Questions tagged [dice]

For questions on dice, small throwable objects with multiple resting positions, used for generating random numbers.

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Calculating Expected Throws for All Die Faces to Appear Twice [duplicate]

I'm working on a problem where I need to find the expected number of throws required for each face of a six-sided die to appear at least twice. I've conceptualized the problem using a triplet $(a, b, ...
The One's user avatar
  • 834
1 vote
3 answers
134 views

A dice is rolled $7$ times. What is the probability the sum of the results is $14$?

In a certain exercise I am asked to find the probability of the event in which a dice is rolled seven times and the sum of the results is $14$, given the fact that the dize is regular (this is, the ...
Daniel C.'s user avatar
  • 1,227
2 votes
2 answers
70 views

Probability of *at least* k same specific digits in an n-digit sequence?

Given an n-digit integer sequence, e.g. $n=5$ [1, 1, 5, 6, 4] where each digit is independent and uniformly random in the range 1-6, what is the probability of ...
Martin's user avatar
  • 123
1 vote
2 answers
56 views

Expected value of a recursive dice game

Context: Consider a dice game that is played with a fair, six sided die. You are handed the die, and asked to roll. If you roll a 2, 3 or 5, then you take double the face value of the the roll, and ...
log x log log y's user avatar
0 votes
0 answers
20 views

Limit probability of a side of a dice showing up more than $p_i + \omega(\sqrt{n})$ times

Consider a dice $D$ with sides $\{1,\ldots,6\}$ and let $p_i$ be the (constant) probability of each side). Let further be $A_n$ the event that any side shows up more than $p_i + h(n)$ for $h(n) = \...
3nondatur's user avatar
  • 4,128
1 vote
1 answer
49 views

For me a difficult dice roll probability calculation

I'm not good with math which is why I'm turning to you here :) So, I'm preparing for a tabletop role playing game session and I'm not happy with the rules when it comes to character creation. The ...
binerkin's user avatar
3 votes
1 answer
94 views

Maximising Score in Dice Game

We are playing a game with a die where we roll and sum our rolls. We can choose to stop at any time and take the sum as our score, but if we roll the same face twice in a row (consecutively), we lose ...
Harsh's user avatar
  • 178
1 vote
2 answers
55 views

Probability of successfully deciding which of the two six-face dice (Fair and Rigged) was rolled?

Question statement: You are handed a dice which is either fair (all outcomes with probability $\frac{1}{6}$) or produces only the outcomes 2, 4, 6, each with probability $\frac{1}{3}$. If you can roll ...
Jared's user avatar
  • 13
0 votes
5 answers
86 views

If you roll a dice four times, what is the probability to get two consecutive threes?

I was reviewing brainteasers and this one is stumping me for some reason. Let X be a non-3. you have 3 cases. 33XX, XX33, and X33X where we have the successes. I suppose you also have 333X and X333, ...
jd_h2003's user avatar
  • 101
7 votes
4 answers
511 views

Infinite dice roll problem

The following is an interview question: Two players A and B play a game rolling a fair die. If A rolls a 1, he immediately reroll, and if the reroll is less than 4 then A wins. Otherwise, B rolls. If ...
Ria's user avatar
  • 183
4 votes
4 answers
143 views

Dice probabilities and stars/bars

I'm trying to apply stars and bars to answer a dice question: if $n$ players throw $k$-sided dice, what is the probability that exactly $i$ players throw a unique number (where $0 \leq i \leq n$)? For ...
Miguel Matador's user avatar
2 votes
1 answer
82 views

Expected sum of three dice if same value are cancelled

I came across with the problem of calculating the expected sum of two fair dice where if the two numbers are the same, the sum is zero. This can be done by simply summing all possible cases and then ...
Van Tom's user avatar
  • 93
7 votes
4 answers
244 views

Probability of subsequence 123456 in $n$ rolls, combinatorics approach?

I was trying to solve this problem: We roll a 6-sided die n times. What is the probability that all faces have appeared in order, in some six consecutive rolls (i.e., what is the probability that the ...
DeadKarlMarx's user avatar
2 votes
1 answer
55 views

Why are the Binomial and Poisson probabilities different for frequency of a successful dice roll?

Why do I get different results using a Binomial vs Poisson process for calculating the frequency of a successful roll of a 6 sided die? Should I get the same answer calculating the same scenario with ...
Frank's user avatar
  • 125
0 votes
2 answers
67 views

Probability of getting a total less than 8 from three dice given that the total when two dice are rolled is less than 4.

I've been struggling with this question involving probability and dice rolls: A die is rolled three times and the scores are added. The total obtained after it has been rolled twice is 4 or less. ...
Developer's user avatar
1 vote
1 answer
179 views

Probability of rolling each number at least once, if the die is rolled 10 times

Question: If you roll a $6$-sided die $10$ times, what is the probability of rolling each number at least once? My attempt: It is fair to assume that the probability of not rolling a number is $5/6$, ...
Roland Baki's user avatar
0 votes
1 answer
25 views

Creating a binomial die with constraints

I had an idea for making a custom 20-sided die that would have a binomial distribution of numbers printed on it, but I'm not sure exactly how to pick the numbers to put on the die itself. So we have a ...
ThePiachu's user avatar
  • 619
0 votes
1 answer
73 views

Distribution of the sum of points for non-standard dice

Question from my last exam: A cubic die is called fair if its sides are labeled with integers, and each side has an equal probability of landing face up. When multiple fair dice are rolled, the ...
Michał's user avatar
  • 665
0 votes
0 answers
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Highest score when rolling three of a kind to score

Here is the game: You are rolling 6 six-sided dice each dice has the faces: 1, 2, 3, X, X, X (X sides don't matter) After you roll them all once, you can choose to pick up one or more and reroll them....
Bromide's user avatar
  • 101
1 vote
1 answer
86 views

Mass Function for a Geometric distribution with two non-fail outcomes.

Let's say we roll a fair $d$-sided die, and if the die rolls $x$ or higher, we add 1 to the success count (let's define this as $h$) and roll again, but if we roll $y$ or lower, we subtract one from ...
Lee Davis-Thalbourne's user avatar
0 votes
0 answers
39 views

Probability that the maximum number of dice with the same face is k

Let say we have $N$ dice with 6 faces. I'm asking my self, what is the probability that the maximum number of dice with the same face is $k$? In more precise terms, what is the size of this set? \...
Lorenzo Vittori's user avatar
8 votes
3 answers
271 views

Rolling a dice until the average of the outcome hits a specific value.

I roll the dice until the average of the outcomes is $2.5$. Once the average is $2.5$, I will stop rolling. For example, if I get a sequence of 2, 6, 4, 1, 1, 1 outcomes, I will stop rolling the dice ...
Hyeonggyun Ko's user avatar
0 votes
1 answer
133 views

A fair die is rolled 5 times. What is the probability that a 5 is obtained on at least one of the rolls? [closed]

A fair die is rolled 5 times. What is the probability that a 5 is obtained on at least one of the rolls?
TPatterson89's user avatar
0 votes
1 answer
72 views

How to find the probability that 5 appears twice before both 4 and 6 appear when a fair six-sided die is rolled

This is from QuantGuide(Doubly 5 II): Jenny has a fair 6−sided die with numbers 1−6 on the sides. Jenny continually rolls the die and keeps track of the outcomes in the order they appear. Jenny rolls ...
Md Kaif Faiyaz's user avatar
19 votes
5 answers
3k views

Roll a dice infinitely many times, what is the probability of getting a 5 before a 6

My proof: For all possible events, based on the order of appearance between 5 and 6.l, they can be categorised into 2 groups. $A:$ event with 5 appear before 6 $A^{c}:$ event with 6 appear before 5 ...
TJT's user avatar
  • 480
0 votes
2 answers
102 views

Terminating Sequence expected length

I was preparing for a quant interview and I came across a puzzle on QuantGuide(named Sequence Terminator): A fair 6−sided die is rolled repetitively, forming a sequence of values, under the following ...
Md Kaif Faiyaz's user avatar
4 votes
1 answer
90 views

What is the probability to get a value of 11 or 12 in 10 rolls or less?

Suppose I have a 3-sided die with each side contains different number of 1, 2, and 3. In this problem, each time I roll the die I will add up the number that shows up with previous rolls. The target ...
fjrdrgmbz's user avatar
0 votes
0 answers
28 views

Conditional Probability with Cumulative Sum [duplicate]

Suppose you roll a fair 6-sided die and accumulate the sum until you've reached a sum $>= 1000$. What is the probability your final roll is a $6$? your final roll must be on an integer in $[994, ...
shrizzy's user avatar
  • 712
1 vote
1 answer
35 views

Distinct Dice EV of Product

Suppose we roll 2 n-sided dice, but we keep re-rolling the second while it is equal to the first (we guarantee different face values). What is the EV of the product? Now clearly if they could be the ...
Kelly C.'s user avatar
2 votes
2 answers
358 views

A fair six-sided die is rolled repeatedly until the product of the rolls is square.

I'm stuck on this problem. A fair six-sided die is rolled repeatedly. On average how long does it take until the first time that the product of the numbers rolled is a square? (For example, if the ...
ikea's user avatar
  • 23
1 vote
2 answers
58 views

expected sum after rolling dice until getting 6 five times

We are rolling dice until we get 6 exactly five times. What is expected value of total sum? My approach: Lets denote $X_i$ - number rolled in $i$-th roll, and $S_n = \sum_{i=1}^{n}X_i$. So now i want ...
Kombajn's user avatar
  • 444
0 votes
0 answers
35 views

Calculating the Probability of Landing on a Specific Face of a Non-Uniform Die

I'm working on a project involving non-standard dice where each face can have a different size, but the overall shape and weight distribution of the die are uniform. I'm interested in finding out how ...
Panayotis's user avatar
  • 101
1 vote
2 answers
78 views

Probability of average of N samples of an unfair dice bigger than 5.

Imagine we have a dice: Side probability 1 0.1 2 0.1 3 0.1 4 0.1 5 0.2 6 0.4 We will throw the dice N times (ie. 7 times) And we want to calculate the probability that the average of the 7 ...
Oscar Flores's user avatar
3 votes
2 answers
389 views

Fairvalue of the two tetrahedral dice game

I've written below my answer for the following expectation question: Two tetrahedral dice (red & blue) are rolled in each turn. If blue shows more than red, you are paid the difference, otherwise ...
loose the fools juice's user avatar
5 votes
1 answer
160 views

Number of Rolls of Die Until Sum Exceeds 6

What is the expected number of rolls of a 6-sided die until the sum exceeds 6? As the expected value of one roll is 3.5, why is the answer not just $\frac{6}{3.5}$?
Anon's user avatar
  • 427
2 votes
1 answer
124 views

rolling two dice and take the money

In a dice game, there are 9 piles of money valued from 1 to 9. The game involves rolling two dice multiple times. If the total of the dice is 10, 11, or 12, you re-roll until the total is between 1 ...
Sue's user avatar
  • 19
1 vote
2 answers
150 views

Probability Mass Function for Limited Exploding Dice Pools

Scenario in Question Say we roll $n$ $d$-sided dice. We look at each dice to see if the dice face reads our target number $t$ or higher, and if it does, we count it as a "hit". The result of ...
Lee Davis-Thalbourne's user avatar
0 votes
3 answers
69 views

Strategies for Calculating Dice Roll Probabilities for Specific Sums and Conditions

I'm working on some probability problems involving multiple dice rolls, and I'm uncertain about how to approach them systematically. I hope someone could guide me through the correct method for ...
Jakov Glavač's user avatar
0 votes
0 answers
39 views

Rolling dice -- prove that $X$ and $5-X$ have the same distribution

Suppose there'a tetrahedral dice with numbers $1,2,3,4$. Let's denote by $X$ a rolled number. Prove that $X$ and $5-x$ have the same distribution. So, for $X$: $$F_X(t) = \mathbb{P}(X \leq t) = \...
Adam Bogdański's user avatar
0 votes
0 answers
94 views

Optimal stopping: dice game

This problem has been asked lots of times, but I could not find a completely satisfactory answer. The statement is as follows: we have a standard 6-sided die. Each time we roll it, if we get a number $...
user_12345's user avatar
0 votes
0 answers
43 views

Different Sums On a Die - Trouble With the Solution

How many ways are there to choose six distinct integers from ${1, 2, . . . , 11}$ such that it is possible to attach each integer to a face of the cube where the sum of the integers on all pairs of ...
John Doe 's user avatar
1 vote
2 answers
74 views

Obtain a sum of $4$ before a sum of $2$

I am trying to solve the following problem. Suppose you a roll two fair $6$-sided dice repeatedly. What is the probability that you obtain a sum of $4$ before a sum of $2$. It is clear to me that ...
Bell's user avatar
  • 262
0 votes
1 answer
66 views

Probability of 2 exploding dice exceeding a threshold [closed]

my question is regarding exploding dice. Exploding dice are dice that can be rolled again if the maximum number has been rolled. At the end, the rolls are added up. For example, for a 6-sided die like ...
Schmandalf's user avatar
2 votes
1 answer
108 views

Sum of four dice is 20

Suppose we roll $4$ $6$-sided dice, what is the probability that their sum is equal to $20$ ? Let $X_1,X_2,X_3,X_4$ denote the rolls' outcomes. I usually deal with this kind of question the same way : ...
Kilkik's user avatar
  • 1,867
1 vote
1 answer
75 views

Sum of die until bust expected value

You are offered a game where you roll 2 fair 6-sided die and add the sum to your total earnings. You can roll as many times as you'd like however, in the case where both die land on the same face, the ...
shrizzy's user avatar
  • 712
2 votes
2 answers
49 views

Chaces of get $b$ points throwing dices of set $D$

I'm currently working on a casino game involving throwing different dice. To adjust the fair pay of each play, I'm trying to develop the formula that describes this scenario: Number of combinations ...
Alejandro Bergasa Alonso's user avatar
1 vote
2 answers
51 views

How to get probability of rolling dice above average?

I've seen someone say that he did $64$ rolls of D$20$ dice with lowest roll $6$ and average $15.5$. How do I calculate probability of this to know how lucky he must be? I can calculate probability of ...
Real Ambush's user avatar
2 votes
1 answer
109 views

Basic Die Game expected payout after re-roll

Alice rolls a fair 6−sided die with the values 1−6 on the sides. She sees that value showing up and then is allowed to decide whether or not she wants to roll again. Each re-roll costs $1. Whenever ...
Md Kaif Faiyaz's user avatar
0 votes
1 answer
55 views

Number of possible results with rolls

I have tomorrow a Combinatorics exam and I am practising with an exercise which asks me to find how many possible results are there if we throw $6$ identical dices so that there must be at least one ...
Daniel C.'s user avatar
  • 1,227
5 votes
1 answer
379 views

What's more likely to show up first when rolling a die, 556 or 234?

What's more likely to show up first when rolling a $6$-sided die, $556$ or $234$? The expected number of rolls of getting $556$ is solving for $a$ in the following equations: $$a = {5\over6}(a + 1) + {...
Emperor Concerto's user avatar

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