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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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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Uniform distribution or Poissonian distribution?

Suppose I take a 6-sided dice and roll it N=1000 times; then I organise the measures in a histogram whose bins are the 6 faces and each of them contain the number ...
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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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Rolling Die Game Probability

Two persons, $A$ and $B$, play a die game which works in the following way: They trow a die once each after each other and person $A$ throws first. The person who first rolls a $6$ is the winner. Let $...
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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 dice 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 dice but it does not ...
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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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(python) dice roller, odds that groups or players win?

I am trying to simulate a dice game. All players roll a 1d6 and the highest number wins. (if multiple people win, they win.) I am getting proper odds for one player by redoing the game 10000x and ...
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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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What is the probability of getting exactly doubles when rolling N number of dice

For example if i roll 2 dice the probability of getting exactly doubles is 6/36. similarly if i roll 3 dice the probability of getting exactly doubles not considering triples is 90/216. How can i ...
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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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sum of n dice divisible by k

There are a few similar questions on the site. For instance, the probability of the sum of n=50 dice divisible by k=3 is \begin{align} P(S_{50}\>{\rm divisible\>by}\>3) =\sum_{m=0,1,2}P(S_{50}...
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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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Calclulating Probability of a Distribution of a set of Two-Dice rolls

I was calculating the odds of a set of dice rolls in a game of Catan recently. In 35 rolls, we rolled 0 3's, and 0 5's. To calculate the probability of this, I calculated the probability of rolling 0 ...
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Calculating the probability that one distribution is greater than another

I have a problem which I think should actually be really simple, but I can't see the solution and either it's more complicated than I realize or I just cannot figure out how to word it for Google. I ...
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How many rolls of sum of 6d6 for an expectation of 90% chance of hitting three consecutive 6d6 totals each less than or equal to each other?

each Roll is the sum of six six-sided dice ( therefore a value of 6 to 36). How many times would I have to roll (and take the sum of 6d6) before I would have a 90% expectation of seeing three 6d6 ...
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Cracking a safe: matching $n$ unique numbers with $d$ dice. What is the expected number of rolls?

This problem is inspired by the board game Burgle Bros. In the game there are safes to crack. You have to match $n$ unique numbers with $d$ dice, where $n = 1,...,6$ and $d=1,2,...$. For example, ...
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Which game is more advantageous?

I got a pretty simple problem but I'm not sure about my solution. Game $A$: We roll a fair die 4 times. If we get the "6" at least one time, we win. Game $B$: We roll a fair die 8 times. If we get ...
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What is the probability of getting three pairs that makes up seven when six dice are rolled?

Stumbled upon this question in a game of dice where a point is dealt for each pair that makes seven. In the game there were a total of six dice that were to be thrown up to three times. Each time a ...
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Expected Return of Die Game

The game is as played: To preface you can roll a die at most three times. You roll the die the first time, if you get a six you get \$6 and you roll the die again, if you don't get a six the game ...
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Interpreting frequency statistics to find fair dice

I was just in a lecture where my (bayesian evangelist) professor claimed that for questions like 'Is this a fair die?', frequency statistics gives an answer of {0, 1}, meaning that the probability is ...
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Probability of getting a 6 on at least one die from a pair of dependent dice

I am stuck on this particular question: Suppose you have two dice. These dice however are not independent: the probability that both dice will roll a 6 is 0.29. What is the probability that at least ...
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How to win this dice probability game?

The game is a variation of Pig. Here is how the game works: There are about 20 players. Each round, a single six sided die is rolled. All players add that rolled number to their "bank." However, if a ...
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597 views

Calculate Probability of 50 different Dice Roll to Same Number

The Problem: Provided there are 50 different dice with 50 sides. What is the probability any two dice or more will roll the same number? My Attempt: So, I know the probability of two different dice ...
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bootstrapping resampling for unfair dice

Let's say I've been given an unfair dice. After 1000 throws, these are the empirical frequencies: 1, 100 2, 100 3, 100 4, 100 5, 100 6, 500 I would like to represent this in a barplot, where each ...
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Two different dice games. What are the odds the game will be won?

Based on the images above, is it correct that the first game should be won 1 out of six times, the second game every time, and the 3rd game 1 out of six times?
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Is it possible to determine a dice pool from a given range?

First off, assuming this problem - or one similar enough to directly apply - hasn't already got an official theorem or conjecture proving it one way or the other, I'd be content with simply being ...
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Using R to calculate probability of rolling 2 numbers in 20 throws [closed]

We have an 8-sided die. Throwing it 20 times, what is the probability of rolling a number larger than 6 at least 12 times and at most 16 times? If you know of an efficient program to write so that I ...
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Draw integers independently & uniformly at random from 1 to $N$ using fair d6?

I wish to draw integers from 1 to some specific $N$ by rolling some number of fair six-sided dice (d6). A good answer will explain why its method produces uniform and independent integers. As an ...
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Rolling a fair dice [closed]

If I roll a dice three times, how do you calculate the probability that at least 2 dice are less than four?
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296 views

comparing probability of two polyhedron dice

I'm trying to figure out the probabilities associated with rolling two different types of dice and one coming out higher than the other. Example: Rolling a 4 sided die vs a 6 sided die, what's the ...
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1answer
574 views

Bayesian posterior pmf for weighted dice with uniform prior

We want to find posterior probability mass function for dice tossing with uniform prior. We are interested in rolling of weighted dice. The outcome is 1,2,...,6. We assume that prior probability ...
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Two dice roll with {1,2,3,4,5,6} and {10,20,30,40,50,60} and importance of RV mapping

We're all too familiar with a two-dice-roll experiment where we start with a uniform sample space of $S_{die}=\{1,2,3,4,5,6\}$ and end up in a non-uniform pmf for the sum of the numbers on the two ...
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If I roll a die 25 times what is the probability that the mean outcome is greater than 4?

Consider a problem: You take a fair die to a party and announce that you will roll it 25 times. You will record each outcome and at the end average the 25 outcomes together to get their arithmetical ...