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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1answer
309 views

what is probability of throwing $n$ dice $m$ times to get at least one 6 for each dice

We have $n$, 6-face fair dice. At each time $n$ dice are thrown independently. I want to calculate the probability of number of times we should throw dices before having at least one 6 from each of ...
3
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1answer
194 views

Three dice having sides labelled 0,1,e,π,i,√2 are rolled. Find the probability of getting the product of the three results a real number.

Three fair 6-sided dice each have their sides labeled $0\,,\,1\,,\,e\,,\,\pi\,,\,i\,,\,\sqrt 2\,$. If these dice are rolled, the probability that the product of all the numbers is real can be ...
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2answers
134 views

Finding a Sicherman Trio of dice

For those of you unfamiliar with the concept of Sicherman dice, the idea is that you can have an alternate arrangement of numbers on the sides of a pair six-sided dice such that when the pair is ...
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2answers
99 views

Tower of dice - Abstracting a practical problem to a mathematical method

This question arose when playing yahtzee with some friends. Not entirely sure if I'm in the right area, but hope you can help. How many dice do you need to create a tower whose walls have the same ...
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1answer
713 views

if multiple dice are thrown, how can I calculate their variance and mean?

from my calculation if 4 6-sided dice are thrown: $$E[x] = 14.0 $$ $$E[x^2] = 207.66666.. $$ $$Var(x) = E[x^2]-(E[x])^2 = 11.666666666666657$$ would there be some general formula for a dice with ...
2
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1answer
212 views

Number of die rolls needed for average to converge to roll expectancy?

I'm aware there are similar questions, but I haven't been able to find what I'm asking. Say we have an $n$-sided die, labeled with 1 thru $n$ and roll it $N$ times. We take the average, call it $m$. ...
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2answers
109 views

Why does multiplying n by a random number give you a random number between 0 and n?

I have been following the tutorial at Codecademy I see that, as part of the process of creating a virtual die we multiply 'a random number between 0 and 1' by 6 to give us a random number between 0 ...
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3answers
311 views

probability of A dice with X faces beating B dice with Y faces

I am looking for a formula to determine the probability of a A Die with X faces rolling higher than B die with Y faces. An example would be: what is the probability of 4d10 rolling greater than 3d12 ...
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1answer
3k views

Variance of a random variable representing the sum of two dice

$\newcommand{\Var}{\operatorname{Var}}$ The formula for the variance of the sum of two independent random variables is given $$ \Var (X +X) = \Var(2X) = 2^2\Var(X)$$ How then, does this happen: ...
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1answer
2k views

Variance and Standard Deviation of multiple dice rolls

I'm trying to determine what the variance of rolling $5$ pairs of two dice are when the sums of all $5$ pairs are added up (i.e. ranging from $10$ to $60$). My first question is, when I calculate the ...
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2answers
735 views

Probability that the sum of all values of 5 pairs of dice will be between 30 and 40

I'm trying to solve a question that asks: If 5 pairs of fair dice are rolled, approximate the probability that the sum of the values obtained is between 30 and 40 inclusive. My approach so ...
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1answer
379 views

“8 Dice arranged as a Cube” Face-Sum 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 ...
0
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1answer
147 views

Independent random variables, throwing dice

We are throwing tetrahedron dice (like in board games) $n>0$ times. Let X and Y denote minimum and maximum from the results respectively. For what $n,k$ variables $(X \mod{k})$ and $(Y\mod{k})$ ...
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1answer
154 views

Probability - Average value of the sum of 3 bigger dices in 4 throws (D&D)

There is a certain game based in a D&D mechanics in which the player throws 4 perfect dices and sums the three bigger values to obtain his score. Which is the average value to be obtained after ...
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1answer
160 views

Probability of getting any number if I roll the die 4 times.

We have a question to investigate any game between two players that have dice, when the dice are rolled $4$ times what is the probability of getting any number say $4$ or $5$.. note that the highest ...
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3answers
1k views

What is the average of rolling two dice and only taking the value of the higher dice roll?

What is the average result of rolling two dice, and only taking the value of the higher dice roll? To make sure the situation I am asking about is clear, here is an example: I roll two dice and one ...
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3answers
408 views

What is the probability on rolling $2n$ dice that the sum of the first $n$ equals the sum of the last $n$?

The Question What is the probability, rolling $n$ six-sided dice twice, that their sum each time totals to the same amount? For example, if $n = 4$, and we roll $1,3,4,6$ and $2,2,5,5$, adding them ...
2
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1answer
93 views

Help with probabilities on a game I am making

I asked over at the RPG stack exchange and they sent me here. I am working on making a RPG and am trying to understand the statistics of the core mechanic so I can determine how effective leveling ...
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3answers
768 views

Probability of rolling 5 dice?

Say you picked $\{4 5 2 6 5\}$ to show up in the dice rolls. You win if you have 3, 4, or 5 numbers in the correct sequence. 3 numbers in correct sequence would be; $\{4 5 2\}$ OR $\{5 2 6\}$ OR ...
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2answers
1k views

Expected sum if a fair die is rolled continuously

The problem statement is : What sum can I expect in rolling a fair die n times? How to determine the mean in a convenient way? Consider the fair die is 6 sided
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1answer
108 views

Probability - Tales Game

A dice game played by two players is like this: each player throw two dice and sum theier results; that is the number of points the player scored. Whoever scores more, wins. One additional detail is ...
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2answers
96 views

Craps game probability

Given 1 roll in a game of craps, a win is if, the sum of outcomes on a fair pair of dice is 7 or 11, otherwise you are said to crap-out . Compute the probability of a win on just 1 roll? Im second ...
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1answer
887 views

Probability of predicting, then throwing, a particular multiset for 5 dice.

My friend shared with me a story that after losing to his SO at Yahtzee, before they put the game away he just randomly predicted he would roll four 5's and a 1. He then got that roll and freaked out. ...
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2answers
649 views

Problem about $n$ six-sided dice and the sum of the values

(AHSME 1994) When $n$ standard six-sided dice are rolled, the probability of obtaining a sum of 1994 is greater than zero and is the same as the probability of obtaining a sum of $S$. What is the ...
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3answers
2k views

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 ...
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3answers
200 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 ...
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1answer
170 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. ...
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3answers
165 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 ...
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2answers
3k 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?
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1answer
117 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 ...
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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 ...
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3answers
622 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 ...
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3answers
2k 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
2k views

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
11k views

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
178 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?
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3answers
319 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 ...
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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 ...
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2answers
155 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 ...
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4answers
595 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
949 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 ...
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2answers
476 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
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2answers
330 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??
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1answer
355 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 ...
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1answer
686 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 ...
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1answer
92 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 ...
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1answer
116 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 ...
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2answers
268 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 ...