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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23 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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23 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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26 views

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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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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48 views

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
63 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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100 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
60 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
87 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
36 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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2answers
73 views

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
162 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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1answer
26 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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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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Uniform prior 3 sided dice marginal probability equation [duplicate]

Given a 3 sided dice with a uniform prior. What is the probability of observing ordered data $D = \{n_1, n_2, n_3\}$. Where $n_1$ is the number of observed 1s. Denoting the bias on the dice by $\...
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123 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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378 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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37 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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132 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
339 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
77 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
2k views

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 ...
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1answer
44 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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189 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
19 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
150 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
580 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
652 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
834 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
334 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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226 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
108 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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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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887 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 ...
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124 views

Formula for dropping 2 dice (non-brute force)

This is a follow up from my previous question: Formula for dropping dice (non-brute force) which asked how to determine the statistics for dropping the lowest die but now I'm asking how to determine ...
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2answers
3k views

What is the probability of rolling an even number and a number greater than 8 for two rolled die?

This is one of the questions asked in the swirl package of R. One of my students however, has pointed out that the correct option of this question is the wrong answer. His assertion is that the ...
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1answer
114 views

Weird dice roll mechanic

There's a game called Cthulhutech which has a dice-based problem resolution system. I'll use a notation of nd+b where relevant, where "n" is the number of 10-sided dice (giving a value from 1 to 10), ...
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1answer
289 views

basic probability questions with respect to dice, potential textbook error, or is it over my head?

I'm going through Schumacker's Learning Statistics Using R. I've come across something that's not making too much sense to me, so I'm wondering if this is a mistake or if I'm just really thick. On ...
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91 views

What Method / Tool Will Help Me Choose The Dice I Need To Fit Particular Specs?

BACKGROUND: I am designing a roleplaying game ("RPG.") I have been researching, and know some basics of probability and the normal distribution, including the equation to generate a standard bell ...
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158 views

Confidence interval of a linear function of a multinomial distribution

Say we have a $K$ sided (unfair) dice, that has unknown probabilities $p_k$ of rolling each side. We roll $N$ trials and observe $n_k$ occurrences of each side (so $N = \sum_{k=1}^K {n_k}$). The ...
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2answers
3k views

roll dice 400 times, what is the probability that the total number of dots is at least 1350?

I know how to solve if roll dice 2 time and the sum is 10, but by drawing table. Therefore, with 400 times and sum is 1350, that is ridiculous. Let's say using Excel to solve the problem. Should I ...
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1answer
343 views

Probability of throwing n different numbers in m throws of a dice

I know how to calculate the probability of throwing the same number in every throw of a dice (die, if you prefer!), and I know how to calculate the probability of throwing a different number in each ...
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641 views

Test for uniformity in R

i am searching for a test for uniformity in R. ks.test(x,'punif') looks quite good, but my data has only 6 different values (results of rolling a die) which leads ...
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1answer
727 views

How can I understand the properties of a Cumulative Distribution Function (CDF)?

Suppose that $F$ is the distribution function of a real-valued random variable $X$. $F$ is increasing: if $x≤y$ then $F(x)≤F(y)$. $F(x+)=F(x)$ for $x∈R$. Thus, $F$ is continuous from the ...
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1answer
92 views

Two sets of dice with equal distributions

For this question, I define a die to generate a random integer from $1$ to $N$ (inclusive) with equal probability. This means that weighted dice or repeating or skipping numbers are not allowed. $N$ ...
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1answer
11k views

What are the difference between Dice, Jaccard, and overlap coefficients? [closed]

I come across three different statistical measures to compare two sets, in particular to segmentation on images (e.g., comparing the similarity between the ground truth and the segmented result). ...