Adding voiced random encounters in Skyrim

I am wondering how I can add random events such as “College Application Denied” and “A Good Death” with the Creation Engine.

https://elderscrolls.fandom.com/wiki/Random_Encounters_(Skyrim)

I looked for tutorials on this, but couldn’t find anything specific. I used the Creation Engine to replace 3d meshes and use them as activators for some small scripts, but beyond that I didn’t do anything.

limit degree distribution in directed configuration random graph

I already know, that the degree distribution in the Erdos-Renyi graph has Poisson distribution in the large limit, and the BA-model is of power law.

Can one say, what the limit degree-distribution is for the directed configuration model? I couldn’t find a clear answer. Or is it not possible to give a general answer, because in the configuration model, the degree of each vertex is pre-defined, rather than having a probability distribution from which the given degree is chosen?

Charts for Random events in battle?

I am looking for a way to give more flavor to my battles, to make them more interesting. You see last session I had my players go attack a military base, the military base was big and most of it was an open terrain, there were only little buildings around where most of the battles took place. They divided themselves in two teams taking out the enemies of each building, a couple of buildings at the time.

During these mini battles I had mini-events, in the first battle in the first couple of buildings, a sandstorm appeared in the battlefield making each characters to only be able to see up to 10Ft in front of them, and that way forcing the players to change their tactics.

In the next area of buildings, the sandstorm already had pass, but now the players not only face regular soldiers, because this time in the middle of battle a Big armored guy with a flamethrower appeared, surprising the players and making a lot of damage to them, of course the players immediately focused all of their next attacks on the big guy and defeat him, but right after that happens the rest of the enemies give up. Discovering that half of these masked soldier were bearly even 17 years old, and so making the players to start to detain enemies in the rest of the base instead of just taking them out.

In the next area they discover the enemy has hostages, so then they start formulate a plan to take these innocent people to safety during the battle.

So this is what I mean with random events in battle, things that can change the dynamic of the battle, things that force the player to change their strategies or even change there initial goal of the battle.

Not long ago I found a chart about random weather, with these chart you could roll a D8 and whatever number you get you got a different weather, number 1 war sunny, number 7 was rainy and stormy, number 5 was Frigid. Then to change the starting weather conditions, you rolled a D6, number 1 was the Tempeture gets warmer, 2 the tempeture get colder, 5 a very strong weather condition happens, like if is snowy a very strong snow storm happen, or if is raining the rain becomes stronger, flooding parts of the town or city, etc.

So I am wandering if there is something like this for battles, where we could roll a dice and get a seemingly random event happing in battle, a change of weather, a new type of enemy, a new weapon in the environment where the battle is taking place that can give eather the players or the enemies the advantage.

I only have around 7 sessions of being a GM and those are the same sessions I have of playing any Tabletop RPG, so that is why i would like to hear from the rest of you if you have something like this, or do these random events in your battles.

I think something like this would be very useful, to plan battle before time and to shake battles while their happening.

For those who want to know, my friends and i are playing a Superhero campaign, using the Fantasy Flight games dice used in the Star wars RPGs and Genesys RPG. But a chart like this could definitely be useful for any RPG system or setting I believe.

Open Problems in Random Graphs

I am a PhD student in mathematics. I’m interested in probabilistic methods in combinatorics and especially random graphs. I am looking for an open problem in this area for my PhD proposal. I know that there are many open problems and conjectures, but I would like to find a “good” problem such that I can get some results during my PhD. It would be very helpful for me if you could suggest a bunch of open problems. Thank you!

Probability that sum of each row is greater than 0 given that sum of each column is greater than 0 for a random matrix

Given a matrix $ W_{n,m}$ whose each entry $ w_{ij}$ is 1 or -1 or 0 with probability $ p$ , $ p$ and $ 1-2p$ respectively, $ 0<p<0.45$

Let $ R_i$ be the sum of $ i^{th}$ row and $ C_{j}$ is the sum of $ j^{th}$ column.

What is the probability that row sums are greater than 0 and column sums are greater than 0, i.e

$ $ P(R_1>0,R_2>0,…,R_n>0,C_1>0,C_2>0,…,C_m>0)$ $

Finding all possible combinations such that row sums and column sums are greater than 0 is not easy. Please help me on how can I proceed, either to find exact probability or upper bound it.

Generating random 6 digit numbers

We can generate a random 6 digit number $ M$ by first generating a random distribution over the 10 digits and then sampling from that distribution.

Formally, let $ x = (x_0, x_1, x_2, \ldots, x_9)$ be a point sampled from the uniform distribution on the unit sphere in 10 dimensions.

Then $ x$ can be used to define a new RV $ D_x$ on the set $ D = [0, 1, 2, \ldots, 9]$ such that $ P[D_x=i] = {x_i}^2$ .

Now consider the RV $ M_{D_x}$ which is defined by first sampling $ D_x$ 6 times (with replacement) to get a set $ \{s_0, s_1, s_2, \ldots, s_5\}$ and then taking the sum $ \sum_{j = 0}^5 10^j s_j$ (that is, use the 6 numbers generated from $ D_x$ as digits of a number between 0 and 999999).

My question is: what is $ P[M = n]$ for $ n$ between 0 and 999999? Is this a uniform distribution over 6 digit integers?

Complexity of generating non-uniform random variates

What can we say about the complexity of generating (negative) binomial and (negative) hypergeometric random variates? In particular, it is possible to generate (negative) binomial and (negative) hypergeometric variates in (expected) constant time (i.e. independent of the distribution parameters)?

There is quite a bunch of literature; however, it’s hard to understand a lot of the papers. Moreover, I found some statements that seem contradictory to me (probably due to wrong understanding).

For example, Stadlober (or similar here) mentions a “generalization [of the ratio-of-uniforms approach] to any unimodal discrete distribution”. The ratio-of-uniforms approach has been called uniformly fast, which is a synonym for constant time, I suppose (?). That would mean that we can generate random variates for each discrete distribution in (expected) constant time.

However, in another paper, I found the following theorem: On a RAM with word size $ w$ , any algorithm sampling a geometric random variate $ Geo(p)$ with parameter $ p \in (0,1)$ needs at least expected runtime $ \Omega(1 + \log(1/p)/w)$ .

Apparently, this means that it is not possible to generate negative binomial variates in time independent of the distribution parameters.

Ad&d 1e new dungeon master question on random encounter chance

Alright im trying to set up a campaign and im not great at math but anyways we play old school 1e ad&d, my question is the 1e DMG states on page 47 for chance of an encounter, it then states base chance of encounter based on these tables that I don’t understand how to, how do you roll for this or what does this even mean, im just being brain dead probably but help a old man out.

so example it gives 1 in 20 roll 3 times for morning, evening, night

so does that mean 1 in 20 means if I roll 1d20 theres only encounter everytime I roll 20 or 1

Like I said bad at math lol. any help would be great thanks.