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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Expected number of different faces in multiple die roles

I roll 6 6-sided regular dice. What is the expected number of unique up-facing sides I will find among those dice?
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2answers
246 views

Rolling dice Probability that Sum

If 10 pairs of fair dice are rolled, approximate the probability that the sum of the values obtained (which ranges from 20 to 120) is between 30 and 40 inclusive. I dont know where to start with this ...
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1answer
263 views

What are fair point values for Zombie dice?

Described below is a modified version of Zombie dice ( http://www.sjgames.com/dice/zombiedice/ ) which the kids and I play. As in the original game, the idea is to sequentially roll sets of 3 ...
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1answer
320 views

Statistics question on probability

Suppose that one hundred fair dice are tossed. Estimate the probability that the sum of the faces showing exceeds 370. Include a continuity correction in your analysis.
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3answers
112 views

Probability of a dice game

Here is my question... n players playing a dice game which any of them who trows a 6 the game is over and he wins. They do it 1 by 1 .So what is the probabilty of winning for any 1 of them ? My ...
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2answers
76 views

Three equal die rolls in a row in a $3\times 3$ array

If 9 six-sided dice were rolled consecutively and displayed in a $3\times3$ format, what is the probability of a line of 3 of the same number occurring? Considering the 8 ways that are possible; 3 ...
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2answers
160 views

Probability of winning blackjack dice game?

I know a little bit about probability but I am not sure how to calculate this: In a dice game of blackjack, there are two parties. The player and the dealer. The aim of this game is to get as ...
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2answers
1k views

Solve for numbers to appear on two six-sided dice

I have a small wooden calendar that uses two six-sided dice to display day of month. One die carries numbers 0, 1, 2, 6, 7, 8 and the other carries 0, 1, 2, 3, 4, 5. The six of course doubles as the ...
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1answer
1k views

Dice question: Probability of rolling at least 2 of 3 dice with score 3 or less

my first post here. I've recently gotten back to boardgaming (Labyrinth: The War on Terror in this case) and would like to get clear on the probability of various actions. I've learnt about 'basic' ...
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1answer
91 views

Dice game modelling: Lose everything on “3”, double everything on “1” or “6”

I was recently playing a quite easy dice game: You trow a fair dice: if you get a "3" the next player continues, if you get something else it is up to you to continue. If you continue and you throw ...
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1answer
50 views

Finding range, partiton and finding the dependency of a random variable

How to do this question part (a) range(X) =(2,3,4,5,....12) right the range is usually from 2 to 12 range(y) =(2,3,4,5,6) the range is usually from two to 6 right? range(z) = (0,1,2,3,4,5) ...
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5answers
5k views

Probability of rolling three dice without getting a 6

I am having trouble understanding how you get $91/216$ as the answer to this question. say a die is rolled three times what is the probability that at least one roll is 6?
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1answer
152 views

Two dice roll questions related to rolling a Yahtzee

I watched a video on youtube which stated the probability of rolling a yahtzee in a single roll (same value on 5 six sided dice) before 1296 rolls is 63%. The probability of rolling a yahtzee on any ...
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2answers
109 views

Yahtzee large straight strategy.

I've recently got into playing Yahtzee with my brother. During a game we had on my first roll for my last round I got (5 4 4 2 1). I only had my large straight left, so naturally I was hopeful with ...
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3answers
46 views

probability proof requiring conditional probability

Consider the experiment where two dice are thrown. Let $A$ be the event that the sum of the two dice is 7. For each $i\in\{1,2,3,4,5,6\}$, let $B_i$ be the event that at least one $i$ is thrown. ...
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1answer
2k views

Rolling 2 fair, 6 sided dice find P(sum=12, 2times in 36 rolls)

I have a dice problem. If we roll 2 fair dice, and the sum is 12 then our test is a pass, otherwise its a fail. What is the probability that the number of passes in 36 tests is greater then 1. ...
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2answers
71 views

Probability of a unplayable layout in a boardgame

I was at the store the other day and saw a game called Rubik's Race. The game consist of: two 5x5 sliding puzzle boards each populated with 4 tiles of each of the 6 colors of a Rubik's cube, 9 six ...
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1answer
89 views

Rolling 5, 6 sided dice where top 3 equal 15. How many rolls? How in Recursion?

Let's say that I have 5 (n), 6-sided (d) normal dice. How would I figure out how many possible rolls there are, where the top 3 (k) numbers rolled, equal 15 (t)? How would I do this using recursion ...
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2answers
129 views

Choosing between $n$ things using dice?

For which $n$ is there a finite algorithm to choose between $n$ things with the same probability using a die? For example, we can choose between 2 things, 3 things, 4 things, 6 things, and 8 things, ...
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1answer
228 views

What's the optimal strategy of this dice game?

I'm working on dynamic programming problems this week. The following is a dice game. I'm trying to find the optimal strategy using dynamic programming. The game's description : The player rolls ...
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2answers
306 views

What's the optimal strategy of this dice game?

I'm working on a dynamic programming problem. I want to find the optimal strategy and simulate it. The game's description: The player rolls two dice. If the numbers shown by the two dice are ...
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1answer
113 views

Probability of A given B & C?

I would like to sum the probability that given 3 (potentially biased) die rolls, all 3 rolls will be different-- what is the correct way to do this? So far, I have: $$ 1 - ...
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2answers
493 views

Probability of dice double - why not count duplicates?

What is the probability of getting double dice? (one throw) All possible dice rolls are 36 (counting even rolls like 1-4 and 4-1). But when counting the doubles, why not count 1-1 twice, for ...
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2answers
2k views

Probability, Expected Value and Variance of a Dice Roll

Roll 5 fair six sided dice. Let X be the number of sixes. 1) Find $\ P(X=2)$ 2) Find $\ P(X <= 1)$ 3) Find $\ E[X]$ 4) Find $\ Var(X)$ I've been able to find the first two answers on ...
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1answer
121 views

Find E[N]. (Absorbing States MC)

Assume we toss a dice until odd number appears four consecutive times, and in such a case we stop the game. Let $N$ be the total number of times we will toss the dice. Find $E[N]$. Lets say for ...
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1answer
273 views

Probability problem of dice game

I heard a problem from a riddle book: $A$ and $B$ roll two standard dice and record the sum of two numbers. $A$ wins when two consecutive outcomes are $7$ and $B$ wins when three consecutive outcomes ...
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0answers
138 views

probability of rolling at least $n$ on $k$ 6-sided dice

Is there a simple form for the probability of rolling at least $n$ on $k$ 6-sided dice? Of course you can do it by recursion (see here). But is there a way to do it with just a few binomial ...
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2answers
271 views

Multiple dice rolls (D&D Skill challenge)

In Dungeons and Dragons there is something called a skill challenge, which involves rolling some dice (no surprise there). An example of a skill challenge: Skill challenge DC 25 thievery. Roll a d20* ...
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2answers
72 views

What are the probabilities in this particular spin-off of BlackJack

A few of my friends are playing on a gaming server where this game exists. I was curious about the probabilities in it but i was unable to derive them. Any help would be MUCH appreciated. Note: For ...
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1answer
3k views

Probability of rolling the same number twice

Math novice here. With a 10-sided die, the probably of rolling '1' is 10%. I'm tempted to think the probability of rolling '1' with two consecutive rolls is 20%. Would I be correct? Not sure if I ...
5
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1answer
282 views

What are the probabilities of a tie when rolling to see who goes first in a board games for various numbers of dice and various numbers of players?

When playing many board games, the first step is to have everyone roll a die to see who goes first, with a roll off in the case of a tie. While doing that over the Christmas break, my husband ...
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1answer
199 views

Probability of a certain dice roll sum disregarding lowest rolls

The number of ways to obtain a total of $p$ in $n$ rolls of $s$-sided dice is: $$c=\sum_{k=0}^{\lfloor(p-n)/s\rfloor}(-1)^k\binom{n}k\binom{p-sk-1}{n-1}\;.$$ What I'm interested in is making the $n$ ...
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3answers
2k views

2 heads or more in 3 coin toss formula

what is the formula to calculate the probabilities of getting 2 heads or more in 3 coin toss ? i've seen a lot of solution but almost all of them were using method of listing all of possible ...
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2answers
85 views

Probability distribution of number of times required to roll all of a certain set of k numbers?

Consider a 12-sided fair die. What is the distribution of the number T of rolls required to roll a 1, a 2, a 3, and a 4? Taking inspiration from the Coupon Collector's Problem, I believe that the ...
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1answer
150 views

Determine the probability the number $j$ will appear $n_j$ times when $n$ dice are rolled

Suppose that $n$ balanced dice are rolled. What is the probability that the number $j$ will appear exactly $n_j$ times $(j=1,\ldots,6)$, where $n_1 + n_2 + \cdots + n_6 = n$? I have derived two ...
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1answer
169 views

Probability of a fair die appearing to be biased

I'm interested in the probability of a die appearing to be biased when it is, in fact, fair. I'm trying to derive a result given, without proof, on YouTube: http://youtu.be/6guXMfg88Z8?t=1m29s The ...
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1answer
186 views

Why is the best position for LCR not the last person?

For the uninitiated, LCR is a game in which each player starts with three "tokens" and rolls up to three dice (at most as many as tokens they have). Each die has three sides which indicate that ...
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2answers
288 views

What is the most unfair set of three nontransitive dice?

In a set nontransitive dice, each die is superior to another die, but is inferior to a third. It is similar to the game of rock-paper-scissors. Here is one example: ...
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2answers
147 views

Question about an 8 sided die

I have a question about an 8 sided die problem. I will put up my work what I have if someone can tell me how to proceed I will appreciate it. We roll an 8 sided die numbered 1 to 8 six times and ...
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1answer
706 views

“$n$-Yahtzee” question

Suppose that you have $n \geq 1$ standard 6-sided dice. If all the dice display the same number, we call this an $n$-Yahtzee. Follow this algorithm: Roll all the dice. Set aside those dice with ...
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1answer
218 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 ...
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1answer
173 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
109 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
86 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
421 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 ...
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1answer
171 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
102 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
199 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
2k 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
1k 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 ...