Liner Player, Quadratic DM; Or Why Your DM Says "No"

So I'm sure we've all experienced something like this: the party is sneaking through a dungeon. They hear what sounds like someone walking around on the other side of a door. Players are planning with each other, and Player 1 says, "I want to ready the Sleep spell as soon as Player 2 opens the door!" And then the other two players will chime in, "I want to grapple!" "I'll have my sword ready!" From there, the DM will either allow it, or interrupt and say "You can't ready actions outside of initiative."

Now I'm not going to get into why DMs might allow it, but I know exactly why DMs don't: because it has more implications than you think. There is something in this game called "Surprise." There are no "surprise rounds," but there is a surprise pseudo-condition that heavily penalizes your first turn in combat. Surprise, in 5E, is notoriously difficult to actually get because it's an incredibly powerful thing.

Allowing this "pre-combat round" basically guarantees you're getting a whole round of surprised creatures every single time, and nullifies the whole point of it. From a player perspective, you don't understand why the DM is being so picky about the rules. But from a DM perspective, you already understand how strong players are, and guaranteeing a "surprise round" every single time they want to ready actions before initiative is rolled is only going to make this game even easier. Not to mention, if the DM started "readying actions" outside of combat against the players, I'm sure the party would start to protest.

Similar situations may arise like "Hey DM can I try to climb on top of this barrel and do a plunging attack for advantage on my attack roll?" Sounds pretty harmless, right? In fact it sounds really thematic and cool, and I'd love to say yes. But I can't. As a DM, I've seen the "If you give a mouse a cookie" story play out in D&D several times. You as a player might see an opportunity to do something cool for a little power boost. But as a DM, I see a player who might start a painful adventure of constantly trying to climb on top of things or use thematic descriptions to gain power. "Can I do a kick off the wall for advantage?" "Can I do a 'called shot' to go for his neck?" "Can I do a 'Dark Souls' roll to avoid the opportunity attack?" "Can I stand on the Barbarian's shoulders to get out of melee range?"

A lot of players don't think very far ahead about the mechanical implications of some of the things they may ask for. Players are mos

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Using some deductions from quadratics, metallic ratios, and continued fractions, I came up with this neat little formula. I couldn't find anything online about this; is this well known?
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Does anyone understand this math? These are linear quadratic systems, but I’m not sure how to solve them using substitution.
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Differential Equations and Stellaris: How the new pop growth model reduces long-term population trends from quadratic with time to linear with time

TLDR: The pop growth model in 2.8 ultimately trended towards total pop count being proportional to time squared; the new pop growth model in 3.0 now trends towards total pop count being proportional to time.

Warning: Mathy analysis post! You'll probably need to remember some first-year calculus to fully understand it, though luckily you probably won't need to have taken an actual differential equations class - hell, I've forgotten most of my DE knowledge by now!

This entire post is analyzing very long term trends, where all tech is researched, all planets are colonized, no wars or anything, etc. Ultimately this means we can ignore lower order terms; t^2 >> t >> 1, etc.

First, analysis for 2.8's pop model. Let P stand for the total population count in an empire, C stand for the total number of colonies in the empire, and t for time since game start. Roughly speaking, pop growth per colony per unit time is constant, so total pop growth per unit time is proportional to the total colony count:

(that's a freehand \"is directly proportional to\" symbol, BTW)

Colony count is itself roughly proportional to time (after all planets are colonized, you get more colonies from building habitats and/or ringworlds; since those depend on megastructure capacity and influence income, both of which are constant, the rate you gain colonies is also constant):

https://preview.redd.it/1p1zxpdxob271.png?width=200&format=png&auto=webp&s=dd969e803ee14bcd36a67edc04e35eff78f6e5d4

https://preview.redd.it/shhgdr2zob271.png?width=200&format=png&auto=webp&s=c352722a3ac5f8d1c9dc6f751a9631202cf78099

Since proportionality is transitive, we can plug this back into our previous formula for pop growth:

https://preview.redd.it/z8hj64dpqb271.png?width=200&format=png&auto=webp&s=bd30d9521371ced0a389d97194788702c1a67462

https://preview.redd.it/gugj516qqb271.png?width=200&format=png&auto=webp&s=db110d0c1f3dedc6de9a3eb4d89dca563160a5d4

This explains why pop counts always spiraled out of control; and since no matter how much optimization PDX does, pop calculation time will always be directly proportional to pop count, so pop calculation time also always spiraled out of control.

Now, the same analysis with 3.0's pop growth model. For now, we'll still assume the accumulation of pop growth points

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Quadratics help. How did they go from x^2 + 4x + 4 -> (Γ—+2)^2. What happens??
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I’m aboutta use the BOFA method to solve quadratic equations quicker
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Parsing can become accidentally quadratic because of sscanf github.com/biojppm/rapidy…
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Quadratic equations at the DMV from someone studying in line.
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Success-counting dice pools: quadratic pool size β‰ˆ linear roll-over modifier

Link to the article.

The main takeaways are:

  • It takes a quadratically increasing pool size/target number of successes in a success-counting dice pool to produce a similar effect to a linearly increasing modifier/DC in a roll-over system.
  • Even with the above nonlinear relationships, the corresponding roll-over system still converges to a Gaussian distribution as the pool size increases, albeit more slowly.

Unfortunately, this one is heavier on the math than usual, and the transformation is mostly of analytical value rather than something that I recommend to be used directly.

At some point I will write an overview article that more comprehensively motivates these transformations to roll-over equivalents. The obvious question is why didn't I write that part to begin with. The answer is that I needed to make sure that the math actually worked first, but there are so many different types of dice systems that I didn't want to go through all of them before seeking feedback for the first time. So, thanks for reading even though the presentation isn't in the best order so far.


Apart from that, possible future topics include:

  • Efficient computation of roll-and-keep dice pool probabilities, perhaps most notably (old) Legend of the Five Rings. None of AnyDice ([highest 5 of 10d[explode d10]]; no link because I don't want to direct a bunch of futile requests to the server), Troll, or SnakeEyes can compute this in a reasonable amount of time. This site has probabilities; however, if you look at the source of the webpage, you'll see that a) all the data was precomputed and stored in static arrays, and b) there is noise in the data, indicating that these were generated via Monte Carlo rather than a closed-form method.
  • Even trickier is if the dice pool contains different types of dice, as in e.g. Cortex.
  • How does roll-and-keep compare to keep-highest and success-counting? The obvious guess is that it's somewhere in-between, but is there more that can be usefully said?
  • Two-sided binary outcomes, where a loss has a negative rather than zero effect.
  • Systems with 3-4 possible outcomes, such as *Powered by the Apocal
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[Grade 10 math] this is a quadratic equation. Got question on this part (-3)Β² = -9. I got -9 but why does it turn into positive number on the equation?
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[HELP ME] I’m looking for someone to complete my Grade 11 Quadratic Relations and Trigonometry work, we can negotiate the pay
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Use quadratic formula for best Sosig setting 😎
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Are there Real Life Applications of the Discriminant? (Algebra – Quadratics)

I'm trying to improve as a teacher by relating the mathematical concepts we learn to real life, and I can't for the life of me figure when anyone would ever need to find the discriminant. Does it have any practical use at all? Or is it an observation for observation's sake?

The closest I've found is that it's a "double check" for the number of solutions you end up getting, but the discriminant is the longest and most complex part of the quadratic formula. It seems ridiculous to, at that point, not just compute the rest of the formula, which is almost trivial. In short, if you're going to calculate the discriminant, why not just use the quadratic formula entirely?

Thanks in advance.

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PhD in the quadratic formula.
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Factorization of Quadratic Trinomial of Leading Coefficient one.
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Pulls out quadratic formula to get to the x
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Question about a property of Quadratic functions

I was looking at the function X^2 + 4x = 0

Then I was like β€œI wonder what The X values are, when Y = 2”

Then I got the function X^2 + 4x - 2 = 0 And then I realized the β€œ-2” was the Y intercept. It got me confused, why -2 has to be the intercept when we want to solve for X values?

Why does Y have to equal 0, anyways If we want to solve for X in quadratic equations? Is it just because it’s the easiest way?

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Quadratic equation: the sum of the squares of two consecutive even numbers gives the number 52. What are those numbers?

It must be written in the form of an equation

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Quadratic formula fans, give a cheer !!
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cursed quadratic equation
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help with quadratic question

A parabola has the equation y = (ax + b)(x + c). When x = 5, its graph cuts the x-axis and when y = -10 the graph cuts the y-axis.

Show that y = ax^2 + (2 - 5a)x - 10

Now I know that the quadratic has an x-intercept at (5, 0) and y-intercept at (0, -10).
I rearranged the quadratic to y = ax^2 + (b + ac)x + bc
I tried subbing in the intercepts, and then I got
[1] sub (5, 0): 0 = 25a + (b + ac)5 + bc and
[2] sub (0, -10): -10 = bc

I got stuck here, so I tried eliminating bc by subtracting [2] from [1] and got:
2 = 5a + b +ac

But now I don't know how to solve for b or c, am I meant to continue solving simultaneously or.. ?

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We must not change the quadratic formula at any cost!
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Martial Techniques for quadratic fighters

Scroll down to the dash line if you want to read the traits and not my justification for making them. Despite the name, these features are also meant for barbarians, monks, and rogues.

β€œLinear fighters, quadratic wizards” is a common lament about how classes progress in the late game. Casters not only often have a solution for almost every problem out of combat, they excel in combat with their high-level slots, sometimes while the martial is stuck on the ground totally ineffectual.

And while non-magical classes are far from obsolete, new 5e content from Wizards of the Coast has added lots of magical subclasses, spells, and +X items for casters that can seem to widen an already noticeable gap.

If not all players feel equal, it is the DM’s job to make sure everyone can shine. A full adventuring day is a good way for martial classes to pull their weight, but is also difficult for many DM’s, myself included, to implement. A common solution is to dole out awesome magic items that even the playing field. I don’t disapprove of this, but would like to suggest another type of reward, particularly for non-magical characters. These characters get by on their skill, training, and prowess, and while we all love magic items, I believe many martial-class players would love to receive a reward that emphasizes their characters dedication, rather than just some nifty magic doohickey they’ve found. Enter: Martial Techniques.

These are not meant to be features your players can theory-craft around, they are meant to be rewards the DM chooses from and offers within the narrative. I recommend a period of training with a noteworthy NPC to learn any of these techniques, which gives a different feeling from items, which are bought or found, and boons, which are given by magical/divine beings. These skilled NPCs may require the player to test their mettle somehow before they will agree to train the PC.

A note about design:

The Tabaxi’s β€˜Feline Agility’ has always been one of my favorite racial traits. It’s effect is simple, yet powerful. It doesn’t rely on short or long rest mechanics, and doesn’t have any resources to track. I’ve tried to follow a similar design philosophy when making these Martial Techniques (including ripping Feline Agility’s wording for one.)

I’ve also named the techniques pretty generically, intending for them to be viable on any martial class, but consider renaming them to be more flavorful. If a technique is taught to a player character by a

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Question about the Quadratic Formula

Disclaimer in Sweden we dont actually use the quadratic formula, but its very similar. My question is

Y = 2x^2 + 2

In order to use the formula, we have to divide the equation by 2. But that gives us a completley different graph, but with the same X intercepts. Why do we have to change the graphs in the first place?

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{Solving quadratic equations}{high school maths} which of the following answers is correct x=- 1+square root 5 over 2 or x= -1-square root 5 over 2 please help reddit.com/gallery/njjzdn
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What would be the 6 version of quadrant/quadratic (4)?

Hey guys!
I'm working on this design (architecture related) and initially I had to work on a quadrant of the whole model but now instead of the whole model divided into 4 parts, its now divided into 6 parts, can anyone let me know what will be the correct terminology here, I initially guesses "Hexatic" but I'm not sure.
if you let me know about the 8th and the 12th, that would help as well.

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I need help with quadratics

So, I have a math problem that's puzzled the crap out of me. 8th grade algebra honors. The equasion is this y=2x^2+8x. Were doing parabolas, and the x values were working with are 2, 1, 0, -1, and -2. My problem is that when you graph it, the parabola isn't symmetrical. Am I stupid, what am I doing wrong?

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quadratic sequences

just learn how to solve quadratic sequences and they arnt too complicated once you learn the steps but have no idea why the steps you take work in the first place, first of all once you find the second difference which is linear, why do you halve it and then square n?

i really dont understand why you take the steps you do to work out the second half of the equation, to the point where i dont even know what questions to ask?

if anyone can explain why the steps you take work when working out quadratic sequences.

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Can any degree polynomial be solved? Like quadratic or cubic but for higher powers?

More specifically is there an equation to solve n degree polynomials? Is it even possible to have a equation like that? I’m sure this has been asked before but I’m not sure what to search for, and all I see on google is basic algebra help.

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Quadratic effect of Agility on DPS visualized
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Can anyone please help me solve this? I have to write the quadratic in Vertex Form
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(March 2021 QasQ14 Calculator section) Greetings everyone! Is there a way to solve this by modeling a quadratic equation? I think I encountered a similar problem and we used the vertex form of the quadratic equation to solve for the maximum value of y. What would the vertex equation be in that case?
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Quadratics x-x Need some help getting started

A soccer ball is kicked and follows a parabolic path. It lands 100 meters from starting position. The ball reached a max height of 25m.

-What is the equation of the flight of the ball?

-What is the axis of symmetry?

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Bungie apparently just disabled all special characters from display names, so I can't be the quadratic formula anymore. My disappointment is immeasurable and my day is ruined. Please someone tell me this was an accident. It just happened today.
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Quadratic Residue Problem

Dear all,

I am looking at the quadratic residuosity problem and I am wondering if the problem of factorization can be reduced to this problem.

In the book "Handbook of Applied Cryptography" by A. Menezes et al there is a section about this problem. They claim it is a difficult problem and that it can be reduced to factoring. However, for the other reduction I only found the following paper:

Jager, T., & Schwenk, J. (2008). The Generic Hardness of Subset Membership Problems under the Factoring Assumption. Retrieved from http://eprint.iacr.org/2008/482

However, the authors only consider straight line programs. Any nice reference is welcome.

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You think the quadratic equation is difficult to put in a rap? Hold my (apple juice).
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Greatest US Quadratic Achievments
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Can someone help with the quadratic formula?
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How many types of equations are there? (linear, quadratic...)
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