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12:25 AM
@Xirema "Negative probabilities"... wat?
 
 
1 hour later…
1:34 AM
@Himitsu_no_Yami SSSshhhhhhhhhhhhhhhhh.
You didn't see anything.
 
 
15 hours later…
4:07 PM
I did though and I want to know what I'm seeing
 
@Himitsu_no_Yami Non-trolly answer: it was a bug in my code. The code that just converts an average into a roll has to basically construct the probability map by hand, and it had an error that caused it to misbehave when dealing with negative numbers.
 
@Xirema In plain English please?
or rather than plain English, how about an ELI5
 
The table that I keep spitting out is a "probability map", it just stores A) the outcome of a roll, and B) the odds of that outcome.

So like for a 2d6 roll, the outcomes are 2,3,4,5,6,7,8,9,10,11,12, and each outcome has, respectively, odds of 1/36, 1/18, 1/12, 1/9, 5/36, 1/6, 5/36, 1/9, 1/12, 1/18, 1/36.
Normally, to get that map I take elementary dice (d6's, d8's, etc.) and smash them together using some math.
But for stuff like "describe a roll that has an average of 14.35", it's easier to just manually construct the probability map, instead of trying to find permutations of dice to do it.
(Although maybe I should find a ML solution for figuring that out...?)
Anyways, the way I solved it was by creating a map containing two outcomes, 14 and 15, and giving each of them odds proportioned just right to produce an average of 14.35.
But that number is directly used to calculate the odds of each outcome, so if I supply a negative number, weird things can happen as a result.
I dunno, I can't think of a less mathy way to break it down.
 
4:27 PM
ok if you can't break it down any further then it's probably too much for me lol
 
@Himitsu_no_Yami To be fair, if this approach isn't simple enough, then that's kind of an indictment of my approach, since the whole point of it was to make it easier for people who don't have education in formal mathematics (which technically includes me).
Does the post I linked to make any kind of sense?
 
the first half did but I got a call at work so I had to stop reading
 
@Himitsu_no_Yami Alright, fair enough.
 
two calls and two misdirected cases so far... First we have a woman who wouldn't let me verify her email which we have to do at the start of any call. Second we have a student and we only support school, district and DoE staff so I tell her she needs to talk to her school and she says the school told her to call us... The joys of Pearson State Assessments
That post was making sense... now it's not
 
5:05 PM
Sanity check: Did I misunderstand something in this Q/A or is it really that simple?
 
@Sdjz Your answer is correct, but I would dispute the claim that it really is that simple. ;)
We can mathematically show that things like Advantage, Elven Accuracy, etc. do boost overall damage output, and if that boost were substantial enough, it could offset the gains from having extra attacks.
But I was able to mathematically prove that, at least in this situation, that is not the case.
\begin{array}{|l|r|r|r|r|r|r|r|r|r|r|r|r|}
\hline
\text{Name} & \text{AC 0} & \text{AC 11} & \text{AC 13} & \text{AC 15} & \text{AC 17} & \text{AC 20} & \text{AC 25} & \text{AC 26} & \text{AC 27} & \text{AC 28} & \text{AC 29} & \text{AC 30}\\ \hline
\text{Swift Quiver x4} & 37.891 & 37.891 & 35.010 & 32.043 & 28.935 & 23.879 & 13.934 & 11.653 & 9.258 & 6.741 & 4.097 & 4.097\\ \hline
\text{Greater Invisibility x2} & 20.281 & 20.281 & 20.220 & 19.987 & 19.469 & 17.909 & 12.268 & 10.556 & 8.615 & 6.433 & 3.994 & 3.994\\ \hline
 
Well I mean if you are effectively rolling 3 d20 and a hit happens when the best result is a hit vs just making 3 attacks, it seems that 3 attacks is strictly better or equal for any 3 d20 results. In any situation where at least 1 of the d20 was enough for a hit, the elven accuracy attack hits, but then so does at least 1 of the individual attacks
 
@Sdjz You're forgetting that stuff like Advantage, Elven Accuracy, etc. also increase the odds of rolling a Critical Hit. So if rolling a Critical hit is a great enough boost in damage, that could make the difference.
 
well but if EA is a crit, so is 1 of the attacks
 
That's not usually a substantial factor in normal combat, but if you were up against an opponent whose AC was high enough that only crits were hitting, that would be a very substantial increase in power.
 
5:17 PM
for any array of 3 d20 results, having those be normal attacks is always at least as good as having those be a single EA attack
 
@Sdjz Hmm, that's actually probably true.
 
Unless I am forgetting something I don't think it couldn't. Maybe I need to detail the explanation better though
 
Yeah, you can see for the AC29 results in those stats I dumped, the damage on a regular attack is near-to-but-slightly-greater-than one-third of the damage of an Elven Accuracy attack.
 
it's the same reason that in a void, having 2 attacks is always better than simple advantage
 
@Sdjz Well, unless you're a rogue.
@Sdjz But yes, barring extenuating circumstances, I think that's correct.
 
5:21 PM
sure, other circumstances and such, that's what I meant by "in a void"
I edited the answer, hopefully making it clear
I do like that your answer not only says that it's better, it says by how much :)
 
@Sdjz Fun fact, possibly proving your response: for Swift Quiver (6 d20's) and Greater Invisibility (6 d20's), the odds that either approach deals 0 damage is always equivalent.
You can dig through the detailed stats to see the evidence.
 
I mean I removed one EA attack from each, which shouldn't change things
@Xirema yeah, that makes sense, in both cases, 0 damage just means all rolls are below the target
And since the number of rolled dice is the same, having all rolls be below a certain number is the same in both cases
 
5:39 PM
Yeah.
 

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