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Given a pair of fair six-sided dice, pay $1 to throw them, and win $3 for each 5 or 6 in a throw. If I play this game ten times, how much will I gain/lose?

Short article on probability

This looks like maybe a calculus problem, but I know very little of calculus and regression analysis. I have a function of x, f(x) = log(x) / log(0.9) which produces a graph like so: And I get the feeling like there's some point on that curve that represents a sort of balance point. Maybe I...

Was watching this video, supposedly part two of a three-part series, but the author never did get around to making the final part which he advertised as answering the question set up in part one. The question asked "2 defects found in 100 samples; what can we say about the probability of a...

Here's the big three logic gates, that take as inputs a binary 0 or 1: But what if those inputs were free to be any value across the range 0..1? For the sake of example let's say A=2/3 and B=1/4 I can surmise that NOT(A) = 1 - 2/3 = 1/3, and also that NOT(B) = 1 - 1/4 = 3/4 But what of AND and OR?

Alice and Bob each roll 2d6 but Alice gets a +1 bonus to her roll: What is the probability Alice won the toss? I've created a spreadsheet where given Bob's toss I can calculate P(Alice won), P(A>B|B)

I start with a 1-dimensional list of a few random numbers {6, 5, 7, 8, 2, 1, 3, 4} This seems like maximum entropy for a 1D list of numbers. Then I make a second set, which is a copy of the first set rotated by one 'slot' {5, 7, 8, 2, 1, 3, 4, 6} The relationship between these two is very...

I was a research subject in a data gathering interview, and it involved a lot of questions of the form "On a scale of one to ten..." I found my answers to the questions asked were uncomfortably arbitrary, and believed the results would probably have to go through some sort of normalization...

Introduction Chance weights are integer values that represent outcomes to a random event. A flip of a coin has two outcomes, each with a chance weight of 1. A roll of a pair of dice has 36 chance weights partitioned across 11 possible outcomes like so: {1,2,3,4,5,6,5,4,3,2,1}. Problem I start...

I have been tasked with assisting in the improvement of a piece of video game software. The problem involves a kind of loot drop mechanic that isn't behaving in a way that could be described as normal or expected. So I want to clarify exactly what is normal and expected. Description of problem...

Staging the scenario A casino offers you a gamble with a 1% chance of winning a try. How many tries will it take to win at least once? The answer involves two variables, the chance of success each try and an allowance to be wrong in exchange for predictive accuracy. For this example, I choose...

I'm a video game player and sometimes modder, exploring the limits of what we can measure, infer, and extrapolate from the virtual worlds we create. Current project: A study of Research Points for the game Stellaris

I have a set of data that fits nicely to a quadratic equation Since the factors of a quadradic equation can be interpreted as Acceleration + Velocity + Location, I can characterize this data as containing an acceleration component. But this non-linear aspect of the data makes the use of...