# 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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### 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 ...
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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### 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 ...
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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### 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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### 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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### 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 ...
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### 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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### 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 ...
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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### 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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### 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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### 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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### 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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### 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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### 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). ...
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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### 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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### 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" ...