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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3answers
76 views

Die roll, value of 4 must follow value of 1 to win

I came across a "die roll" probability question that has me stumped. Two fair die are being rolled by players A and B, who alternate, with A rolling first (ie. A then B then A then B...so long as the ...
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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 ...
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1answer
71 views

Probability Dice Game Question

I have the following problem to solve that deals with probability (something I haven't done since Grade 8 (6 years ago)) This is a one player game and it is described for $q$ sided dice. You start by ...
-1
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1answer
29 views

Calculating probability of a dice with different numbers [duplicate]

I was given a problem in class: ...
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1answer
405 views

Probabilities of rolling a fair die twice?

a) One of the dice is a 4 b) Sum of the dice equals 4 c) Neither dice is a 4 I get really confused with these exercises (I don't know why)
0
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1answer
33 views

Probability of occurrence vs. Probability of x successes

I've been reading for two hours and I'm having a hard time getting the grasp of these two concepts. I'm developing a tool for a game, in which I'm given n dice and a success threshold (ie. roll at ...
0
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1answer
83 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) = ...
1
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1answer
50 views

$95$ percent confidence interval for roll of two dice

Given a roll of two fair six-sided dice, we know the expectation for a specific result (e.g. a $4$ and another $4$) is $\frac{1}{36}$. But with what certainty could you expect that result in $N$ ...
3
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1answer
104 views

Expected duration of a die game

In a 2 person game, the player who first obtains a $6$ wins. I'm trying to determine the expected number of die rolls needed before a winner is determined. (One turn consists of two die rolls, ...
2
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2answers
172 views

Probability of always rolling 6 on a dice

Suppose I roll a six-sided die $10$ times and each time it shows a $6$. What is the probability of the next roll coming up $6$? You might say $1/6$. But it was never declared to be a fair die. In ...
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2answers
53 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 $P(X = i, Y = j)$ for $i = 1,2,\cdots,12$ and $j = 1,2,\cdots,36$. Trying to figure out if there is a easier way to figure this out rather than writing out all the values.
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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 ...
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4answers
127 views

2 player dice game probability

For some homework in one of my classes, we are given this problem: In a certain dice game, player $A$ rolls six six-sided dice vs. player $B$ who rolls nine four-sided dice. Each player rolls ...
2
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2answers
597 views

Rolling two dice 10 times, what is the probability of getting all possible “doubles”?

Rolling two dice 10 times, what is the probability of getting all possibble "doubles": (1,1),(2,2),(3,3),(4,4),(5,5),(6,6) among our rolls? For instance, ...
0
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1answer
113 views

Dice Math, odds and probability

DISCLAIMER: This will be done with fake money for education purposes. I'm working on a Dice simulation site for a school project, where you play the house and you as a player have to get a higher ...
3
votes
1answer
159 views

Toss a die until SIX appears. E (number of ONEs | at leat one TWO) =?

A fair die is tossed repeatedly until a Six appears. Let $X$ denote the number of One's that are thrown in this game/experiment. Let $A$ denote the event that at least one Two was thrown. Compute$ E(X ...
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2answers
33 views

When the game is fair

One player throws dice twice. If he has 2 x 6 on the dice he is receving 8*a. If he has one 6 he will collect 4*a. Otherwise (when he has no 6 at all) he is paying a. For which value of a game is ...
2
votes
2answers
182 views

What is the theoretical expected value of the sum of the highest 3 values of 4 fair dice?

Many have estimated the expected value of the common "4d6, drop lowest" roll or averaged a complete enumeration of the possible outcomes. I would like to know the theoretical expression of this value, ...
2
votes
2answers
356 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 ...
4
votes
3answers
95 views

Probability Questions! [duplicate]

Alex, Bret, and Chloe repeatedly take turns tossing a fair die. Alex begins; Bret always follows Alex; Chloe always follows Bret; Alex always follows Chloe, and so on. Find the probability that Chloe ...
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... ...
0
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1answer
17 views

What is the expectation of the first time dice-rolls Z and Z+1 are similar?

We roll a dice. Let $Z=$ the first time the rolls $Z$ and $Z+1$ are similar. What is $E[Z]$ ? What is $E[Z^2]$ ? The problem sounds unnatural to me because i'm asked about a roll $(Z+1)$ that ...
4
votes
1answer
52 views

Deciding to place a bet on outcome of a dice roll based on the probability

I have encountered several question of the following format. I have no trouble answering the first half but second half I have no clue on how to proceed. a: If you roll 5 standard six-sided dice, ...
3
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1answer
147 views

What is the expected number of k-length streaks in n rolls?

Given $n$ flips of a coin with success probability $p$, what is the expected number of $k$-length win streaks in $n$? (I've looked for this question online, but the answers always restrict $n$ to be ...
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2answers
384 views

DICE - Rolling at least *k* on *n* six-sided dice - with a twist!

I am putting together a table of dice probabilities for a project I am working on and have found myself intimidated by a little "special case" I'm trying to work with. For determining the probability ...
0
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1answer
136 views

Game Dice Probability

In the realm of statistical analysis I'm about as green as they come, so forgive me if my question isn't stated perfectly, I'm trying my best to explain. There's a table-top game my friends and I play ...
2
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3answers
56 views

Probability Dice Game

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... What is the ...
5
votes
2answers
252 views

Roll a die, pick that many balls from an urn

An urn has $5$ white and $10$ black balls. A die is rolled, and that many balls is drawn from the >urn. What is the probability that all the balls drawn are white? My thinking is that each die ...
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 ...
4
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3answers
104 views

Probability of rolling a “1” on a die conditioned on when all rolls are different.

So I have this problem: I am rolling a six sided die 3 times. Conditioned on the rolls all being different, what's the probability at least one die is a "1" So I worked it out like this: ...
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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 ...
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2answers
43 views

What is the probability there are a higher total of red “5’s and 6’s” than white “5’s and 6’s”?

You have 3 red 6-sided dice and 3 white 6-sided dice. When you throw the dice, what is the probability there are a higher total of red “5’s and 6’s” than white “5’s and 6’s”? Note: When any 6-sided ...
0
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1answer
60 views

rolling a seven when at least one die is a four?

I have been working on some stuff like this and I am fairly confused, I wrote some code to see how it works when simulated and I am further from an answer. ...
4
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1answer
241 views

Expected sum of all the n-sided dice rolls until we get n

So the problem is the following. We have an $n$-sided die. We throw it until we get $n$. What's n, if the expected sum of all the throws including the $n$ one is $21$. Now, I did manage to solve it ...
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2answers
60 views

Probability number comes up before another

In craps, say I roll a 5 for the place bet. What is the probability that I roll another 5 before rolling a 7? Is this correct?: $P(5 \text{ before 7}) = P(5) + P(\neg 7 \neg 5, 5) + P(\neg 7 \neg 5, ...
0
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1answer
132 views

Dice roll game fair price

You and I each roll 1 die each at the same time. I win if I roll a six on one roll, and then a five on the next. You win if you roll two sixes in a row. Who would you bet your money on? Note that You: ...
0
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2answers
308 views

How to calculate probability of dice rolls [closed]

I'm playing board game of Zombicide. One of the actions in there is attack, where you roll a number of 6 sided dice, and you get a hit for every dice that showed more than "m". For example - roll 4 ...
0
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1answer
77 views

Four sided dice rolled to match number

I've been cracking my brain about this one for some time now. I've just started this statistics course. The problem is: A four sided dice is rolled once and then rolled as many times to not get the ...
0
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3answers
119 views

How can I linearly decrease chance?

Suppose there are 10 different people, each holding 1 lottery ticket, and I give each of them 10% chance of becoming the 'winner'. Now let's say one of those 10 people (I dont know which one) ...
2
votes
3answers
122 views

I flip M coins, my opponent flips N coins. Who has more heads wins. Is there a closed form for probability?

In this game, I flip M fair coins and my opponent flips N coins. If I get more heads from my coins than my opponent, I win, otherwise I lose. I wish to know the probability that I win the game. I ...
0
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0answers
169 views

Probability In Multi-Throw Dice Game

I am having some trouble coming up with a probability table for a game that I wrote. The game uses 6 dice. The player can throw the dice multiple times, but must retain at least 1 on each throw. In ...
1
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2answers
169 views

dice roll of 20

what formula would be correct to find the odds of rolling 2 dice "X" number of times without a seven showing. There are 36 combinations when rolling 2 dice with six sides. Im wondering how often one ...
1
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3answers
155 views

If we roll a dice 10000 times and we gain 1€ if the result is odd, 2€ if it's 2 or 4 and 5€ if it's 6, what is the prob of gain 22000€ or more?

In the end I modeled a random variable as { 1 = 3/6; 2 = 2/6; 5 = 1/6 } And the situation is that we roll a dice 10,000 times and we want to know ...
6
votes
4answers
191 views

Probability that $ax^2+bx+c$ has no real roots after rolling 3 dice.

Suppose that I roll $3$ dice and write down the outcome as the coefficients $a,b,c$ in the polynomial $ax^2+bx+c$ respectively. What is the probability that this polynomial has no real roots? So, I ...
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2answers
41 views

Probability problem and number theory

A standard fair 6-sided dice is rolled $n$ times. Let $X_k$ be the spot which faced up inthe k-th round. What is the probability that $X_1+X_2+...+X_n$ is divisible by 7? I tried to solve it by ...
5
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2answers
81 views

Asymptotics of probability of Newton-Pepys problem

In Newton-Pepys problem one is interested in probability $p_n$ of getting at least $n$ sixes in $6 n$ independent throws of regular 6-sided die. The number of sixes $S_m$ obtained in $m$ throws ...
3
votes
2answers
155 views

Probability of two rolling dice

As I am taking some distance course on probability theory, I have no other option to ask my question than here. If they sound too basic, please bear me. Q: I roll two dice. What's the probability I ...
4
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1answer
181 views

Some dice roll questions relating to probabilities…

There is a game I play that utilizes a particular mechanic that I am trying to assess mathematically. Me being a layman, I am having some problems figuring out one of the aspects for myself. The ...
11
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2answers
396 views

Optimal Strategy for Bar Dice

This game is played in bars in Wisconsin, USA, but I'm sure variations are played many places around the world. The game has practical value, since once mathematicians figure out the best strategy, ...
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2answers
53 views

Dice problem, with image explanation.

Four dice are rolled SIMULTANEOUSLY. $X_1$ is a random variable that represents how many 1's you get in a single roll. $X_2, ... , X_4$ are defined in the same fashion, like in the picture below. ...