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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2answers
65 views

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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25 views

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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2answers
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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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0answers
24 views

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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5answers
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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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1answer
37 views

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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1answer
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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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3answers
199 views

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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0answers
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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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845 views

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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2answers
36 views

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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1answer
37 views

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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Let N be the number of times you roll a 6-sided die until you roll a 1. Let M be the sum of rolling N six-sided dice. What is the pdf of M?

I understand that a geometric distribution can be used to determine the pmf for N, but am lost on finding the distribution for M. Also, if done in reverse order: Let N be the result of rolling a 6-...
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1answer
36 views

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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0answers
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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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1answer
66 views

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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1answer
110 views

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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1answer
81 views

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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1answer
94 views

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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1answer
47 views

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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1answer
263 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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25 views

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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1answer
30 views

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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1answer
22 views

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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2answers
151 views

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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4answers
410 views

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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2answers
38 views

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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2answers
171 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
414 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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1answer
79 views

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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2answers
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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 ...
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1answer
46 views

Probability of 3 dice with rethrown [closed]

In a game, three ordinary dice are thrown. If the first throw results in just two dice showing the same number, the die with different number if thrown again. If all numbers are different in the first ...
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1answer
4k views

How many times must I roll a die to confidently assess its fairness?

(Apologies in advance for use of lay language rather than statistical language.) If I want to measure the odds of rolling each side of a specific physical six-sided die to within about +/- 2% with a ...
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0answers
222 views

Generating Function for sum of N dice [or other multinomial distribution] where lowest N values are “dropped” or removed

Background I found this interesting question Formula for dropping dice (non-brute force) and excellent answer https://stats.stackexchange.com/a/242857/221422, but couldn't figure out how to ...
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1answer
22 views

Distribution of a dice pool [duplicate]

The article Three Basic Distributions from AnyDice shows the distributions (and cumulative distributions) of 1d10, 2d10 and 3d10. Looking at the graphs, it seems there is a pattern here: 1d10: the ...
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1answer
153 views

R dice support problem [closed]

Could someone please help me with the code for the following problem (I am brand new to R so it is being a bit complicated for me): Consider the variable X, the sum of three, fair, 8-sided dice ...
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3answers
590 views

Rolling a $6$ Sided Die

If I roll one $6$ sided die, the chances of getting one number, say $6$, is $1/6$ or $16.6\%$. If I roll $2$ dice simultaneously, then the probability of rolling that number twice is $1/36$ or $2.7\% (...
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2answers
683 views

Probability of a specific event when rolling a 6 sided die five times

I am stuck on computing probability problem that goes as follows: I am rolling a 6 sided die 5 times in total. What is the probability that I roll at least one 3, but no 1 or 2 at all (= probability ...
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1answer
43 views

Probability that side k does not occur in a die

If there is a die with n sides (1,2,..k,..n) and it is rolled n times. What is the probability of the side labeled 'k', not occurring in n rolls?
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Die 100 rolls no face appearing more than 20 times

I am trying to wrap my head around this problem. A die is rolled 100 times. What is the probability of no face being appearing more than 20 times? My first thought was using the Binomial distribution ...
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1answer
1k views

Rolling one die after another

If I roll 1 6 sided die, the chances of getting one number, say 6, is 1/6 or 16.6%. If I roll 2 dice simultaneously, then the probability of rolling that number twice is 1/36 or 2.7% (1/6 x 1/6). ...
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1answer
536 views

How to calculate probability distribution of rolling n dice? (with a twist!)

I'm trying to work on a project in code that asks this question. I'm currently able to get the right answer by breaking it up, but I'm wondering if there's a mathematical formula I can address this ...
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1answer
260 views

minimum number of rolls necessary to determine how many sides a die has

For example, say you have a black box that has a number of n-sided dice in it. You have 4-sided dice, 6-sided, 8, 10, 12, 20 and so on. The die sides are all A except for one side that says B, e.g. ...
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1answer
113 views

Number of rolls to get my desired result with a set probability

I want to know the number of rolls or throws of a die or a coin with an equal distribution to get to my desired result with a given probability. In my specific case I want to roll at least one "1" ...
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0answers
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probability of sum of 5 dice is a certain number [duplicate]

If I throw 5 dice, then the sum of numbers should be integers from 5 to 30. How can I get the probability that the sum is n? (n = 5,6,...,30) I used the formula: no of ways to get 8: 5_H_2 = 6_C_2 = ...
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2answers
988 views

Dice Probability Game

We are playing a game in my AP Stats class called Greed. To play the game, everyone stands up and the teacher rolls the dice. If any number other than a 5 is rolled in the first round, 100 points are ...