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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21 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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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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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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89 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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61 views

Does Sørensen–Dice Coefficient (Dice Score) only account for true positives?

I'm working in a project on medical image segmentation which uses the Dice Score as part of the loss function, but I got some doubts with the commonly adopted implementation. The definition of Dice ...
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288 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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35 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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83 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
103 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
68 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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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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41 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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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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118 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
14 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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113 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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535 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
568 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
42 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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355 views

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
138 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
122 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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169 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
93 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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31 views

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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574 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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103 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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2k 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
102 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
182 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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60 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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136 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
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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
251 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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480 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
521 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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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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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). ...
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1answer
36 views

Expected rolls to get n result k times non-consecutively

I've searched through several questions trying to get the answer to this but been unable to find the answer I need. Most questions deal with consecutive results, but I am looking for non-consecutive ...
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2answers
201 views

Reach true probability distribution in fewer simulations

I am playing a board game (Settlers of Catan) in which the outcome of the sum of two dice ($D_1+D_2$ = X), in each round, determines much of the game. However, since one only plays a limited amount of ...
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1answer
87 views

Can a dice-roll experiment involving re-rolls and “negative successes” be modeled as a distribution?

I’ve been looking into statistical distributions lately, having little background in statistics myself, and the way it allows you to modelize complex experiments is absolutely fascinating to me. ...
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How do we know that the probability of rolling 1 and 2 is 1/18?

Since my first probability class I have been wondering about the following. Calculating probabilities is usually introduced via the ratio of the "favored events" to the total possible events. In the ...
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1answer
296 views

Die Probability Question

I have this question which I can't figure out, maybe because the answer I got is not correct (trying to match the answer). A six-sided die is thrown twice, but not a normal die. If X is the result of ...
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50 views

transitive dice in pseudorandom number sequences

Background: Transitive several dice that act individually as if they are uniformly random but they are built to work against each other. If you know which one your opponent chose, there is a ...
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1answer
366 views

How to determine xdy dice roll from a sample?

I'm playing an RPG based on DnD xdy dice damage rolls, where x is the number of dice rolled and y is the number of sides on each die. So, normal double-sixes dice people are familiar with would be 2d6....
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1answer
222 views

How to prove Markov Chain formula?

I saw an question about how often should I roll a 6-face dice to get every number at least once. I have read a lot of interesting answers but one of them caught my attention. It is one which imples ...
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Why isn't the prob of rolling two 6s =5*5/6*6?

Say we roll 2 die. What is the probability of getting two 6s? Why is $1-(1/6)^2 \ne (5/6)^2$? The prob of 1-5 happening twice and the prob of 6s happening twice should be the compliment of eachother ...
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1answer
1k views

Probability of the maximum of n dice rolls being equal to k

As part of my recent interest in university-level statistics, I'm trying to figure out what the probability distribution is for the following scenario, without having to resort to counting the number ...
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2answers
94 views

Error of empirical probability for unfair die

I roll an unfair $256$-sided die $n$ times ($n > 1'000'000$) and count the rolled numbers in a histogram. I then calculate the empirical probabilities ${p_e}_i$ for $i=1, ..., 256$ by taking the ...
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4answers
34k views

What are the variance and standard deviation for a standard six-sided die?

I'm having trouble imagining what variance and deviation mean with a series of die rolls. That is, a fair die will fall with a flat distribution on all its values 1-6. Does the concept of variance ...