For questions on dice, a small throwable object 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.

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Keep the value of an 8-sided die roll, or gamble by taking a 12-sided die roll. What's the best strategy?

Consider a dice game in which you try to obtain the largest number (e.g. you win a prize based on the final dice roll). You roll an 8-sided die, with numbers 1–8 on the sides. You may either ...
1
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3answers
197 views

Creating multiple sided dice which roll avg. high numbers with controlled sum of die-faces.

I need to create: One 4 sided Die : Numbers add up to 14 One 6 sided Die: Numbers add up to 21 One 8 sided Die: Numbers add up to 28 Which combinations of numbers would result in my rolling the ...
4
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1answer
166 views

What is the probability of rolling a 1 on the Catenative Doomsday Dice Cascader?

As seen here. Assume that each cascader bubble begins with a d6, as opposed to being determined by the prime bubble along with the number of cascader bubbles; the scene makes it ambiguous. ...
3
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3answers
161 views

Calculating mean after removing smallest items

I'm having a tough time wrapping my head around this question. Lets say that I am doing an experiment where I roll 10 dice. Each time I roll the dice, I record the average value and repeat the ...
2
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2answers
2k views

Probability of throwing multiple dice of at least a given face with a set of dice

I know how to calculate the probability of throwing at least one die of a given face with a set of dice, but can someone tell me how to calculate more than one (e.g., at least two)? For example, I ...
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4answers
8k views

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?
2
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1answer
115 views

Throwing the dice, sum of the points

We are throwing the die (original cube for the board games). How many are ways to get the sum of the points equal to $n$ ? I've heard this problem today in the morning and still can't deal with ...
2
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2answers
1k views

Roll six dice. Probability of at least one pair.

I roll 6 fair dice. What is the probability that at least one pair shows up?
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2answers
277 views

The Odds of A Dice Game Ending

A fair dice roll: On a 6 you win €1 on everything else you lose €1. The game continues until you profit €500. What are the odds of the game ever ending? Update: While initially I hadn't clarified ...
4
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3answers
598 views

Statistical Significance Dice Probability

I think I just need to be pushed to the right formula or algorithm... Imagine you've got a "real" dice which is not an optimal one. And you want to know the confidence intervals for each result. So ...
2
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3answers
1k views

Please help me understand conditional probability in relation to dice

If 2 fair dice are rolled, what is the probability that the sum is 6, given both dice show odd numbers? When the sum is 6, there combinations are: (1,5),(2,4),(3,3),(4,2),(5,1). Probability = 5/36 ...
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0answers
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Dice Game: Creating Probabilistic Models for a Casino

*The Dice Game: Creating Probabilistic models * a. Consider a game with two players, Ann and Bob. Ann has a red die and Bob a white die. They roll their dice and note the number on the upper face. ...
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3answers
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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 ...
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1answer
169 views

Continuous Dice rolls

A dice is being rolled continuously. Suppose you roll a 3 ( or any number ). What is the probability that you will get the next "3" exactly after n rolls?
4
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3answers
313 views

Probability that no side of a dice is rolled more than $k$ times

Suppose, we roll a fair die $n$ times. The expected value of how many times each side of the die will appear is $\frac{n}{6}$. The question is, what is the probability that any side of the die will ...
8
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3answers
1k views

“Go-first” dice for $N$ players

I'm interested in sets of dice that can be used to determine who "goes first" (hence the name) in an $N$-player game; more generally, I want to determine a complete ordering of the players with a ...
2
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2answers
154 views

Given $3$ dice, which number is the most likely to appear

Given $3$ dice, what is the value of the sum of the number of the $3$ dice most likely to appear? I know that by symmetry, there would always be $2$ different values with the same probability to ...
0
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4answers
580 views

Solving for $E(X^2)$ if I know $E(X)$

I am trying to find the variance but I don't know how to calculate $E(X^2)$, but I do have a process that will enable me to find $E(X)$. How can I find $E(X^2)$? In my case I have two 6-sided dice, ...
9
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2answers
933 views

Most Probable Sum [duplicate]

Possible Duplicate: Probability of dice sum just greater than 100 A fair dice is rolled and the outcome of the face is summed up each time. We stop rolling when the sum becomes greater than ...
8
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2answers
469 views

“8 Dice arranged as a Cube” Face-Sum Equals 14 Problem

I found this here: Sum Problem Given eight dice. Build a $2\times 2\times2$ cube, so that the sum of the points on each side is the same. $\hskip2.7in$ Here is one of 20 736 ...
4
votes
2answers
327 views

Probability of getting two consecutive 7s without getting a 6 when two dice are rolled

Two dice are rolled at a time, for many time until either A or B wins. A wins if we get two consecutive 7s and B wins if we get one 6 at any time. what is the probability of A winning the game??
1
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1answer
348 views

Probability and distribution function

Can some one please tell me how to do it? Let $(i,j)$ denote the numbers on the top faces when a pair of fair dice is rolled. Let $X(i,j)=i+j-3$. Find the range of $X$. Find the probability ...
2
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1answer
672 views

Expected Value of the Difference between 2 Dice

What is the expected value of the absolute difference between 2 N faced dice? What about the difference between 2 dice one with N faces and one with M faces? While finding the expected value ...
1
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1answer
91 views

Probability of hitting a deep downswing in a sequence

This is really a poker tournament/payout/bankroll question but I think I can frame it in a dice game for easier understanding. If a player starts with $X$ units, and plays a game where on each throw ...
1
vote
1answer
115 views

dice probability issue

In the game Settlers of Catan, territories/tiles are each (effectively) randomly assigned a number from 2-12. When that number is rolled as the sum of two dice, the tile generates resources for the ...
0
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2answers
257 views

Sum of 3 loaded dice

I am given 3 loaded dice $D_1$, $D_2$ and $D_3$ and their probability tables $P(D_i = k), 1 \leq k \leq 6$. I ought to write an algorithm that computes $P(\text{Sum} \mid D_1)$, the sum of all three ...
0
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1answer
163 views

Can you Fourier transform probabilities?

If I have a rect function , and I convolute it with it's self, I get a triangle function. If I convolute with a rect function again, I get a bell-curve. I can continue, so long as I know how to ...
2
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2answers
277 views

probability dice experiment

I am currently taking a probability course and I am stuck on a supposedly easy discrete probability question here: Problem: Consider the experiment of rolling a fair die independently until the same ...
0
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1answer
373 views

Are X and Y independent?

We roll two dice once. Let X denote the number of 1’s and Y the number of 6’s obtained. Are X and Y independent?
2
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1answer
392 views

Simple Dice Rolling Problem

If you play poker dice by simultaneously rolling 5 dice, why is $P\text{{five alike}} =.0008$? I guess I understand the fact that each dice has the probability to land on the same number $1/6$ of the ...
4
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2answers
782 views

Find the expected value of a dice sum

If fair dodecahedron is rolled until at least $k$($k$ is fixed between 2 and 12) is gotten, and $X$ is the sum of all numbers appeared until the last time, what is $E(X)$?
1
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1answer
127 views

Probability on a Die

The normal probability of a number in a regular die (6 faces) is $\dfrac{1}{6}$. Let in an addicted [that is, "loaded"] die, the probability of a even number (2, 4 and 6) be twice the normal ...
5
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2answers
211 views

Probability of throwing the same multiset twice in a row with six dice

Six dice are thrown. The six dice are thrown a second time. What is the probability of getting the same numbers as in the first throw? If the order of the six numbers matters, the problem is easy, but ...
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1answer
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How do you calculate probability of rolling all faces of a die after n number of rolls? [duplicate]

Possible Duplicate: Expected time to roll all 1 through 6 on a die Probability of picking all elements in a set Im pretty new to the stackexchange, and posted this is statistics, and then ...
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3answers
988 views

What is the expected number of dice one needs to roll to get any monotonically increasing series of 1 to 6?

Similar to: "What is the expected number of dice one needs to roll to get 1,2,3,4,5,6 in order?" but we allow repeats so 1,1,2,2,3,4,4,4,4,5,5,6 would count. My answer (or simulation) is flawed as I ...
6
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2answers
1k views

What is the expected number of dice one needs to roll to get 1,2,3,4,5,6 in order?

If I have a fair die and throw it until I get a run of 1,2,3,4,5,6 in order, how many times on average must I throw the dice?
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3answers
1k views

What equity is necessary to offer the doubling cube in Backgammon (dice game)

Edit: This question is a lot shorter than it is. Don't get intimidated. If you know backgammon, just skip to question 2. In Backgammon, each game is played for one point (or one dollar) between two ...
2
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1answer
2k views

dice throwing probability. Get face 1 at least one time by throwing a die 6 times.

How can I calculate the following probability: Throwing a die 6 times, what is the probability of having face no. 1 showing at least one time.
4
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3answers
6k views

Probability question (Six dice)

If six fair dice are rolled what is probability that each of the six numbers will appear exactly once?
3
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1answer
894 views

dice problem - throws necessary for sum multiple of n

A die (with six sides) is rolled repeatedly and summed. Show that the expected number of rolls until the sum is a multiple of $n$ is $n$. In ...
2
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1answer
2k views

Poker dice probability

I am working on a maths excersice and got stuck on this question where I need to calculate the probability of poker dice. The game poker dice is played with 5 dice. It's possible to get one of the ...
2
votes
2answers
154 views

How do I think about solving this sort of problem without having to count intersections?

I have asked this sort of question before, and I have a new similar question here. The latter question got me thinking about this specific question. When throwing 5d20 (rolling five twenty sided ...
2
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3answers
301 views

What function accurately describes the likelihood of getting X successes when rolling Y dice?

Pardon my statistical illiteracy and feel free to correct any silly/wrong terminology I use in this post. There is an RPG system called Storytelling where the vast majority of dice rolls are ...
4
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1answer
252 views

Probability greatest roll of z dice exceeding greatest roll of h dice?

Let's assume there are two players in a dice game; zombie and hero. The Zombie rolls z fair 6-sided dice. The Hero rolles h fair 6-sided dice. If the heroes greatest dice roll is larger than the ...
65
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9answers
17k views

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?
4
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2answers
3k views

Probability of either dice showing a specific number

If I throw 4 dice together, what is the probability that either one of them will show the number 3 ? I tried to calculate it and got to $\frac{(4)}{6}$ (which is highly unlikely to be correct).. any ...
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0answers
110 views

Boggle dice set letter distribution algorithm [duplicate]

Possible Duplicate: Boggle letter probability What algorithm have the creators of the word game Boggle used to come up with these dice sets? ...
6
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3answers
438 views

Probability of rolling a die

I roll a die until it comes up $6$ and add up the numbers of spots I see. For example, I roll $4,1,3,5,6$ and record the number $4+1+3+5+6=19$. Call this sum $S$. Find the standard deviation of ...
3
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1answer
178 views

The probability of obtaining at least one roll of x from k dice each with a different number of faces

Assume you have k dice, each with some random number of sides, 1...n. I'm trying to figure out, after rolling all k dice, what is the probability of obtaining at least one roll with a given value x - ...
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7answers
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New to probability - Is this true?

I read this somewhere and can't find it to verify: "If you don't have a dice with 12 sides, but do have one with 20 sides and you need to make rolls for 12 sides, you can use the numbers 1-12 on the ...