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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Probability of a dice being in a set of dice

I have no formal background in math, statistics, or anything. Just trying to figure out a fun problem with a game of dice. Lets say you have 3 people sitting a table rolling dice (including ...
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3answers
59 views

Probability Puzzle: Mutating Loaded Die

Take an (initially) fair six-sided die (i.e. $P(x)=\frac{1}{6}$ for $x=1,…,6$) and roll it repeatedly. After each roll, the die becomes loaded for the next roll depending on the number $y$ that was ...
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2answers
57 views

What is the best strategy for this dice game?

Given the following game, what is the best strategy to maximize your total score? Each game play starts with a random point value. You are then given a chance to multiply that value by choosing ...
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3answers
92 views

Expectations and variance with rolling a dice 10 times

Let's say you roll a fair dice 10 times and X is the number of sides that never show up. (i.e. Roll 1 - 10 = 1424145221, X = 2 because 3 and 6 never show up) Values of $N=0,1,2,3,4,5.\\ P(N=6) = 0$ ...
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2answers
28 views

clarify basic probability question

You have a loaded die. $A =$ even numbers $B =$ odd numbers $P(A)=3/4$ $P(B)=1/4$ $P(\{1\})=1/12$ $P(\{2\})=1/4$ How was $P(\{1\})$ and $P(\{2\})$ calculated? Is it beacuse there are 3 odds ...
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1answer
76 views

Analysis of “Tiny Dice Dungeon” (I)

Consider the following one-player game: Initially, there is a pot of $\$0$. On each turn, the player may opt to end the game and collect the contents of the pot, or roll a single die. In the latter ...
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1answer
30 views

Conditional Probability in Dice

Please forgive me if this is an easy question, because I have never had a class in probability. Lets say two people are each going to roll a D6 to determine who is going to go first in a board game. ...
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1answer
281 views

Highest average value when rolling dices

This question is in reference to a game called "Tiny Dice Dungeon." In this game, damage is calculated based on rolling dice. I want to know how I can achieve the highest average damage. This is the ...
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1answer
45 views

What are the chances of getting at least 3 fours when rolling 5 dice?

What are the chances of getting at least three or more "fours" or higher number when rolling a fair six-sided die five times? Actually, this is a problem I am curious about the answer and I can't ...
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2answers
38 views

Six dice, six different figures (model problem)

I am thinking about the same problem as posted here: Probability question (Six dice). If one rolls six dice, what is the probability of attaining six different figures. I do understand the solution ...
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1answer
44 views

probabilities for obtaining 3 dice result

I am developing an app that needs a 3 dice result and there are two methods I can use: method a) create a matrix of 216 possible combinations and choose 1 randomly method b) or generate 3 ...
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2answers
104 views

Sum of 3 dice rolls

If we roll a fair dice 3 times, what is the probability that the sum of values of the three rolls is greater than 9? I approached it like this: Let X be the result of a single dice roll. Let Sn = X1 ...
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35 views

Chance of rolling at least five 3s on fifteen dice [closed]

What is the formula to calculate rolling fifteen dice and at least five of them show 3?
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1answer
28 views

Variance of a modified sum of dice rolls

Suppose one rolls 3 (fair) dice with 20 numbered faces and sum the results. Call that sum $X$. The distribution will resemble a normal distribution with mean $3\cdot 10.5=31.5$ and variance ...
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3answers
46 views

Are the number on the dice placed on these sides for a reason?

To further explain the title: Is there a probabilistic reason as to why a 6-sided die has the opposing sides suming to 7? My argument begun when a friend decided to use this die instead of this die. ...
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0answers
54 views

On an average How many times must I throw $r $ die with $N$ faces, such that I see all $N$ faces?

For an $n$-sided die, the number of rolls needed, on average $n\log n$ for large n. For one die the question is here: "A Collection of Dice Problems" by Matthew M. Conroy. What about $r$ dice?
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5answers
135 views

game theoretic die rolls

Suppose player X has a 6 sided die and player Y has a 10 sided die. They each get two rolls and they can each choose to stop rolling on either one of the rolls, taking the number on that roll. Whoever ...
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1answer
84 views

How Many Permutations of Die Rolls Add Up to a Fixed Total?

I'm toying around with the idea of designing a board game. I like the idea of a hexagon-tile setup (a la Catan). There would be some number of different resource categories; I'm trying to determine ...
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2answers
35 views

Probability of obtaining equal number of each outcome of a fair die at the nth trial

Suppose a fair die is tossed repeatedly. I am concerned in deriving the probability of the occurrence of obtaining equal number of each possible outcome at the nth trial. Clearly this is only possible ...
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1answer
50 views

What is the chance of this dice appearing twice in a row? [closed]

3 friends roll a 6-sided dice. What is the probability that any of them roll the same number?
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1answer
80 views

Probability of rolling 3 sixes in 6 rolls

I roll a dice six times. What is the probability of rolling at least 3 sixes? Please share the formula as we'll, so I can figure it out myself in future. Many thanks!
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3answers
58 views

Strange Dice probability

I started a discussion with some friends trying to understand: if I roll 1 dice of 10(1d10) and 1 dice of 4(1d4) 20 times, and do it again 1000 times. Why the d4 have the probability to score the ...
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1answer
143 views

A fair dice is tossed 6 times. What is the probability that there is at least one pair of identical consecutive face values?

For example, 231146 is a valid sample point but 131213 is not. This is a question on past exam that i have no idea to solve. Please help me!
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2answers
56 views

Rolling a balanced die 10 times

A balanced die is rolled 10 times by 5 different people. What is the probability that at least two people rolled exactly 4 twos, 3 fours and 3 sixes? So I know I'm looking for $P(X\ge 2)= ...
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1answer
40 views

Expectation of conditional event for throwing a fair dice

A fair die (with face numbered $1,\ \ldots\ ,6)$ is independently rolled repeatedly. Let $X$ denote the number of rolls till an even number is seen and let $Y$ denote the number of rolls till $3$ is ...
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37 views

Probability of 3 dices

Been looking through past exam papers and came across this question: Three fair dices are rolled. The probability that all three dices show 5 is 1/216. Is this true?
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1answer
112 views

Best strategy for rolling 20-sided and 10-sided dices

There are a 20-sided (face value of 1-20) dice and a 10-sided (face value of 1-10) dice. A and B respectively roll the 20 and 10-sided dices. Both of them can roll the dice twice. They may choose ...
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1answer
81 views

Roll 2 dice adding and rolling one die, probability of being equal

Roll two dice, add the results, call the number x. Roll one die call that number y. What is the probability that x and y are equal? Help please.
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1answer
64 views

How many times to roll a die before getting $n$ consecutive sixes given $m$ occurences?

Given a unbiased dice how to find the average number of rolls required to get $n$ consecutive sixes given already $m$ number of sixes occurred where $m\leq n$. I know how to solve using n consecutive ...
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2answers
105 views

Number of dice rolls taken to reach a certain sum

I was reading about sums of dice rolls and Chernoff bounds, and I thought of a question I couldn't obviously answer with the techniques I know. You're given some number $x$ and told it was generated ...
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1answer
53 views

Probablility of a Dice Game

Player A rolls $m$ dice, while Player B rolls $m + 1$ dice. If Player A rolls $a$ $n$'s and Player B rolls $b$ $n$'s, then Player A wins if $a > b$ . Otherwise, Player A rolls up to $k$ of the $m$ ...
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1answer
30 views

Changing Faces of Six-sided Die to replicate the probabilities of a normal pair?

So, in my computer science class, we are given this problem here: Is it possible to modify the faces on a pair of conventional six-sided dice so as to exactly replicate the probabilities of a ...
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3answers
72 views

Die roll, value of 4 must follow value of 1 to win

I came across a "die roll" probability question that has me stumped. Two fair die are being rolled by players A and B, who alternate, with A rolling first (ie. A then B then A then B...so long as the ...
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2answers
76 views

Finding the coefficient of a generating function

Given $f(x) = x^4\left(\frac{1-x^6}{1-x}\right)^4 = (x+x^2+x^3+x^4+x^5+x^6)^4$. This is the generating function $f(x)$ of $a_n$, which is the number of ways to get $n$ as the sum of the upper faces of ...
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1answer
62 views

Probability Dice Game Question

I have the following problem to solve that deals with probability (something I haven't done since Grade 8 (6 years ago)) This is a one player game and it is described for $q$ sided dice. You start by ...
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1answer
26 views

Calculating probability of a dice with different numbers [duplicate]

I was given a problem in class: ...
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1answer
217 views

Probabilities of rolling a fair die twice?

a) One of the dice is a 4 b) Sum of the dice equals 4 c) Neither dice is a 4 I get really confused with these exercises (I don't know why)
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1answer
32 views

Probability of occurrence vs. Probability of x successes

I've been reading for two hours and I'm having a hard time getting the grasp of these two concepts. I'm developing a tool for a game, in which I'm given n dice and a success threshold (ie. roll at ...
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1answer
75 views

Probability of a tetrahedron (die with 4 faces)?

I have been doing some questions from an exam review with no solution and I have no idea how to work this problem. I know that $Pr(A_1) = \frac{1}{2}$, $Pr(A_2) = \frac{1}{2}$, $Pr(A_3) = ...
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1answer
42 views

$95$ percent confidence interval for roll of two dice

Given a roll of two fair six-sided dice, we know the expectation for a specific result (e.g. a $4$ and another $4$) is $\frac{1}{36}$. But with what certainty could you expect that result in $N$ ...
3
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1answer
98 views

Expected duration of a die game

In a 2 person game, the player who first obtains a $6$ wins. I'm trying to determine the expected number of die rolls needed before a winner is determined. (One turn consists of two die rolls, ...
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2answers
140 views

Probability of always rolling 6 on a dice

Suppose I roll a six-sided die $10$ times and each time it shows a $6$. What is the probability of the next roll coming up $6$? You might say $1/6$. But it was never declared to be a fair die. In ...
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2answers
48 views

Consider throwing two six-sided dice. Let X be the sum of the two values and let Y be the product of the two values.

What is the value of $P(X = i, Y = j)$ for $i = 1,2,\cdots,12$ and $j = 1,2,\cdots,36$. Trying to figure out if there is a easier way to figure this out rather than writing out all the values.
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2answers
57 views

Consider throwing two six-sided dice.

Let X be the sum of the two values and let Y be the product of the two values. What is the value of P(Y = i) for i = 1,2,3...36. I am having trouble approaching this problem. We are learning about ...
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4answers
111 views

2 player dice game probability

For some homework in one of my classes, we are given this problem: In a certain dice game, player $A$ rolls six six-sided dice vs. player $B$ who rolls nine four-sided dice. Each player rolls ...
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2answers
480 views

Rolling two dice 10 times, what is the probability of getting all possible “doubles”?

Rolling two dice 10 times, what is the probability of getting all possibble "doubles": (1,1),(2,2),(3,3),(4,4),(5,5),(6,6) among our rolls? For instance, ...
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1answer
104 views

Dice Math, odds and probability

DISCLAIMER: This will be done with fake money for education purposes. I'm working on a Dice simulation site for a school project, where you play the house and you as a player have to get a higher ...
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1answer
140 views

Toss a die until SIX appears. E (number of ONEs | at leat one TWO) =?

A fair die is tossed repeatedly until a Six appears. Let $X$ denote the number of One's that are thrown in this game/experiment. Let $A$ denote the event that at least one Two was thrown. Compute$ E(X ...
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2answers
32 views

When the game is fair

One player throws dice twice. If he has 2 x 6 on the dice he is receving 8*a. If he has one 6 he will collect 4*a. Otherwise (when he has no 6 at all) he is paying a. For which value of a game is ...
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2answers
131 views

What is the theoretical expected value of the sum of the highest 3 values of 4 fair dice?

Many have estimated the expected value of the common "4d6, drop lowest" roll or averaged a complete enumeration of the possible outcomes. I would like to know the theoretical expression of this value, ...