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... keep reading on reddit ➡
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:
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):
Since proportionality is transitive, we can plug this back into our previous formula for pop growth:
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... keep reading on reddit ➡
The main takeaways are:
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:
[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.
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.
I was looking at the function X^2 + 4x = 0
Then I was like “I wonder what The X values are, when Y = 2”
Then I got the function X^2 + 4x - 2 = 0 And then I realized the “-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?
It must be written in the form of an equation
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
 sub (5, 0): 0 = 25a + (b + ac)5 + bc and
 sub (0, -10): -10 = bc
I got stuck here, so I tried eliminating bc by subtracting  from  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.. ?
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.
“Linear 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 ‘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... keep reading on reddit ➡
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?
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.
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?
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.
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.
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?
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.