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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.

2
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1answer
26 views

How to minimize the expected value of the resulting sum in this dice & number game?

The game is as follows: I place nine tiles numbered 1-9 inclusive lying on the table face up. I then roll two standard, six-sided dice and note their outcomes. I now have two options: Flip over the ...
0
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1answer
60 views

Probability of winning with dices

I've been studying probability for a few couple weeks. Today, I've given a homework, and I am really struggling with it. The type of question is unfamiliar to me and I don't have any idea how to solve ...
0
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1answer
36 views

Probability of rolling $T$ or higher on at least $M$ of $R$ dice of $S$ sides

I am trying to figure out how to write an equation to solve the following problem: S = # of sides on a die R = # of dice being rolled T = Minimum result to count as a success event on each die (Aka ...
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2answers
27 views

Formula for calculating probability on customized dice.

Given the following: Player may choose from among the following: 1-10 White dice [0,0,0,1,1,2] 0-40 Blue dice [0,0,1,1,1,2] 0-10 Red dice [0,1,1,1,1,2] and rolls ...
3
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2answers
22 views

You throw a dice 3 times,probabilty whats the probability of the number k to be the highest?

You throw a fair dice 3 times, let X be the highest number you will get. What is the PDF of $P(X=K), K=1,...6$ ? The answer is : $$\frac{k^3-(k-1)^3}{216}$$ However, I can't understand it, could ...
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0answers
39 views

Probability of rolling a straight in Yahtzee

I am trying to compute a very specific probability given a game of Yahtzee. Here are the rules: There are 5 fair, 5-sided dice with equal probability of rolling each number. You have 3 rolls to ...
1
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1answer
23 views

Probability of the first die

I am working on the following problem. If you toss two dice, what is the probability that the first dice shows a face of 6, given that the sum of both faces is an 8? Am I wrong to assume that both ...
0
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1answer
44 views

Rolling $N$ indistinct dice and $1$ distinct die, what is the chance that the distinct die is part of the Top 3?

Rolling $N$ indistinct dice and $1$ distinct die, what is the chance that the distinct die is part of the Top 3? Ties favor the distinct die being included over an indistinct die. I'm at the point ...
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3answers
45 views

Ways for Two Dice to Sum to 8: $x_1 +x_2 =8$

I am trying to determine the number of ways two dice can be rolled to have a sum of 8. This question can be easily brute-forced, but I want to use a technique that can be applied to similar questions ...
1
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4answers
54 views

Probability of sum of N dice being above certain value X

In Dnd, sometimes you have to roll n, m-sided dice (say 5, d20s) and have the sum be greater than or equal to a certain value, x (say 90). This is easy for me to calculate by brute force, for most ...
0
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1answer
46 views

Dudo Game - Conditional Expectation

Say there are $n$ dice in the game. I have $p$ dice. Among them, I have $m_1$ aces and $m_2$ three. Let $X$ be the random variable: X="Number of dice which are either aces or three" and $B$ the event:...
1
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1answer
31 views

Possibly flawed probability computation in Red Dward XI?

I watched the new episodes Red Dwarf series XI. In episode 3 there is a scene where Rimmer and Lister play a game called minopoly. Rimmer is throwing a pair of dice while he wishes the outcome NOT to ...
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0answers
36 views

Probability Game with Dice

I keep throwing dice until I have seen 8 consecutive fives, after which I stop. What is the probability that under this scheme I will at any point have seen 10 consecutive sixes? Is there any way to ...
1
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2answers
27 views

Rolling Dice 5 Times

A fair 6-sided die is rolled 5 times and the result is recorded for each roll. a) How many different sequences of results are possible? b) Of the possible sequences of results, how many of them ...
1
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1answer
18 views

Nets of Dice - how to know if it is a Nets of Dice

I am school student and learning Visualizing Solid Shapes. In this chapter we have a concept that if piece of paper is cut in a net shape we need to prove that the same can be formed into a dice (...
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0answers
13 views

Determining the sample space of a random experiment problem

A die is rolled continually until a 6 appears, at which point the experiment stops. What is the sample space of this experiment? Let $E_n$ denotes the event that $n$ rolls are necessary to complete ...
1
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1answer
24 views

Optimal stopping for dice game (rolling until any repeated value)?

I was at an interview workshop today and was posed this question: I keep rolling a die, and my score is the sum of all my rolls. However, if I roll a value I had rolled before, I lose all. What is ...
0
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3answers
25 views

Probability of sum 15 when roll 3rd dice, and first roll of 2 dice at least 10

enter image description hereTwo dice have been thown, giving a total of at least 10. What is the probability that the throw of a third die will bring the total of the three numbers shown to 15 or ...
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0answers
26 views

What are the chances to have three same numbers on dices, three times in a row?

So, my friends and I were playing a game with dices, and we used to get three same numbers for three times in a row. So we are wondering what are the probabilities for something like that to occur?
0
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1answer
26 views

Chance of getting $3$ same faces and $3$ different faces when $6$ dice are thrown

What is the probability of showing $3$ faces same and $3$ faces different when $6$ dice are thrown simultaneously? Here's my approach: $6$ dice thrown. Total number of outcomes that first $3$ dice ...
0
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2answers
24 views

joint probability of dice and coin

I have a question where $X_1$ is the number on a die $(1,2,3,4,5,6)$ and $X_2$ is the number of die plus the value of indicator on coin $(H=1, T=0)$. Find the joint probability of $X_1$ & $X_2$ , ...
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2answers
45 views

Bayes Theorem to find probability of getting a sum given a coin toss

Suppose you flip a fair coin, and if the result is heads you will roll a pair of fair dice, and if the result is tails you will roll the biased dice. Using Bayes’ Theorem: a. derive the probability ...
0
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1answer
25 views

Is it possible to simulate a seven sided die without rerolling?

In front of me, I have an arbitrary number of four-sided, six-sided, eight-sided, ten-sided, twelve-sided, and twenty-sided dice. Using any number and combination of these, is it possible to exactly ...
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1answer
46 views

simple dice game played with a single die

A player pays £1 to play and rolls the die once. Before each subsequent roll the players have to guess if the roll will be higher or lower than the previous roll. If the player guesses correctly for 7 ...
3
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1answer
76 views

Help calculating probability of dice rolls in a board game

What is the probability of rolling a 6 symbol combination using 8 identical 6-sided dice (each dice having one duplicate symbol ie. d={A,A,B,C,D,E}), where the player is allowed discard one dice in ...
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0answers
36 views

Mean Value of a six faced die that have 5 3's and 1 6,after 6000 rolls

This question is asked today in an exam and perplexed me.I can't quite fit the 6000 rolls in the solution.I want to know how the roll number effects the outcome of mean value(expected value) of this ...
2
votes
1answer
39 views

Recursive algorithm probability

I'm trying to find the probability of obtaining a six on a dice roll following these rules: You roll a dice and if you roll $6$, then you win. However, if it is not $6$, you roll another dice....
0
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0answers
22 views

Theoretical probability of PIG variation dice game

In my variation of the PIG dice game, rolling a 1 or 2 forces the player to receive a sum of 0, and the turn ends. Otherwise, the player continues to roll and adds each roll for a total sum for that ...
1
vote
1answer
28 views

Prime-Sided Dice Problem

Given a $p-$sided Dice, where $p$ is a prime number. Show that in a discrete model of a single throw of the dice $(\Omega, \mathcal{P}(\Omega), P)$: Events $A, B$ are independent $\iff$ At least $A$ ...
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0answers
21 views

Probability of rolling at least one 6 in each roll when rolling multiple dice a number of times

I roll $n$ fair dice $m$ times in a row. The probability to roll at least one 6 in each roll is $(1 - (5/6)^n)^m$ I think. Is that correct? How can I find $n$ so that the probability of rolling at ...
0
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3answers
46 views

Theoretical Probability of the Sums when Rolling a Fair Die 6 Times

You roll a fair die 6 times. What is the theoretical probability for the sum of each combination? For example, rolling a 1,1,1,1,1,1 has a sum of 6. Or what are all the possible combinations? I know ...
0
votes
1answer
27 views

Probability of obtaining each number on a dice roll

I was just thinking if it really is true that the probability of obtaining each number on a 6-faced fair dice always 1/6? If the die was previously rolled to a 3 for example, would the next die roll ...
0
votes
1answer
15 views

Dice probability counting intermediate results?

I'm having trouble figuring out how to determine the probabilities for this specific dice mechanic (the game in question is Bang, the Dice Game but I'll try to generalize it). In this game, rolls act ...
14
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5answers
2k views

Most efficient strategy for guessing outcome of (fair) dice roll?

I'm starting to learn about information theory and I'm a bit stuck on this one. here's what I have so far: 1 possible strategy is to simply ask 'did outcome 1 occur?' if yes then we have our answer, ...
3
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2answers
20 views

Probability of number of faces with 2 and 5 equaling after 6 rolls of a dice

I have one dice and I roll it six times, recording the number I get each time. What is the probability that the number of 2s I get equals the number of 5s. I try solve this using the trinomial ...
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2answers
35 views

Probability Of Rolling 2 Identical Numbers In 3 Rolls [closed]

A single fair die is rolled 3 times. What is the probability of rolling exactly two identical numbers? I've done the working for if a die is rolled 2 times: There's a 1/6 * 1/6 chance of getting the ...
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0answers
27 views

Calculate the probability that there is no crisis in a ten-year period, to 2 significant digits.

This question is a tutorial question of a Statistics module that I have to take as part of my university graduation requirements. -- A game about the impact of climate change on human life uses ten ...
0
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1answer
59 views

What is the sum of all the numbers on the opposite faces of numbers obtained in three rows is?

I have this: A person threw a standard dice three times. He obtained two distinct odd prime numbers in two throws and an even number which is not a factor of 18 in the third throw. The sum of all the ...
0
votes
1answer
30 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'...
2
votes
2answers
37 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; ...
0
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2answers
75 views

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

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?
0
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1answer
24 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 ...
0
votes
1answer
38 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
33 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
50 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
439 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
94 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 ...
0
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2answers
45 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?
2
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1answer
34 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 ...