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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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, ...
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1answer
149 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
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1answer
200 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
37 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
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2answers
355 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
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2answers
501 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
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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 ...
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3answers
86 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
21 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
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1answer
61 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
251 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
599 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
170 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 ...
3
votes
3answers
71 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
263 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
117 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
125 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
132 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
44 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
63 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
votes
1answer
452 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
73 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
184 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: ...
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2answers
643 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
103 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
127 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
141 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 ...
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2answers
262 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 ...
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2answers
252 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 ...
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3answers
213 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
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4answers
192 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
47 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
votes
2answers
109 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
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2answers
199 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
votes
1answer
210 views

Probability that one player rolls more more 5s or 6s than the other player when one player rolls $X$ dice and the other player rolls $Y$ dice

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
votes
2answers
635 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
57 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. ...
0
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1answer
44 views

Question from a test concerning dice probability

There are 4 dice in the following colors: blue, yellow, black and red. They're rolled at the same time. Consider $X_1$ to be the quantity of dice in which the face value scored was one. Let $X_2, ... ...
0
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1answer
31 views

Question refering to dice probability from a test.

There are 4 dice in the following colors: blue, yellow, black and red. They're rolled at the same time. Consider $X_1$ to be the quantity of dice in which the face value scored was one. Let $X_2, ... ...
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4answers
24k views

If I roll two fair dice, the probability that I would get at least one 6 would be…

11 out of 36? I got this by writing down the number of possible outcomes (36) and then counting how many of the pairs had a 6 in them (1,6) (2,6) (3,6) (4,6) (5,6) (6,6) (6,5) (6,4) (6,3) (6,2) (6,1). ...
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votes
2answers
715 views

If you roll four fair dice, what is the probability that you will end up with two 1's and two 3's?

Can someone help me with this? I'm completely stumped on how to go about it and no one I know can help. I just need to be shown how to do it.
0
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1answer
77 views

Probability that one die will match another

I am working on a Dice game involving players rolling dice to match a shared die. Example: 6 6-sided dice are thrown, one Black and the rest white. Players score more points for each white die that ...
0
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1answer
151 views

Expected length of generating a pattern (throwing dice)

A fair die is tossed repeatedly. The experiment ends as soon as the last six outcomes form the pattern 131131 What is the expected length (i.e. the number of rolls of the die) of this experiment?
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1answer
83 views

Using Generating Series to Find Sum of Sides of Dice

Question: " Let k be a non-negative integer. Use the theory of generating series to find the expected value of the sum of the dots when k (6-sided) dice are rolled. " I know that the generating ...
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2answers
551 views

dice biased such that a 3 comes up twice as often as each other number?

I just attempted to solve a problem that involved the title. So, it turns out I was getting an incorrect answer b/c I computed the probability of getting a 3 as 2/6 as opposed to 2/7. I don't fully ...
3
votes
3answers
357 views

Probability of rolling a cuboid dice

It's easy to count the probability of events on a regular dice because we know the probabilities ($P(1)$, $P(2)$, $P(3)$, $P(4)$, $P(5)$, $P(6)$) of all the basic outcomes ($P(i)=\frac{1}{6}$). ...
0
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1answer
764 views

The Probability of Rolling a Large Straight with 5 Six-Sided Dice [duplicate]

I don't know the probability of rolling a large straight with 5 six-sided dice, so I need to know what the probability is. What is it?
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2answers
360 views

The Probability of Rolling the Same Number with 10 Dice That Have 19 Sides

I like dice and I want to know what the probability is for rolling the same number with 10 dice that have 19 sides. Also, do these dice exist or not?
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0answers
43 views

If you roll a dice twice, and substract result of

If you roll a dice twice, and subtract $ Result_1 $ from $ Result_2 $, in what interval with 97% probability will lie number of all zeros, if we will do this experiment 1200 times. I assume, I ...
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2answers
162 views

Calculating dice probability and risk-reward value

Having trouble how to model this cost-risk question with Probability. Assume that you are given 5 standard six-sided dice, what's the probability you get at least three 2s? I have calculated this: ...