Questions tagged [dice]
Dice (singular: die) are typically small cubical objects marked with spots, numbers (1-6 usually) or symbols to generate random outcomes, particularly in games. Other polyhedral dice are also used in games.
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Comparison of Squared Dice Loss vs. Standard Dice Loss
I've been diving into segmentation tasks and came across two variations of the Dice Loss that I'm considering for my neural network: the standard Dice Loss and the Squared Dice Loss.
The Standard Dice ...
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Interview Question: Expected value of dice game where each subsequent roll determines number of dice sides
Consider the following game:
You are playing a game where you roll a die and earn $1 each time you roll higher than 1. For the first roll you get a 4 sided die, and for each subsequent roll you get a ...
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Why is the distribution of the sum of the values on two dice bell-shaped and symmetric if two uniform dist is triangular distribution?
Why is the distribution of the sum of the values on two dice bell-shaped and symmetric if two uniform dist. sum is triangular distribution via Irwin-hall distribution?
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Number of configurations in which you can roll 2 6's in a row
A colleague at work gave me a problem to think about.
If you throw $n$ dice, how many configurations are there where you get at least 2 6's in a row?
I worked a lot with Pascal's triangle and in the ...
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Hausdorff and IoU are stopped changing while dice metric is decreasing
I am facing a problem in Hausdorff and IoU, where they stop learning when reaching a specific value! While the loss and dice metric keeps changing. surface_distance also has a problem since it is ...
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Probability of a given result with multiples of mixed dice with different number of faces
What is the formula to calculate the probability of getting 41 when I throw two 10-sided dice and four 8-sided dice? I’m looking for an algorithm for the general case of throwing multiples of two sets ...
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Quantifying the confidence that the most sampled outcome is the most probable outcome
Let us say we have a cheater's six-sided die, which we can assume to be unfair with an unknown probability distribution. We want to know the most likely roll with this die, and so we roll it $N \gg 6$ ...
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Is it possible to generate a Pareto distribution with dice?
So I know that there's a really easy way to generate a normal distribution with dice (simply add them). Is there a way to generate a Pareto distribution?
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What are the odds for winning this drinking game?
Out of pure boredom during the corona period back in 2020 I 'invented' a drinking game which seemed to have a fair outcome, but I am not sure. We were sitting on the couch and after a lot of beer, and ...
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Non-transitive dice probabilities
I got the following question on non-transitive dice, as shown in the following picture.
Suppose you roll two white dice against two red dice. What is the probability that the sum of the white dice is ...
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Roll 4 Dice, What's the Expected Value of the Sum of the highest 3?
After writing a simulation in python (code at bottom) I realized my calculations are incorrect but can't figure out where I went wrong.
Let {$D_1$, $D_2$, $D_3$, $D_4$} be the ordered dice rolls. Let $...
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Pseudo-dice probability distribution
Given the following data, is there an algorithmic way to generate a probability distribution?
Data: min, max, and average results of "die".
Known Trend: results will always be weighted ...
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Probability of same outcome for a pair of dice/urn draws with correlation $\rho$
This is surely a simple problem, but there are so many probability questions with dice, urns, etc. that I have not been able to find an answer to this specific problem. Say you have a pair of $n$-...
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Is there a formula for finding the number of ways 3 dice throws can add to 6?
Consider 3 dice throws: t1,t2,t3
Let E be the event that t1+t2+t3 add up to 6
What is the probability of event E?
I know the denominator is an example of ordered repetition. So with n=6 and k=3 there ...
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what is the probability of this event?
given this outcome of the dice {2, 3, 4, 6, 6}. You decide to re-roll both sixes. What is the probability that you roll either a small straight (four dice are in a row) or a large straight (all five ...
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Difference between geometric distribution expectation and 1 - failure with Binomial
I'm trying to understand a simple problem:
How many times you'd need to roll two dice to get two ones in a single roll.
One way I see this is as a problem the geometric distribution describes. You ...
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Super noob requesting help testing dice balance [duplicate]
So, I have a few sets of polyhedral dice (77 individual dice) that I'd like to try to test for balance. I'm thinking a decent sample size is to roll each of them 100 times, then plot the proportional ...
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How much compensation is needed to take on risk?
We roll three, 8 sided dice. If same face appears 3 times we win 80 dollars. We have a bank of 10,000 dollars. How much are we willing to pay to play? What if we increase the prize to 80,000 dollars? ...
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Covariance between two binomial RVs
Suppose we toss a fair dice $n$ times. For $i=1,\dots,6$, let $X_i$ denote the number of times the dice comes up with value $i$. Find the $\textrm{cov}(X1, X2)$.
By definition, $\textrm{cov}(X1, X2)=E[...
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D&D Probability question: why am I wrong?
In Dungeons and Dragons, the primary die used for success or failure is the D20, or 20 sided die. A 1 is a critical failure, and a 20 is a critical success. When one has advantage, one rolls 2 dice ...
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Is there a 1 in 20 or 1 in 400 chance of guessing the outcome of a d20 roll before it happens?
My friends are in a bit of an argument over Dungeons & Dragons.
My player managed to guess the outcome of a D20 roll before it happened, and my friend said that his chance of guessing the number ...
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A method for simplifying manual random number generation? [closed]
Is there a good way to take a more complicated dice-rolling mechanism and create a simpler dice-rolling mechanism that gives roughly similar results?
Example 1: Say you have a game where both sides ...
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Probability that sum of x dice greater than sum of y dice
If I roll a 6-sided die x times (or roll x 6-sided dice at once), what is the probability that the sum of the result is greater ...
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Probability - How to approach Unfair Dice Problem?
I am working on a problem to use probabilities for a game with 2 dice. I have researched many methods (Bayesian, etc.) but I am not sure what the right path would be to answer these questions. Here is ...
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How to test for significance for binomial count data where the expected outcome is unknown?
Description of the data:
The study is investigating whether conversations on a messaging app are greater or less than 8 words long. The variable is the count of messages that contain more than 8 words ...
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How can I simulate the frequency of each face for N die rolls? [duplicate]
I want to simulate a fair die roll N times without actually rolling a die.
To be clear, I want to achieve something like this:
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Dice roll question [closed]
Suppose you roll a fair die two times. Let A be the event "the sum of the throws equals 5" and B be the event "at least one of the throws is a 4 ". Calculate p(A|B)?
How to ...
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Fluctuating loss curve/ steady dice score. Why? And How to improve? [duplicate]
I am training 3D data with multi-class 3D target ground truths(9 tissue labels) for segmentation. Using dice Loss and focal dice loss as loss criterion. Updating optimizer every second batch (...
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Have I found something new? (a formula for the odds of rolling at least one 1 when rolling an n-sided die n times)
The formula
First, the formula I found for the odds of rolling at least one 1 when rolling an n-sided die n times:
Math.round(1 - ( ((n-1)/n)^n -1 )*(n^n-1) )/n^n
...
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Combined probabilty for 1 to 6 between a cube and a dodecahedron, not counting 7 to 12
We have two dice, one with six sides (a cube)
and one with twelve (a dodecahedron)
The cube bears the numbers 1 to 6. The probability for each number is $\frac{1}{6}$. The dodecahedron bears the ...
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Interpreting chi-squared value returned by Excel 2010
I'm trying to assess whether the number of doubles (dice) being rolled by my opponents on a backgammon website are fair; to the naked eye they most definitely aren't but I need some science to back up ...
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Mean number of throws to exceed a threshold [duplicate]
Say that you have a die with n faces, and you need to throw the die until the sum of your results exceeds a given threshold.
What is the average number of throws needed?
I think that to compute that ...
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Distribution of sums with multiple dice of differing sides for a probability of success. Why do distributions vary with probability?
Intro
I have been looking into dice distributions within the context of rogue-like or D&D type games. I found this question.
In lots of these types of games you will be attacked by something with ...
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How do I find the probability of getting specific, distinct, dice rolls on an unfair die in the same group of trials?
I play gacha games, and recently I've wanted to compare the rates of the one that I play compared to competitors in the market to warn some friends of mine from starting one with rates that I feel are ...
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Trouble finding var(ax)
So the variance of a 6-sided (1,2,3,4,5,6) die is $291.6$ using the formula:
$$
\text{Var}(X) = \frac{(b-a+1)^2}{12}
$$
Also, $\text{Var}(10X) = 10^2 \cdot \text{Var}(X)$, so that would mean $\text{...
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What is the probability that in 3 rolls of a pair of six-sided dice, exactly one total of 7 is rolled?
I tried to solve the exercise and it seems meaningful, but the problem is that in the book the result is $25/72$, while mine is $1/7776$. I don't know if maybe I didn't understand the problem, but by ...
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Halving time for a population of dice
The following question arose today on a Norwegian facebook forum for math teachers, with some unclear definitions and a lot of simulation.
We have a population of $K$ (regular, 6-sided, equal-...
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How many unique values can you expect after throwing a die with k sides?
I ended up asking here.
My problem might be familiar with the coupon collector's problem and related to this post Probability of throwing n different numbers in m throws of a die but it does not solve ...
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How far from "even" is (or is not) significant?
If a six-sided die is rolled 600 times, an even distribution would be 100 rolls for each number. If I actually rolled 600 times and tallied the results...
How far away from 100 would a count need to ...
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Generalization of a boy or girl paradox with die!
Here is the link to the boy or girl paradox Wikipedia page. The question I have is: Let's say you have two fair 6-sided dice and you roll them simultaneously. If at least one is 6, what's the ...
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How many rolls required for 90% chance to reach expected values of consecutive dice rolls in tabletop game?
I'm trying to work out if random variance in dice rolls is more likely to influence a given situation in a game rather than the overall expected values of those dice rolls being significant. The game ...
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Variance of one die with binary result
I have a task that is worded:
"You have a deciding die-throw ahead of you in a game (using a fair 6-sided die) and you realize that you will win if you get a 4 and lose in every other case. You ...
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A fair die is rolled 1,000 times. What is the probability of rolling the same number 5 times in a row?
A fair die is rolled 1,000 times. What is the probability of rolling the same number 5 times in a row? How do you solve this type of question for variable number of throws and number of repeats?
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10-faces dice "emulation" from N 6-faces dices [duplicate]
I want to play a game which uses one 10-faces dice, but I only have 6-faces "classic" dices at my disposal.
Is it possible to approximately recover, to an arbitrary precision, a 10-faces ...
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Probability that number of heads exceeds sum of die rolls
Let $X$ denote the sum of dots we see in $100$ die rolls, and let $Y$ denote the number of heads in $600$ coin flips. How can I compute $P(X > Y)?$
Intuitively, I don't think there's a nice way to ...
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How many flips are needed to confirm a coin's intentional bias?
I've made some 'special' coins and I know for a fact that they have a very small but known/designed bias $\epsilon$. I define bias as the probability $(\frac{1}{2} + \epsilon)$ towards heads and $(\...
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What are the chances rolling 6, 6-sided dice that there will be a 6?
More generally, what is the probability that n n-sided dice will turn up at least one side with the highest number ("n")?
My crude thinking is that each side has 1/6 probability, so that 6 ...
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Calculating the variance of dice rolls?
I am having trouble understanding how to find the variance for the proportion of times we see a 6 when we roll a dice. The question is below:
Suppose we are interested in the proportion of times we ...
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Expected number of rolls until a number appears $k$ times
Roll a fair die, what is the expected number of rolls until a number appear $k$ times? Not necessarily consecutive.
Let $N$ be the number of rolls until a number appear $k$ times. For $k=2$, we know ...
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Expected rolls to roll every number on a dice an odd number of times
Our family has recently learned how to play a simple game called 'Oh Dear'. Each player has six playing cards (Ace,2,3,4,5,6) turned face-up, and take turns to roll the dice. Whatever number the dice ...
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