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.

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28
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2answers
16k 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 ...
19
votes
2answers
2k 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 ...
5
votes
3answers
2k views

How can I (algorithmically) count the number of ways n m-sided dice can add up to a given number?

I am trying to identify the general case algorithm for counting the different ways dice can add to a given number. For instance, there are six ways to roll a seven with two 6-dice. I've spent quite ...
7
votes
2answers
435 views

What is the most unfair set of three nontransitive dice?

In a set nontransitive dice, each die is superior to another die, but is inferior to a third. It is similar to the game of rock-paper-scissors. Here is one example: ...
2
votes
2answers
727 views

Probability that the sum of all values of 5 pairs of dice will be between 30 and 40

I'm trying to solve a question that asks: If 5 pairs of fair dice are rolled, approximate the probability that the sum of the values obtained is between 30 and 40 inclusive. My approach so ...
65
votes
9answers
17k 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?
6
votes
4answers
8k views

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

Basically, on average, how many times do you have to roll a fair six-sided die before getting two consecutive sixes?
1
vote
0answers
93 views

probability of consecutive row of at least m by n<=2m events. Is there a shorter route?

Inspired by this I started to generalize it. Go out from independent events $E_{1},E_{2},\cdots$ that succeed or fail. This with $p$ as probability of succes, and $p+q=1$. Event $A_{m,n}$ occurs if ...
4
votes
2answers
327 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??
11
votes
3answers
10k views

The expected payoff of a dice game

There's a question in my Olympiad questions book which I can't seem to solve: You have the option to throw a die up to three times. You will earn the face value of the die. You have the option ...
4
votes
3answers
1k views

What is the average of rolling two dice and only taking the value of the higher dice roll?

What is the average result of rolling two dice, and only taking the value of the higher dice roll? To make sure the situation I am asking about is clear, here is an example: I roll two dice and one ...
4
votes
3answers
6k views

Probability question (Six dice)

If six fair dice are rolled what is probability that each of the six numbers will appear exactly once?
1
vote
3answers
164 views

Dice probability puzzle

What is the probability of a run of at least 3 sixes when a die is thrown 5 times? I think I have the answer but from what I have been told its not the correct answer. Would someone like to help?
7
votes
2answers
1k 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 ...
3
votes
5answers
440 views

Probability of 1x six from seven dice?

Could someone help me with how the following is calculated: What is the probability of rolling a die seven times and getting at least one six? My instinct told me it would be $1/6+\cdots + 1/6$ but ...
3
votes
1answer
893 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 ...
2
votes
3answers
80 views

Probability Dice Game Follow Up

Original Question: Paul, Dave and Sarah are rolling a fair six sided die. Paul will go first, always followed by Dave, who is always followed by Sarah, who is always followed by Paul, and so on... ...
2
votes
1answer
194 views

probability of rolling at least $n$ on $k$ 6-sided dice

Is there a simple form for the probability of rolling at least $n$ on $k$ 6-sided dice? Of course you can do it by recursion (see here). But is there a way to do it with just a few binomial ...
0
votes
3answers
105 views

A dynamic dice game

I learned the following dice game from another forum. It was not solved there. The dice game is as follows. Toss 6 dice. Each toss you can keep one or more up to the total number of dice tossed. You ...
8
votes
2answers
469 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 ...
6
votes
1answer
370 views

“8 Dice arranged as a Cube” Face-Sum 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 ...
4
votes
1answer
100 views

What is a good strategy for this dice game? [duplicate]

I learned the following dice game from another forum. It was not solved there. The dice game is as follows. You start tossing six dice. After each toss you must put aside at least one of the dice ...
12
votes
3answers
613 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 ...
6
votes
3answers
438 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 ...
2
votes
2answers
357 views

Is there a way to simulate any $n$-sided die using a fixed set of die types for all $n$?

I am assuming that we can increase the number of dice based on $n$, but they have to be $k$-sided, $k\ge3$. When I say die types, I mean that we are allowed to use non-standard dice such as ...
2
votes
1answer
4k views

Probability Distribution of Rolling Multiple Dice

What is the function for the probability distrabution of rolling multiple (3+) dice. The function is a bell curve but I can't find the actual function for the situation. Example, what is the function ...
1
vote
2answers
87 views

Finding the coefficient of a generating function

Given $f(x) = x^4\left(\frac{1-x^6}{1-x}\right)^4 = (x+x^2+x^3+x^4+x^5+x^6)^4$. This is the generating function $f(x)$ of $a_n$, which is the number of ways to get $n$ as the sum of the upper faces of ...
0
votes
4answers
950 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 ...
8
votes
3answers
373 views

What is the probability that $n$ dice tie on successive rolls?

The Question What is the probability, rolling $n$ six-sided dice twice, that their sum each time totals to the same amount? For example, if $n = 4$, and we roll $1,3,4,6$ and $2,2,5,5$, adding them ...
5
votes
1answer
87 views

Analysis of “Tiny Dice Dungeon” (I)

Consider the following one-player game: Initially, there is a pot of $\$0$. On each turn, the player may opt to end the game and collect the contents of the pot, or roll a single die. In the latter ...
4
votes
1answer
166 views

What is the probability of rolling a 1 on the Catenative Doomsday Dice Cascader?

As seen here. Assume that each cascader bubble begins with a d6, as opposed to being determined by the prime bubble along with the number of cascader bubbles; the scene makes it ambiguous. ...
4
votes
2answers
786 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? ...
3
votes
1answer
2k views

Roll 5 dice and find the probability that at least 3 dice are 4

My approach is find P that exactly 3 dice are 4 + exactly 4 dice are 4 + exactly 5 dice are 4. $(5C_3 * (1/6)^3 * (5/6)^2) + (5C_4 * (1/6)^4 * (5/6)^1) + (5C_5 * (1/6)^5)$ = 276/6^5 Is my ...
2
votes
2answers
219 views

Yahtzee large straight strategy.

I've recently got into playing Yahtzee with my brother. During a game we had on my first roll for my last round I got (5 4 4 2 1). I only had my large straight left, so naturally I was hopeful with ...
2
votes
1answer
857 views

Probability of predicting, then throwing, a particular multiset for 5 dice.

My friend shared with me a story that after losing to his SO at Yahtzee, before they put the game away he just randomly predicted he would roll four 5's and a 1. He then got that roll and freaked out. ...
2
votes
1answer
672 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
65 views

Throw X dice, sum face $1,2,3,4$ minus Y, then add $ 5,6$ formula

I am trying to program something to find out the probability of all sum possible when I throw $X$ dice, sum all the face showing $1,2,3,4$ then I minus $Y$ from that sum (with a minimum of $0$, no ...
1
vote
2answers
108 views

Why does multiplying n by a random number give you a random number between 0 and n?

I have been following the tutorial at Codecademy I see that, as part of the process of creating a virtual die we multiply 'a random number between 0 and 1' by 6 to give us a random number between 0 ...
0
votes
1answer
84 views

Probability of a tetrahedron (die with 4 faces)?

I have been doing some questions from an exam review with no solution and I have no idea how to work this problem. I know that $Pr(A_1) = \frac{1}{2}$, $Pr(A_2) = \frac{1}{2}$, $Pr(A_3) = ...
0
votes
2answers
60 views

Consider throwing two six-sided dice.

Let X be the sum of the two values and let Y be the product of the two values. What is the value of P(Y = i) for i = 1,2,3...36. I am having trouble approaching this problem. We are learning about ...
0
votes
1answer
73 views

The number of rolls of $6$ dice with exactly $4$ distinct values.

I know the answer is $${6 \choose 4}{5 \choose 3}$$ However, I don't understand why this is true?
0
votes
3answers
625 views

Rolling 6 dice and 4 on the same side

Guys I made myself a question to answer and its this. What is the probability of having 4 dice land on the same side if I toss 6 dice. I got this answer, I don't know if its correct. I dont want to ...
-1
votes
1answer
66 views

Probability Rolling a dice until you get 1/2 or 2/2 [closed]

You roll $1$ die repeatedly until you get a $1$ immediately followed by a $2$ or a $2$ immediately followed by a $2$. What is the probability that a $1$ then a $2$ is rolled before a $2$ then a $2$? ...