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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.

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1answer
23 views

Dice counting problem

Six standard 6-sided dice are rolled, and the resulting numbers are multiplied together. What is the probability that the product is divisible by 125? I know that at least 3 of the dice have to be 5'...
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0answers
34 views

Probability every dice side appears at least once [on hold]

Formulation: We have a dice with N equal sides. We throw it K>N times. What is a probability every side of the dice appears at least once? P.S. if this is the solution - I don't understand how it ...
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2answers
33 views

Probability of getting a number in 4 throws of a dice

Lets say we are rolling a fair 6 sided dice 4 times and recording the number we get after each roll. What is the probability of getting a number $m$ with $m\in \{1,2,3,4,5,6\}$ say one or four times; ...
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2answers
47 views

A four sided die (tetrahedron) and a $6$ sided die (cube) are rolled together. [on hold]

A four sided die (tetrahedron) and a $6$ sided die (cube) are rolled together. The values on the bottom of each are observed. What is the probability of a $1$ or $3$ being rolled, but not both?
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1answer
39 views

Three different dice which should I choose? [on hold]

Alice brought three of her own dice (red, yellow and blue) and she wants to play a game in which you will always play with die you chose at the beggining. In each round the winner has the highest ...
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1answer
18 views

Expected value in a dice game

Consider two people, person $A$ and person $B$. Person $A$ has a $30$-sided dice and Person $B$ has a $20$-sided dice. Both players roll and the person with the highest roll wins. The loser pays the ...
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1answer
31 views

Sum of m dice rolled n times where sum of each dice is lower than some value

Let there be $m$ dice (not neccessarily all same-sided, but even when they are I don't have a solution). Each dice is rolled $n$ times. The sum of $n$ rolls of all dice needs to be $T$. The sum $X_i$ ...
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3answers
1k views

Seemingly tricky dice question-probability that one event occurs before another event?

The question is as follows: You roll two fair dice over and over. Let $A$ be the event you see two even sums. Let $B$ be the event you see a sum of $7$ four times. What is the probability that ...
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2answers
32 views

Probability with 3 dice

My friends and I play a dice game with three dice. One of the winning combinations is 4-5-6. Which can be made with any of the dice as long as the sequence comes via any of the three dice. I ...
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3answers
46 views

Guessing the sum of $10$-sided die and a $6$-sided die

Consider two dice. One $10$-sided, one $6$-sided, both fair. Guess a number between $2$ and $16$, if the sum of the dice shows that number, you get that number of dollars. What is the best number to ...
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2answers
430 views

Probability that in one rolling of 5 dice we obtain two '6' and one '5'?

First I made a mistake of not taking into account that this event is dependent. So to get two '$6$' the probability would be: $$ P_5(2) = \frac{5!}{2!(5-2)!} \cdot \left(\frac16\right)^2\cdot\left(...
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0answers
58 views

Dice game - how do find the expected number of rounds?

I've been struggling trying to find an analytical solution to this problem. Let's say we have a dice game, played with n players rolling n, k sided dice, with k >= n. The dice determine the order of ...
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2answers
27 views

What are the odds of rolling a 1 and a 20 in two d20 dices?

So, one of these days a friend of mine rolled two d20 dices and got a 1 in one of them and a 20 in the other. I was thinking, what are the odds of this happening?
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1answer
33 views

probability of false alarm for a loaded die

A loaded 6-sided die has probability 1/4 for 3 & 4 and 1/8 for 1,2,5,6. If i decide whether a die is loaded or not based on one roll what is the probability of falsely classifying a fair die as ...
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1answer
38 views

Expectation and variance of iterated dice rolling

For the rest of the post, we'll assume when I say "die" or "dice" that I mean a standard 6-sided die or some number of standard 6-sided dice. Suppose I roll a die and get a number $n$, and then I roll ...
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1answer
15 views

Variance of rolls needed for rolling a 6

I have an random variable that counts the number of dice rolled until I rolled a 6. Let's call it $X$. I understand that $E[X] = {1\over 6} \sum n({5\over 6})^n = 5$ I wonder, though, how to find ...
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3answers
661 views

Probability of 2 Dice Throws Equal to Sum

I'm aware this is a very simple question, I must be missing something obvious. Given that the numbers coming out of two independent dice throws are different, find the probability that the sum of ...
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3answers
3k views

Chances of rolling “Snake Eyes” at least once in a series of rolls.

So I know that if you roll a standard pair of dice, your chances of getting Snake Eyes (double 1s) is $1$ in $36$. What I'm not sure of is how to do the math to figure out your chances of rolling ...
6
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1answer
134 views

Dungeons and Dragons: Ability Score combinations

I am trying to figure out how likely it is to roll a certain combination of 6 ability scores in Dungeons and Dragons. edit: Dungeons and Dragons is a tabletop role-...
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1answer
33 views

Dice Expected Value - Game of chance [closed]

Suppose you repeatedly roll a fair six-sided dice until you roll a 1 (and then you stop). Every time you roll a 2, you lose x points, and every time you roll a 6, ...
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2answers
50 views

Advanced Dice Probability: 3d6

I know how to calculate basic probabilities: 1 in 6 x 1 in 6 = 1 in 36, for example; and 1 in 36 x 1 in 6 = 1 in 216. However, I have forgotten, and cannot find instructions for, how to calculate for ...
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2answers
79 views

Strategy to get high score in 2 dice game.

In this game numbers are added to a list, the sum of all the numbers in the list at the end of the game is your score. The game consists of 10 rounds, in each you roll 2 (6-sided) dice and choose one....
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2answers
77 views

70 6-sided dice Question re: Gaming

I play a game where a d6 (a regular, fair 6 sided die) is used to determine whether or not a weapon hits an opponent's vehicle. There is one possible scenario where the attacker can roll 70d6 in one ...
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0answers
23 views

Compararive Dice Probabilities across 2 sets with negation

I am working on proving that 2 dice sets are radically different in terms of favourable outcomes in a scenario involving concepts that negate certain results. For the purposes of this exercise, we ...
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13answers
2k views

Intuition: Why chance of getting at least one ace when rolling a dice six times is not close to $1$?

So probability of getting $1$ ace (the one dot in dice) = $1/6$ i.e. in one out of six times we will get an ace. But when we calculate the probability of getting at least one ace in six rolls, we get ...
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2answers
70 views

Explanation for counter-intuitive discrete probability results

Suppose there're two players $A$, $B$ playing a dice game, $A$ has a normal dice whose faces are numbered 1 to 6, $B$, on the other hand, has a (regular) icosahedron dice with faces numbered 1 to 20. ...
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0answers
43 views

How many times to roll a die before getting two consecutive sixes.

Andre Nicolas provides a nice solution to this problem in the link below but I am confused by one step: How many times to roll a die before getting two consecutive sixes? I have pasted his solution ...
1
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1answer
29 views

Conditional probability with two fair dice

You roll two fair $6$-sided dice. Given at least one of the rolls is a $4$, what is the probability that the sum is even? I feel like one could approach this problem using probability laws or Bayes' ...
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0answers
16 views

Three dices are rolled, what is the intuition behind 6**C**3? [duplicate]

When three dices are rolled why the number of ways we can get 1st dice> 2nd dice>3 dice is defined by 6C3? I get it that there are 3 coins and we can get 6 on each coin, but how does 6C3 ...
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1answer
75 views

Probability of increasing order of a $3$ rolls of a die. [closed]

A six-sided die is rolled three times. What is the probability that the value of every next roll is greater than the value of the previous one?
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5answers
791 views

Guessing the other dice number, given two dice were rolled, and one of them rolled a 3

An argument i had with a friend followed this question: "Given two dice were rolled, and one of them rolled a 3. What would you bet the other dice rolled?" The phrasing is just to enhance that there ...
2
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1answer
53 views

Having problems seeing how two events are conditionally independent (Craps dice game)

Background: $$\text{Show}: \quad E[R\mid\text{win},S=4] = E[R\mid S=4]$$ where $R$ is the number of rolls of the dice in a game of craps $S$ is the initial sum and for this question let's say it's $...
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1answer
28 views

Probability of getting x dices with the same numbers of n dices thrown once together

There are 6 dices, where each dice consists of 6 values (1,2,3,4,5,6), they are all thrown once at the same time, what is the probability of getting three pair dices with the same numbers shown i ...
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0answers
31 views

Does the probability of rolling a specific 3 digit number [including permutation] with 3 dice change if that specific number has a double or triple?

Is there a difference in probability when rolling a specific number with 3 dice [with permutation] of the specific number digits are unique, doubles or triples? In other words is the probability of ...
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0answers
27 views

Probabilities of a complex dice-game

Intro I am currently developing a board-game and am trying to balance things around my dice-mechanic, but for that I need the probabilities of the outcomes and after countless fruitless hours of ...
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1answer
21 views

Confidence interval on 2 dice rolls

Lets say we are rolling 2 dice of different sides. Example: Dice 1 has 128 sides and Dice 2 has 256 sides. I created a 2D array of size 128X256 to bin the result of dice1,dice2 combination. If it is ...
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2answers
43 views

Formula for how many possible end states any number of 6 sided dice throw can result in?

I want to create a board game where you throw dice to determine where you land on a matrix of tiles. The problem is I want to find out how many dice would be optimal for a fair chance of landing on ...
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1answer
39 views

What are the symmetries of a Trigonal trapezohedron?

The asymmetric version of a Trigonal Trapezohedron is supposed to be a fair die just like a cube, meaning I can start with one face and rotate it about the center of the solid to get each of the other ...
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2answers
43 views

The expected value of $C$ is equal to $\frac{a}{b}$ for coprime positive integers $a$ and $b.$ What is $a+b?$

A fair, $6$-sided die is rolled $20$ times, and the sequence of the rolls is recorded. $C$ is the number of times in the 20-number sequence that a subsequence (of any length from one to six) of rolls ...
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1answer
39 views

Name the problem: Numbers of dice throws to get result with rerolls allowed

Here is the problem: You have N dice of size D. You throw all dices, then for each dice: if a dice face is ...
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2answers
108 views

Interview Question on Probability: A and B toss a dice with 1 to n faces in an alternative way

A and B toss a dice with 1 to n faces in an alternative way, the game is over when a face shows up with point less than the previous toss and that person loses. What is the probability of the first ...
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votes
1answer
50 views

Why variance is not squared before scaling for rolling dice problem?

I am trying to calculate mean $E[Y]$ and variance $Var[Y]$ of sums, when rolling a dice of 6 outcomes $(1,2,3,4,5,6)$, 10 times. I get the mean as below. Mean of sums for 10 tosses $ Y = 10X, \\ \...
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0answers
32 views

Calculate no of sequences with sum k, out of die toss n times, with die having m outcomes

I am trying to calculate total no of sequences possible with given sum k, out of a die (with m outcomes), tossed n times. I could go after each combination, but $m^n$ grows very large quickly, so ...
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1answer
25 views

Probability Question with 2 rolls

I have a probability question. Say that there is a 2% chance of something occuring and then a 1d5 (20%) of it being a critical success. So technically its a 0.4% chance of a critical success. If ...
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0answers
30 views

How to find solution to a nontransitive dice problem

The problem is following: given two dice with numbers between 1-6 (but the same number can repeat in the same dice), find a third dice such that the three dice form a nontransitive set of dice, i.e. ...
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1answer
23 views

Calculating probability of High+Low = T on N dice with S sides

I'm trying to create a little tool for comparing dice roll probabilities (for table top gaming). I've got a way of calculating "Roll $n$D$s$ pick highest" and "Roll $n$D$s$ and sum" (where $n$ is the ...
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1answer
41 views

Probability of throwing exactly $V$ distinct sides on $N$ sided dice by $K$ rolls

I'm struggling with finding a non-recursive formula for calculating the following probability: Probability of throwing exactly $V$ distinct sides (numbers) on $N$ sided dice by $K$ rolls Example for ...
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1answer
15 views

Checking to see if a Random amount of Dice are the Same

The motivation for this question comes from a simple program that I tried to write. The game is simple. I want to roll some dice. If all the dice are the same, then I win. If they are different, then ...
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2answers
24 views

Mean square convergence of number of 5s and 6s in dice throws

Let $N_n$ be the number of occurrences of 5 or 6 in $n$ throws of a fair die. Show that as $n\to\infty$, $$ \frac{1}{n}N_n\to \frac{1}{3}, \mbox{ in mean square.} $$ My thoughts so far: I order ...
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vote
1answer
48 views

Probability of Normal Dice

An urn has $100$ normal dice, plus $75$ dice whose face numbers are $2, 2, 4, 4, 6, 6,$ and plus $25$ dice whose face numbers are $1, 1, 3, 3, 5, 5$. One die was chosen at random. If I just rolled one ...