- Location
- The Star Kingdom of Manticore
Inserted tally
Forge of Destiny(Xianxia Quest)
- Thread starter yrsillar
- Start date
- Original Fantasy
DeAnno
Sometimes words have two meanings
So a separate thing, which doesn't even matter probably because it's mechanics, is that 4 dice (and dice in general) are a lot better than people give them credit for, and rerolls are a lot worse as anything but insurance.
Let's assume we have exactly one important check we want to do well in. Let's assume we will use our reroll to maximize our result: if we roll under average, we use the reroll. If we roll same or over, we don't. How many dice do you think need to be in our pool before the reroll is better than four dice, in terms of mean results? I want everyone to guess.
Let's assume we have exactly one important check we want to do well in. Let's assume we will use our reroll to maximize our result: if we roll under average, we use the reroll. If we roll same or over, we don't. How many dice do you think need to be in our pool before the reroll is better than four dice, in terms of mean results? I want everyone to guess.
The answer is intuitively surprising. Your dice pool must be sixty-seven dice before either bonus if the reroll is better in this situation than the 4 die bonus. Dice are strong. This system has low variance. This system is not d20 or d100, where rerolls are stronger because the distribution is flat and not normalized.
If mathy people are surprised by this, they shouldn't be. A reroll basically moves you to the 62.5%tile on a distribution. If you look it up on a normal table, thats about +0.32 z scores. The standard deviation of one of these rolls is about 0.5*SQRT(N). With N=67, 0.5*SQRT(67)*0.32 = 1.3. Coincidentally 0.4*4=1.6. It's a very believable result.
In this system rerolls are not really for fishing to be randomly better at things in general. They are pretty specifically for fixing disasters that come as the result of terrible rolls.
If mathy people are surprised by this, they shouldn't be. A reroll basically moves you to the 62.5%tile on a distribution. If you look it up on a normal table, thats about +0.32 z scores. The standard deviation of one of these rolls is about 0.5*SQRT(N). With N=67, 0.5*SQRT(67)*0.32 = 1.3. Coincidentally 0.4*4=1.6. It's a very believable result.
In this system rerolls are not really for fishing to be randomly better at things in general. They are pretty specifically for fixing disasters that come as the result of terrible rolls.
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This is doing things wrong. Total dice pool is irrelevant. What matters is your dice vs the test dc or your dice vs the enemy dice.
To put things another way: say we have an opposed roll. If dice pools are equal then we have ~44% odds of winning the clash (assuming defender wins on draw), or 66% odds of losing.
A reroll means our odds of losing are now .66x.66 =44% - a significant gain.
Going up to +4 dice advantage reduces our odds of losing to 38%. This is slightly better.
For the clashes that they both apply to, +4 dice is slightly stronger. The reroll is broader in application, but can only be eused once a scene. Don't know about how Test DC play out.
I'm not sure where you are getting this. By my calculation, the z score benefit for gaining reroll of a normal distribution is +1/sqrt(2*pi), or numerically, about +.40. Basically, 50% of the time (when your first roll is sub-average), you gain E(X) in expectation where X is the half-normal distribution. E(X) evaluates to exactly sqrt(2)/sqrt(pi) sigma (source). Thus, in total you gain 1/sqrt(2*pi) sigmas of expectancy.
Arkeus
Crazy cat guy
- Location
- France
Again, we aren't voting for mechanical reasons... and I don't think anyone said rerolls were good for hard checks, but rather they are good in order to dimnish outlier roll pain. Perception tests are a pain because failing them can have significant consequences after all.
Anyway, the difference between the vote is not 'dice vs rerolls', it's "being better at something vs helping our loved one not being bad at something". It's not just about Ling Qi. If, say, we keep Zhengui in the future (which I think we all want) this means Zhengui also has a reroll. Obviously I prefer thinking about our loved ones when we are at home and the domain is dozen of kilometres, but even if we insist on only thinking about immediate things like "Ma Jun uses Diapson against Ling Qi and Zhengui", well, zhengui could have his reroll to make sure he doesn't fail the diapason test.
Another obvious example is when we got the Argent Vent, and Su Ling/Suyin/Ling Qi all failed their perception tests to detect Huang Da, so all three of us would have had a reroll if we loved them more.
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It shouldn't. The benefit of +4 dice depend on how many dice are in the opposed roll. If both sides are tossing a million dice, +4 to the result on either side won't matter, much less +4 dice. If both sides are tossing one die, then you chance of losing or tying goes down to almost nothing. So you need to specify what your baseline is before you can actually get numbers out of the scenario.
DeAnno
Sometimes words have two meanings
My guess was the first distribution you roll would be from 50-100 and center on 75 since you discard the first half of it. I was then averaging that with the 50% likely second roll centering on 50. But that's a pretty sloppy method, and that was just to justify the result anyway. Your 0.4z is probably more accurate and will be closer to the result I got by brute forcing the binomial theorem sums.
EDIT fixing double:
This just isn't true. Your total dice pool determines the standard deviation of your roll, it's about 0.5*SQRT(N). If both sides have more dice then differences in dice pools matter less, scaling with the root of the pool size. +4 dice at dice pools of 50 means about twice as much statistically as +4 dice at dice pools of 200.
Part of the tone this page, and some earlier comments, were taking was "+4 dice is barely anything, surely the reroll is much better and the +4 dice will be even more trash with time. Even against Illusions the reroll will just be better!" I was getting the impression people thought the cutoff point was around 20-30 dice and not 67. The +4 dice is a much stronger bonus when it applies right now. I'm not sure how low the Test DC would have to be compared to our small dice pool against Illusions for a reroll to be better tha +4 dice now but it would be something hilariously small and unlikely.
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I have still some hope.
[X] Internalize Argent Mirror
-[X] Ling Qi and allies of at least four dots positive relation within one hundred meters may reroll a failed perception test once per combat or scene.
I just want our domain to be cohesive and to help our friends.
[X] Internalize Argent Mirror
-[X] Ling Qi and allies of at least four dots positive relation within one hundred meters may reroll a failed perception test once per combat or scene.
I just want our domain to be cohesive and to help our friends.
- Location
- The Star Kingdom of Manticore
[X] Internalize Argent Mirror
-[X] Ling Qi and allies of at least four dots positive relation within one hundred meters may reroll a failed perception test once per combat or scene.
-[X] Ling Qi and allies of at least four dots positive relation within one hundred meters may reroll a failed perception test once per combat or scene.
DeAnno
Sometimes words have two meanings
As an orthogonal note to this, I think it's probably true that you can vote for a subvote while still counting towards a different main vote if the tally is by line and not by block. Maybe that should be tallying policy for votes like this so you can still steer a main vote you don't want without having to keep switching around?
Ie:
[X] Discard this realization
-[X] Ling Qi receives a four die bonus when attempting to discern lies or see through illusions.
Ie:
[X] Discard this realization
-[X] Ling Qi receives a four die bonus when attempting to discern lies or see through illusions.
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Arkeus
Crazy cat guy
- Location
- France
Not that low or unlikely? PLR Test is 7DC. Our own Perception for PLR would be Wits 5 + Composure 5 + Passives 18 (AM 10, AE 5, EPC 3) = 28 dice, without tech, for a 7DC test. Which means we would have 95.85% chance to make that test if my anydice is not wrong. With 32 dice, we would have 99.09%. However, with a reroll we would have 99.90% chance to make it.
And yes, there is a reason I have been rolling my eyes at the PLR test mechanic.
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DeAnno
Sometimes words have two meanings
To be fair, not everyone is going to have AM with its anti-illusion spec or EPC with its perception focus inside a cultivation Art, forming +8 of dice bonuses we have above and beyond "baseline" passives. I am a little surprised that it's already better by then, but still, we're talking the realm of 1% failure chances.
The first round is 8 prelims that each take place in large square arenas (I think 200 x 200 meters?) All the tourney competitors in all the Outer Sect years, of which we expect to be about 200 total and 25 per prelim, are dumped into these 8 matches. It isn't random though, the Elders muck around with the prelims for various reasons including excitement, politics, kicks, and also sometimes some semblance of fairness. Of each prelim, the final two students standing are the winners and advance to the singles matches.
We don't know much about the actual way the singles tourney is setup, but most people assume it is a single elim tourney where winning your first match qualifies you for the Inner Sect. The brackets here are also heavily rigged in the same manner as they are for the prelims.
Some cursory analysis of the political situation suggests that CRX will be in one half of the singles bracket, with GG, Ling Qi, Bai Meizhen, and Sun Liling all in the other half for various reasons. It's also very likely that one quarter in there has LQ and Sun and the other has GG and Bai.
In addition to the 8 tourney winners that get to go to Inner, there's a separate production track for non-combat types that will admit another 8. There is also rarely an extra student from these 16 let in specifically by the Elders for random reasons.
My opinion diverges somewhat in that if there's even a 5% chance that Ling Qi could beat one of the monsters, and there may well be, then the Elders could be hesitant to put her in the same bracket as Sun Liling and Bai Meizhen, since their fight among the final 4 is an obvious draw they probably don't want to risk not happening. Cai could go up against her own subordinate, but obviously not at the final 16 or even probably at the final 8 stage. This could mean fighting GG at the final 8.
Ultimately though, we just don't have the info to know for sure. High nobles and the Monsters especially are probably going to be fed weaklings for their first matches, but who know past that.
Ultimately though, we just don't have the info to know for sure. High nobles and the Monsters especially are probably going to be fed weaklings for their first matches, but who know past that.
*Snek wriggle*
- Location
- Six feet under
Regarding the "4 extra dice vs. reroll" debate, I think there are two different scenarios that people are making valid arguments about.
One is when the perception test is against a test dc. In this case, unless the test is crazy then we only need to worry about outliers, and therefore the reroll is already significantly better than the 4 extra dice.
The other case is where we face off against an enemy's dice pool. @DeAnno I think your math was based off of just maximizing our number of successes, which fits better to this scenario, specifically when our enemy has a similarly-sized dice pool. In that case, I agree with most of your math, but based on what I did it actually takes quite a bit more than N=67 dice to reach parity. I got an answer of 95 dice... but 67 or 95 dice, that's quite a lot. Here is my work, if anyone is interested:
Lastly, as a couple of people have pointed out, the reroll ALSO affects nearby allies... which in my opinion should easily tip the balance in favor of the reroll over the extra dice.
One is when the perception test is against a test dc. In this case, unless the test is crazy then we only need to worry about outliers, and therefore the reroll is already significantly better than the 4 extra dice.
The other case is where we face off against an enemy's dice pool. @DeAnno I think your math was based off of just maximizing our number of successes, which fits better to this scenario, specifically when our enemy has a similarly-sized dice pool. In that case, I agree with most of your math, but based on what I did it actually takes quite a bit more than N=67 dice to reach parity. I got an answer of 95 dice... but 67 or 95 dice, that's quite a lot. Here is my work, if anyone is interested:
Lastly, as a couple of people have pointed out, the reroll ALSO affects nearby allies... which in my opinion should easily tip the balance in favor of the reroll over the extra dice.
it would tip the balance more if it would actually effect most of the people we work with.
Right now, it only affects two people, one of which we aren't going to see a ton of after today.
People keep saying this, but it's just not true. Positive 4-dot relationships are not friends, and they're not allies. That's 3 and 2 dots respectively(there was a little blending between the two in the specific examples in quest, but that is semantics) 4- dot relationships are lovers or heterosexual life partners or favored kids. I fully expect that the only 4 dots that see combat with us are Zhengui or other bound spirit beasts that can recover/not die from mortal injuries, not just because these relationships are hard to form and maintain but because the fundamental nature of this sort of relationship is that we don't want these people to get hurt if we can at all help it. Yes, this specific example is for a perception check that doesn't necessarily occur mid-combat, but most perception checks we've seen have either been part of combat or as a prelude to combat.
Zhengui is also at 4 dots right now.
- Pronouns
- They/It
[X] Internalize Argent Mirror
-[X] Ling Qi receives a four die bonus when attempting to discern lies or see through illusions.
I'm always a fan of More Dice!!! Also the base lesson seems neat.
-[X] Ling Qi receives a four die bonus when attempting to discern lies or see through illusions.
I'm always a fan of More Dice!!! Also the base lesson seems neat.