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.
0
votes
4answers
263 views
Solving for $E(X^2)$ if I know $E(X)$
I am trying to find the variance but I don't know how to calculate $E(X^2)$, but I do have a process that will enable me to find $E(X)$. How can I find $E(X^2)$?
In my case I have two 6-sided dice, ...
9
votes
2answers
427 views
Most Probable Sum [duplicate]
Possible Duplicate:
Probability of dice sum just greater than 100
A fair dice is rolled and the outcome of the face is summed up each time. We stop rolling when the sum becomes greater than ...
8
votes
2answers
342 views
“8 Dice arranged as a Cube” Face-Sum Equals 14 Problem
I found this here:
Sum Problem
Given eight dice. Build a $2\times 2\times2$ cube, so that the sum of the points on each side is the same.
$\hskip2.7in$
Here is one of 20 736 ...
3
votes
2answers
196 views
Probability of getting two consecutive 7s without getting a 6 when two dice are rolled
Two dice are rolled at a time, for many time until either A or B wins. A wins if we get two consecutive 7s and B wins if we get one 6 at any time.
what is the probability of A winning the game??
1
vote
1answer
188 views
Probability and distribution function
Can some one please tell me how to do it?
Let $(i,j)$ denote the numbers on the top faces when a pair of fair dice is rolled.
Let $X(i,j)=i+j-3$.
Find the range of $X$.
Find the probability ...
2
votes
1answer
335 views
Expected Value of the Difference between 2 Dice
What is the expected value of the absolute difference between 2 N
faced dice? What about the difference between 2 dice one with N faces
and one with M faces?
While finding the expected value ...
1
vote
1answer
74 views
Probability of hitting a deep downswing in a sequence
This is really a poker tournament/payout/bankroll question but I think I can frame it in a dice game for easier understanding.
If a player starts with $X$ units, and plays a game where on each throw ...
1
vote
1answer
83 views
dice probability issue
In the game Settlers of Catan, territories/tiles are each (effectively) randomly assigned a number from 2-12. When that number is rolled as the sum of two dice, the tile generates resources for the ...
0
votes
2answers
141 views
Sum of 3 loaded dice
I am given 3 loaded dice $D_1$, $D_2$ and $D_3$ and their probability tables $P(D_i = k), 1 \leq k \leq 6$.
I ought to write an algorithm that computes $P(\text{Sum} \mid D_1)$, the sum of all three ...
0
votes
0answers
90 views
Can you Fourier transform probabilities?
If I have a rect function , and I convolute it with it's self, I get a triangle function. If I convolute with a rect function again, I get a bell-curve. I can continue, so long as I know how to ...
2
votes
2answers
178 views
probability dice experiment
I am currently taking a probability course and I am stuck on a supposedly easy discrete probability question here:
Problem: Consider the experiment of rolling a fair die independently until the same ...
0
votes
1answer
224 views
Are X and Y independent?
We roll two dice once. Let X denote the number of 1’s and Y the number of 6’s obtained. Are X and Y independent?
2
votes
1answer
149 views
Simple Dice Rolling Problem
If you play poker dice by simultaneously rolling 5 dice, why is $P\text{{five alike}} =.0008$?
I guess I understand the fact that each dice has the probability to land on the same number $1/6$ of the ...
4
votes
2answers
490 views
Find the expected value of a dice sum
If fair dodecahedron is rolled until at least $k$($k$ is fixed between 2 and 12) is gotten, and $X$ is the sum of all numbers appeared until the last time, what is $E(X)$?
1
vote
1answer
100 views
Probability on a Die
The normal probability of a number in a regular die (6 faces) is $\dfrac{1}{6}$. Let in an addicted [that is, "loaded"] die, the probability of a even number (2, 4 and 6) be twice the normal ...
4
votes
2answers
142 views
Probability of throwing the same multiset twice in a row with six dice
Six dice are thrown. The six dice are thrown a second time. What is the probability of getting the same numbers as in the first throw? If the order of the six numbers matters, the problem is easy, but ...
0
votes
1answer
997 views
How do you calculate probability of rolling all faces of a die after n number of rolls? [duplicate]
Possible Duplicate:
Expected time to roll all 1 through 6 on a die
Probability of picking all elements in a set
Im pretty new to the stackexchange, and posted this is statistics, and then ...
7
votes
3answers
811 views
What is the expected number of dice one needs to roll to get any monotonically increasing series of 1 to 6?
Similar to:
"What is the expected number of dice one needs to roll to get 1,2,3,4,5,6 in order?"
but we allow repeats so 1,1,2,2,3,4,4,4,4,5,5,6 would count.
My answer (or simulation) is flawed as I ...
6
votes
2answers
487 views
What is the expected number of dice one needs to roll to get 1,2,3,4,5,6 in order?
If I have a fair die and throw it until I get a run of 1,2,3,4,5,6 in order, how many times on average must I throw the dice?
4
votes
3answers
338 views
What equity is necessary to offer the doubling cube in Backgammon (dice game)
Edit: This question is a lot shorter than it is. Don't get intimidated. If you know backgammon, just skip to question 2.
In Backgammon, each game is played for one point (or one dollar) between two ...
0
votes
1answer
682 views
dice throwing probability. Get face 1 at least one time by throwing a die 6 times.
How can I calculate the following probability:
Throwing a die 6 times, what is the probability of having face no. 1 showing at least one time.
4
votes
3answers
3k views
Probability question (Six dice)
If six fair dice are rolled what is probability that each of the six numbers will appear exactly once?
3
votes
1answer
440 views
dice problem - throws necessary for sum multiple of n
A die (with six sides) is rolled repeatedly and summed. Show that the expected number of rolls until the sum is a multiple of $n$ is $n$.
In
...
1
vote
1answer
727 views
Poker dice probability
I am working on a maths excersice and got stuck on this question where I need to calculate the probability of poker dice.
The game poker dice is played with 5 dice. It's possible to get one of the ...
2
votes
2answers
129 views
How do I think about solving this sort of problem without having to count intersections?
I have asked this sort of question before, and I have a new similar question here. The latter question got me thinking about this specific question.
When throwing 5d20 (rolling five twenty sided ...
2
votes
3answers
253 views
What function accurately describes the likelihood of getting X successes when rolling Y dice?
Pardon my statistical illiteracy and feel free to correct any silly/wrong terminology I use in this post.
There is an RPG system called Storytelling where the vast majority of dice rolls are
...
3
votes
1answer
140 views
Probability greatest roll of z dice exceeding greatest roll of h dice?
Let's assume there are two players in a dice game; zombie and hero.
The Zombie rolls z fair 6-sided dice.
The Hero rolles h fair 6-sided dice.
If the heroes greatest dice roll is larger than the ...
52
votes
8answers
6k views
Given a die, what is the probability that the second roll of a die will be less than the first roll?
If you are given a die and asked to roll it twice. What is the probability that the value of the second roll will be less than the value of the first roll?
4
votes
2answers
1k views
Probability of either dice showing a specific number
If I throw 4 dice together, what is the probability that either one of them will show the number 3 ?
I tried to calculate it and got to $\frac{(4)}{6}$ (which is highly unlikely to be correct).. any ...
1
vote
0answers
109 views
Boggle dice set letter distribution algorithm [duplicate]
Possible Duplicate:
Boggle letter probability
What algorithm have the creators of the word game Boggle used to come up with these dice sets?
...
5
votes
3answers
316 views
Probability of rolling a die
I roll a die until it comes up $6$ and add up the numbers of spots I see.
For example, I roll $4,1,3,5,6$ and record the number $4+1+3+5+6=19$. Call this sum $S$.
Find the standard deviation of ...
0
votes
0answers
80 views
Modelling die roll sequence
I have a die with $N$ sides. It has a hidden transitive order which has to be uncovered. At the start of a trial, I throw the die until I get the highest-ranking side. I then throw the die until I get ...
2
votes
1answer
83 views
The probability of obtaining at least one roll of x from k dice each with a different number of faces
Assume you have k dice, each with some random number of sides, 1...n. I'm trying to figure out, after rolling all k dice, what is the probability of obtaining at least one roll with a given value x - ...
24
votes
7answers
2k views
New to probability - Is this true?
I read this somewhere and can't find it to verify:
"If you don't have a dice with 12 sides, but do have one with 20 sides and you need to make rolls for 12 sides, you can use the numbers 1-12 on the ...
1
vote
2answers
257 views
A coin is flipped when dice hits 6 (conditional probability)
Prof gave us homework on conditional probability that is due on the day of the lecture on conditional probability. Yeah, this has been a bad week and I've no idea what I'm doing.
Q: 3 dice are ...
2
votes
2answers
201 views
Two combinatorics problems. I'm not 100% confident in my answers
These are two problems from my combinatorics assignment that I'm not quite confident in my answer. Am I thinking of these the right way?
Problem 1: On rolling 16 dice. How many of the $6^{16}$ ...
5
votes
3answers
3k views
How many rolls do I need to determine if my dice are fair?
Roughly how many times do I need to roll a 6-sided die to feel confident that it's giving "fair" results? What about a 10-sided or 20-sided die?
Note that I will be actually manually rolling physical ...
0
votes
3answers
391 views
How many times will a consecutive sequence of throws randomly appear if I throw a four-sided die N times?
The problem is related to nucleotides and genomes, but it's better to simplify it using dice.
EDIT 2: My original question wasn't very clear, so I've reworded it
I know that the probability of ...
4
votes
1answer
407 views
Magical Loaded Dice and expected values
Let's say we have a magical biased die that allows us to set the bias of every side to whatever we want (nonzero and add up to 1, of course). And let's say this die enforces the condition that the ...
6
votes
4answers
578 views
Confusion over probability problems
I am stuck with these probability problems,
A pair of unbiased dice is rolled together till a sum of either $5$ or $7$ is obtained. Find the probability that $5$ comes before $7$?
A letter is ...
4
votes
2answers
441 views
What's the probability of rolling at least $k$ on $n$ dice with $s_1,\ldots,s_n$ sides?
Is there a way to determine the chance of rolling at least $k$ on $n$ dice with $s_1,\ldots,s_n$ sides?
Example: What is the chance of rolling a sum of at least 13 on 3 dice with 6, 8, and 10 sides?
...
5
votes
1answer
92 views
Bounds for die roll
Given a $n$-sided fair die, show that the probability $P$ that all faces from $1$ to $11$ show when doing $3n$-rolls is bounded by
$1 - 11 \cdot \frac{(n-1)^{3n}}{n^{3n}} \leq P \leq 1 - 11 \cdot ...
19
votes
3answers
5k views
Expected time to roll all 1 through 6 on a die
What is the average number of times it would it take to roll a fair 6-sided die and get all numbers on the die? The order in which the numbers appear does not matter.
I had this questions explained ...
16
votes
2answers
804 views
Expected number of rolling a pair of dice to generate all possible sums
A pair of dice is rolled repeatedly until each outcome (2 through 12) has occurred at least once. What is the expected number of rolls necessary for this to occur?
Notes: This is not very deep ...
7
votes
2answers
700 views
Probability of 3 of a kind with 7 dice
Similar questions:
Chance of 7 of a kind with 10 dice
Probability of getting exactly $k$ of a kind in $n$ rolls of $m$-sided dice, where $k\leq n/2$.
Probability was never my thing, so please bear ...
19
votes
3answers
552 views
How many times do I roll an unfair die to determine its bias?
This question comes from computer security, but I'll distill it into a probability question:
I have a biased die with 96 sides. 95 sides are equiprobable, each having a 1% chance of landing up. The ...
2
votes
3answers
346 views
Probability of Sum of Different Sized Dice
I am working on a project that needs to be able to calculate the probability of rolling a given value $k$ given a set of dice, not necessarily all the same size. So for instance, what is the ...
7
votes
3answers
454 views
Thought experiment for dice game
Two players in a dice game to see who can roll a total of 60 first, taking turns each rolling 2 dice.
For one player, one die is 4 sided and one is 6 sided. Therefore the average roll for this ...
12
votes
3answers
430 views
Best Strategy for a die game
You are allowed to roll a die up to six times. Anytime you stop, you get the dollar amount of the face value of your last roll.
Question: What is the best strategy?
According to my calculation, for ...
5
votes
2answers
328 views
Probability for twelve dice
In 'An Introduction to Probability Theory and Applications' by W. Feller I encountered this apparently innocuous problem.
A throw of twelve dice can result in
$6^{12}$ different outcomes, to all ...
