# Questions tagged [dice]

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

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1 vote
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### 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 ...
• 11
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### 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 ...
• 178
1 vote
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### 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 ...
• 13
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, ...
• 101
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 ...
• 183
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 ...
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 ...
• 93
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 ...
• 187
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 ...
• 125
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### 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. ...
1 vote
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 $5/6$, ...
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 ...
• 619
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### 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 ...
• 665
44 views

### 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....
• 101
1 vote
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 ...
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? \...
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 ...
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?
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 ...
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 ...
• 480
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 ...