So that means that the final check is 30 - 7. In other words you have two six sided dice you can roll which has to add up to 23. Impossible. This is were Precarious World comes in.

No matter any of that you can also do what's called a critical success or critical failure. If both of the dice come up as 1 1 then even if without them you would have had enough score to succeed in hugging Kim you'd fail automatically. However, if you roll 6 6 then it doesn't matter if that can't bridge the gap, you still succeed in hugging Kim. There is exactly one time in the game where this doesn't apply, a singular fake dice roll where it's impossible to win.

What Precarious World does is add to the range of critical success and critical failure. So with the thought researched if you had rolled 5 and 6 you'd still count that as a critical success and hug Kim. And if you roll a 1 and 2 then you'd still count that as a critical failure.

[WingedDog]

Thank you for the detailed answer.
I was also thinking about something like this, but I didn't find any confirmation in the game. In red or white checks with this thought equipped, game interface still shows me critical success: double six, and critical failure: double one.

[Gness Erquint]

Sounds a bit like a waste, even if one intends to savescum with it.

die_positions = 6.0 # faces per die
# => 6.0
dice_positions = die_positions ** 2 # Squared
# => 36.0
crit_positions = 1.0 # Only (6 + 6)
# => 1.0
precarious_crit_positions = 3.0 # (6 + 6), (6 + 5), (5 + 6)
# => 3.0
crit_chance = crit_positions / dice_positions
# => 0.027777777777777776
precarious_crit_chance = precarious_crit_positions / dice_positions
# => 0.08333333333333333
crit_chance_delta = precarious_crit_chance - crit_chance
# => 0.05555555555555555
frequency_factor = precarious_crit_chance / crit_chance # n times as probable
# => 3.0

Takes you from ~2.8% (1/36) to 8.3% (3/36) by an additive ~5.6% (2/36) increase.
In other words, you go from probability of one crit per 36 to one per 12 rolls.
Crits become 3 times as likely.

It would scale much better if you could raise the roll floor somehow, i. e. if those secret bonuses you get guaranteed your roll to be above their sum or something like that.

[Gness Erquint]

However, if the game doesn't actually simulate individual dice and instead just spits a number from 2 to 12, then…

rng_floor = 2.0 # (1 + 1)
# => 2.0
rng_ceiling = 12.0 # (6 + 6)
# => 12.0
rng_range = rng_ceiling - rng_floor # Offsetting for simplicity
# => 10.0
crit_numbers = 1.0 # 10 (12)
# => 1.0
precarious_crit_numbers = 2.0 # 9, 10 (11, 12)
# => 2.0
crit_chance = crit_numbers / rng_range
# => 0.1
precarious_crit_chance = precarious_crit_numbers / rng_range
# => 0.2
crit_chance_delta = precarious_crit_chance - crit_chance
# => 0.1
frequency_factor = precarious_crit_chance / crit_chance # n times as probable
# => 2.0

Rather takes you from 10% (1/10) to 20% (2/10) by an additive 10% (1/10) increase.
In other words, you go from probability of one crit per 10 to one per 5 rolls.
Crits become 2 times as likely.

Hrm. Which is it..? Could crack the game open in a disassembler to check but not feeling it for now.
Could also do statistical analysis, see how close I get to a crit per every 5 rolls.

[WingedDog]

Well, I finished the game two months ago, but still thanks! :)
I'm sure it would be useful for people with the same question in the future.

[Gness Erquint]

That's the intention. 😉

[Gness Erquint]

As inaccurate as statistical analysis can be on finite sample sets, I've made 100 rolls here.

Method:
I chose to use the ice-cream machine with Kim's standard crowbar, since , even though its outcomes are rigged, dicerolls are unaffected and that's all we care about. That way I'm able to filter all of the non-critical successes to be sure.
Precarious World thought is solved in the thought cabinet.
Made a quicksave and kept rolling, noting down the roll result and reloading the quicksave.
When it comes to what's to be considered a crit: (1 + 1), (1 + 2), (2 + 1), (5 + 6), (6 + 5), (6 + 6).
More on crits later.

Legend:
f: Failure.
s: Success. (None as per method.)
cf: Critical failure.
cs: Critical success.

f, f, f, f, f, f, f, f, f, f, f, f, cs, f, f, f, cf, f, f, f, f, f, f, f, f, f, f, f, cf, f, f, f, f, f, f, cf, f, f, cf, f, f, f, f, f, f, f, f, f, f, f, f, f, f, f, f, cf, f, f, f, f, f, f, cf, f, f, cf, f, f, f, f, cf, f, f, f, f, f, f, f, f, f, f, f, f, f, f, f, f, f, cf, f, f, f, f, cs, cs, f, f, f, f, f.

Yes, I got 2 critical successes in a row by the end there.
Longest streak of failures: 80.
Longest streak of non-crits: 17.

No need to append numbers with a tilde here on out, since none of them can be precise.

That's 12 crits out of 100 rolls — 12%.
Gives a probability of one crit per 8 rolls.
Among which success and failure should in theory be equally likely, yet no such luck:

3 critical successes out of 100 rolls — 3%.
Gives a probability of one critical success per 33 rolls.

9 critical failures out of 100 rolls — 9%.
Gives a probability of one critical failure per 11 rolls.

Conclusions:
These rough results are inconclusive but lean closer to the first case, i. e. the game simulates dice individually and pickings are quite slim. I'd like to think the game does.

Is it worth it? There can't be a concrete answer. You have to decide for yourself.
But I'm quite skeptical after encountering an unbroken streak of 80 failures in a row.
And in this particular test session, it ended up doing thrice more harm than good, guaranteeing failure where I could succeed if it was, say, a 50% challenge. But that's just my rotten luck. Sample set size is never big enough for statistical analysis.

If somebody is reading this before they decide whether to internalize the thought: perhaps save yourself a world of pain that the "problem" phase of it entails and a skillpoint it will take to get rid of it when you have better thoughts to take its place in your cabinet.

Originally posted by WingedDog:

game interface still shows me critical success: double six, and critical failure: double one.

I wanted to check if this is a bug still present in the game.

Turns out not as stated by @WingedDog, no.
Critical successes do come in more variety than (6 + 6) with Precarious World.

But there is a similar bug: in the roll breakdown popup on hovering, it only adds green "Critical Success" text at the bottom for (6 + 6), although you still experience a critical success outcome even without that label. I assume it's the same deal for critical failure.

https://i.imgur.com/zDFEF5e.png (6 + 5)
https://i.imgur.com/HyEjSSd.png (Popup.)

https://i.imgur.com/vHT2ogn.png (6 + 6)
https://i.imgur.com/e5nN2gD.png (Popup with "Critical Success" stated.)

https://i.imgur.com/DpwB7hX.png (6 + 5) [Again.]
https://i.imgur.com/tPPyYGy.png (Popup)

[mupheminsani]

Originally posted by Gness Erquint:

If somebody is reading this before they decide whether to internalize the thought: perhaps save yourself a world of pain that the "problem" phase of it entails and a skillpoint it will take to get rid of it when you have better thoughts to take its place in your cabinet.

Thank you so much for your detailed analysis Gness, I am that somebody and I appreciate this!

[Dante]

Originally posted by Gness Erquint:

As inaccurate as statistical analysis can be on finite sample sets, I've made 100 rolls here.

First I would like to thank you for this huge effort! It is impressive.
And I also have a question, you (or others in this thread) might know the answer: Is there a way to force fail any of the white checks?

[Gness Erquint]

It's been some time and I'm hardly able to remember the mechanics intricacies in regards to forcing a failure on a white check.
Not even quite sure what you mean by "force" there. Is it something that banal savescumming won't be able to accomplish eventually?
🤔Oh, maybe it's for when you have too many bonuses already to prevent it from failing. In that case, a critical failure ignores bonuses, IIRC. But if you need a normal non-crit failure specifically — might be out of luck there.

[Dante]

Originally posted by Gness Erquint:

🤔Oh, maybe it's for when you have too many bonuses already to prevent it from failing. In that case, a critical failure ignores bonuses, IIRC. But if you need a normal non-crit failure specifically — might be out of luck there.

That's basically the case. Bonuses are becoming strong obstacles at times. When I say I wish I could "force" a failure I mean like equipping the Precarious World (red checks always fail). But that is impossible.

An easy example: if you do many subquests after the day 3, they will count as bonuses towards the Feld Mural. And the only way to unlock the Speedfreaks quest (and obtaining an unique item), is by failing Shivers twice. So, you can't be high on PHY/Shivers and also must ignore the sunken carriage, the drunks, The Pigs, the filthy jacket, Lillienne and the villagers, morell, the church, even reaching 100% Titus dialogues. Because those things will be factors that may force a White Shivers bonuses, during interaction. Basically you must abstain from very specific stuff, to avoid softlocking other outcomes.

Other idiosyncratic issues are: the order you choose to dialogue with Joyce change some outcomes; Smoker in the balcony must be ignored until day 2 or 3 for optimal dialogue with Sunday Friend; René/Gaston outcomes change depending on which questions you ask first; Plaisance is another filled with contradictions... Cuno, you can mess up the dialogue, but at least you will be aware when there are changes. One of the Hjelmdall books and lots of dialogues regarding the Man of Hjelmdall are only available temporarily (before speaking with both Roy and Cuno). After that, it is impossible to obtain. The book may also be given to Cuno as tribute, if you fail to punch him. Among a huge lot of other stuff that can be impossible to achieve for no apparent reason.