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Questions tagged [dice]

For questions on dice, small throwable objects with multiple resting positions, used for generating random numbers. This makes dice suitable as gambling devices for games like craps or for use in non-gambling tabletop games.

Traditionally dice are rounded cubes, with each of its six faces showing a different number from 1 to 6. When thrown or rolled, the die comes to rest showing on its upper surface a random integer from one to six, each value being equally likely.

A variety of similar devices are also described as dice; such specialized dice may have polyhedral or irregular shapes and may have faces marked with symbols instead of numbers. They may be used to produce results other than one through six. Loaded and crooked dice are designed to favor some results over others for purposes of cheating or amusement.

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Expected time to roll all 1 through 6 on a die

What is the average number of times it would it take to roll a fair 6-sided die and get all numbers on the die? The order in which the numbers appear does not matter. I had this questions explained to me by a professor (not math professor), but it…
eternalmatt
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Given a die, what is the probability that the second roll of a die will be less than the first roll?

If you are given a die and asked to roll it twice. What is the probability that the value of the second roll will be less than the value of the first roll?
Salman Paracha
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The expected payoff of a dice game

There's a question in my Olympiad questions book which I can't seem to solve: You have the option to throw a die up to three times. You will earn the face value of the die. You have the option to stop after each throw and walk away with the…
Gigili
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Is it possible to get all possible sums with the same probability if I throw two unfair dice together?

I throw 2 unfair dice, suppose that $p_i$ is the probability that the first die can give an $i$ if I throw it, for $i =1,2,3,..6$ and $q_i$ the probability that the second die can give an $i$. If I throw the dice together, is it possible to get all…
Guin_go
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What is the optimal number of dice to roll a Yahtzee in one roll?

Description In the game of Yahtzee, 5 dice are rolled to determine a score. One of the resulting rolls is called a Yahtzee. To roll a Yahtzee you must have 5 of a kind. (5 1's or 5 2's or 5 3's etc..). In the game of Yahtzee you can only have 5…
Michael King
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On average, how many times must I roll a dice until I get a $6$?

On average, how many times must I roll a dice until I get a $6$? I got this question from a book called Fifty Challenging Problems in Probability. The answer is $6$, and I understand the solution the book has given me. However, I want to know why…
Sidd Singal
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Is it possible to create a completely random integer between 1 and 13 using standard dice in a D&D dice kit?

I am asking if it is possible to choose a random integer using a certain set of dice. Assume for these calculations that the dice are perfectly randomly distributed. There are 7 dice in a set, with the following possible outcomes for each dice: 2,…
Sam Weaver
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Expected outcome for repeated dice rolls with dice fixing

Here is another dice roll question. The rules You start with $n$ dice, and roll all of them. You select one or more dice and fix them, i.e. their value will not change any more. You re-roll the other dice. Repeat that until all dice are fixed…
Joachim Breitner
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When to stop rolling a die in a game where 6 loses everything

You play a game using a standard six-sided die. You start with 0 points. Before every roll, you decide whether you want to continue the game or end it and keep your points. After each roll, if you rolled 6, then you lose everything and the game…
Kulawy Krul
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How many times to roll a die before getting two consecutive sixes?

Basically, on average, how many times do you have to roll a fair six-sided die before getting two consecutive sixes?
Joe
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Simulate repeated rolls of a 7-sided die with a 6-sided die

What is the most efficient way to simulate a 7-sided die with a 6-sided die? I've put some thought into it but I'm not sure I get somewhere specifically. To create a 7-sided die we can use a rejection technique. 3-bits give uniform 1-8 and we need…
neverlastn
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A dice is rolled until a $6$ occurs. What is the probability that the sum including the $6$ is even?

A game is played where a standard six sided dice is rolled until a $6$ is rolled, and the sum of all of the rolls up to and including the $6$ is taken. What is the probability that this sum is even? I know that this is a geometric distribution and…
Elk Chu
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What is the probability of the sum of four dice being 22?

Question Four fair six-sided dice are rolled. The probability that the sum of the results being $22$ is $$\frac{X}{1296}.$$ What is the value of $X$? My Approach I simplified it to the equation of the form: $x_{1}+x_{2}+x_{3}+x_{4}=22, 1\,\,\leq…
laura
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What are the odds of hitting exactly 100 rolling a fair die

I roll a fair die and sequentially sum the numbers the die shows. What are the odds the summation will hit exactly 100? More generally, what are the odds of hitting an exact target number t while summing the results of numbers sequentially drawn…
Ohad Dan
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Expected number of rolling a pair of dice to generate all possible sums

A pair of dice is rolled repeatedly until each outcome (2 through 12) has occurred at least once. What is the expected number of rolls necessary for this to occur? Notes: This is not very deep conceptually, but because of the unequal probabilities…
user7917
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