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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Uniform distribution on $\{1,\dots,7\}$ from rolling a die [duplicate]

This was a job interview question someone asked about on Reddit. (Link) How can you generate a uniform distribution on $\{1,\dots,7\}$ using a fair die? Presumably, you are to do this by combining ...
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27 views

probablity question related to 2 die and the classic monopoly game.

While playing monopoly I accidentally figured out that probability for landing on Illionis Avenue is most in the whole game and for landing on orange colored group ...
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1answer
50 views

Dice Game: Probability of rolling three 6's before my opponent

Let's say I'm playing a dice game with a friend. We each get two dice, and we roll all of our dice at the same time. You get one point for each 6 you have. First to score at least three points wins. ...
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2answers
308 views

Probability of winning blackjack dice game?

I know a little bit about probability but I am not sure how to calculate this: In a dice game of blackjack, there are two parties. The player and the dealer. The aim of this game is to get as ...
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3answers
76 views

Roll a dice, probability that game goes beyond one round

There are two people $A$ and $B$. Person $A$ has $8$ chips, and person $B$ has $6$ chips. Each round, both people roll a die then take that number of chips from the other person. The game ends when ...
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4answers
74 views

The average outcome of the sum of a pair of dice and the higher sum of two pairs

I'm helping my son to design a game using dice. He wants to figure out the expected outcome of the sum of a pair of dice(6 sided) if two pairs of dice are thrown and the higher pair is kept. I get ...
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0answers
23 views

Expected number of rolls to roll every number [duplicate]

If I am rolling I die until I roll every number at least once, what is the expected value of times that I will need to roll the die? After a brief computer simulation, I got 15. But why is this the ...
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2answers
54 views

Two identical dice are thrown simultaneously. Find probability of getting a $3$ and a $2$.

Two identical dice are thrown simultaneously. Find the probability of getting a $3$ on one of the dice while a $2$ on the other. I'm pretty sure the answer is $\frac{2}{36}$ but my friend says ...
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0answers
103 views

Probability of consecutive row of at least $m$ by $n\leq2m$ 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 ...
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0answers
35 views

Probability of multiple dice rolls with decreasing amounts of dice

Calculating probabilities over multiple dice rolls is easy, but what do you do if the amount of dice decreases (dependently) from roll to roll? This is a common feature of many games, including Risk, ...
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7answers
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Is it possible to create a completely random integer between 1 and 13 using standard dice in a D&D dice kit?

I am asking if it is possible to choose a random integer using a certain set of dice. Assume for these calculations that the dice are perfectly randomly distributed. There are 7 dice in a set, with ...
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1answer
21 views

$n$ dice, finding $\operatorname{var}(X)$

If we throw $n$ dice. And $X$ is the total number of eyes. Find $\operatorname{var}(X)$. My idea was to label $X=X_1+\cdots+X_n$ where $X_1$ is the outcome of die $1$ etc. And because $X_1,\ldots, ...
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1answer
49 views

A dice and Law of Large Numbers

The dice A has 2 red faces and 4 green, and the dice B conversely: 4 red and 2 green. We toss a symetric coin; if come up heads, we choose the dice A, otherwise - the dice B. Next we execute a series ...
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3answers
148 views

How do I calculate the odds of a given set of dice results occurring before another given set?

Dice odds seem simple at first glance, but I've never taken a Calculus based statistics course or game theory, and I think I may need to in order to solve some of the things I'm trying to solve. I can ...
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0answers
41 views

Probability dice game, multiple turns

Alice and Bob are playing dices, Alice begins. If the current player gets a 6, he wins. If he gets 4 ou 5, he plays again. Else, the other player plays. Let $p_n$ (resp. $q_n$) be the ...
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3answers
97 views

100-Sided Dice “Blackjack” Game

I am attempting to determine two variables in this game: The optimum strategy: (What number the bettor should stay at) The expected value given perfect play: (The percent return on a bet when using ...
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1answer
56 views

exactly $k$ distinct values in $n$ $n$-sided dices

We roll $n$ $n$-sided dices. What is the probability of getting exactly $k$ different values? From the union bound (as every possible $k$ sequence might contain the $k$ different results), I think the ...
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0answers
36 views

How do I calculate the adjusted percentage of dice out comes.

What I’m attempting to do is construct a spreadsheet to calculate the number of wounds and kills for a tabletop board game I play. To give everyone an idea of the situation. You have figure A shoots ...
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1answer
25 views

Player's View: Probability of number of certain die on table given dice in hand

I'm trying to make some AI for a single player version of a dice game named Dudo. The relevant aspects are that there are six players with six dice each (which only they can see until the end reveal), ...
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3answers
1k 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 ...
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4answers
109 views

Use a 20 sided die and a 6 sided die to represent number 1-45 with equal probability

I wonder if anyone could help me with this question: Use a 20 sided die and a 6 sided die to represent all numbers from 1-45 with equal probability. Also, it is okay to use one die repeatedly as ...
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2answers
101 views

Changing-sided dice probability problem.

Suppose you roll a fair $6$-sided dice, and that the number you roll is $m$. If $m=1$, stop. Otherwise, roll an $m$-sided dice. The number you roll is $n$. If $n=1$, stop. Otherwise roll an $n$-sided ...
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2answers
62 views

Dice Game - Probability Theory

There are many dice problems on here so there could be duplicate. If there is I apologize. Here is the question. The game is given as follows: you are given 5 dice, and the goal of the game is to get ...
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2answers
48 views

How many dice would I need to get an $n$ of a kind 100% of the time?

For example, if I wanted to get two of a kind, I would need seven dice. This is because even if the first six were 1, 2, 3, 4, 5, 6, the next one would have to make a pair out of the previous dice. ...
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4answers
228 views

Find the probability that the final score is 4 in a dice game with two throws

A game uses an unbiased die with faces numbered 1 to 6. The die is thrown once. If it shows 4 or 5 or 6 then this number is the final score. If it shows 1 or 2 or 3 then die is thrown again and the ...
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1answer
462 views

Probability of dice roll (board games)

Assume that we have n * 6side dice. We will roll all n dice. I ask what is a probability of getting at least r * 1(number 1 on a die), s * 2, t * 3, u * 4? Number 6 can be used instead of any of other ...
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2answers
39 views

Having two random generated natural numbers between 1 and 255, and generate out of it natural number between 1 and 256

Let's say you have two cube with 255 sides and you have to use them to simulate a single cube with 256 sides, how can I do it? $f(n)$ and $g(n)$ returns random number between 1 and 255. I thought ...
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2answers
57 views

Rolling two dice… [closed]

Let $A_n$ be the number of fives, $B_n$ the number of sixes and $C_n$ the number of eights in $n$ rolls of two dices. For which n do we have: $E(A_n) < E(min(B_n,C_n))$ ?
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1answer
52 views

Rolling a certain total with a dice

Suppose you roll a $k$-sided die repeatedly, totaling your scores as you go, until you reach or surpass $n$. (For a real-world usage ... if you have a non-looping game board and only move forward, ...
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1answer
59 views

Suppose we roll 10 fair six-sided dice. Probability of getting exactly two 2's and three 3's?

Here's my solution, but as usual with combinatorics problems, I tend to be convinced of my errors too early. So I'd like to know what you guys think. Is this correct? $\frac{\binom{10}{2} ...
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0answers
28 views

How good of an approximation is a normal probability distribution for sum of dice rolls?

I want to know how well the normal distribution explains the sum of rolls with n dice with s sides. The mean value and the variance of the dice rolls are $$\mu=n\frac{s+1}{2}$$ and ...
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1answer
25 views

Approximation of distributions with dice

I want to know what dice to roll to get a given probability distribution(mainly normal distributions but exponential distribution would also be helpful). I want a function $f$ so that ...
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2answers
74 views

Probability of dice with a cumulative successes

Needing some Math help! I'm working out part of a system for a game I'm working on, and I need to know if I need to tweak some things, so I'm checking to see if it all adds up (no pun intended). ...
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3answers
50 views

What is the probability that dice are rigged?

Scenario We are given a single six-sided die. We produce a sequence of $n$ dice rolls, all of them rolling six. We do not know whether the die is fair or not. How can we calculate the probability ...
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1answer
55 views

Estimating the number of sides of a die

A friend of mine inspired this question: Given a fair die, can one accurately estimate (within some margin) the size of the die given enough rolls? For example: If I roll a die 1000 times and all the ...
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2answers
274 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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3answers
74 views

What is the probability of two dice getting a sum of 7 without a two?

I am currently working on conditional probability and I am somewhat confused about how exactly to complete this problem. I know that to find conditional probability that you utilize: $$P(A|B) = ...
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2answers
43 views

A probability question - Dice Throw

Sum of three dice (six faced) throws is $15$. What is the probability that first throw was $4$? The way I thought of solving this was... - Given - sum of second and third throw is $11$ - Probability ...
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3answers
125 views

Probability of getting a sum of 14 when rolling 11 dice

So, this is a probability and combinatorics problem... I'm not sure how to solve this. I assume that in P(A) = m/n, n is 6^11, but I don't know how to calculate the number of ways to get a sum of 14 ...
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1answer
80 views

A fair die is rolled nine times. What is the probability that 1 appears three times, 2 and 3 each appear twice, 4 and 5 once and 6 not at all?

A fair die is rolled nine times. What is the probability that 1 appears three times, 2 and 3 each appear twice, 4 and 5 once and 6 not at all? My approach is fairly simple. The dice is fair, so we ...
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5answers
164 views

Dice roll probability, at least 9 total?

If I have two dice with $6$ sides each, what is the probability of me rolling atleast $9$ total? I think I'm correct when thinking that the probability of rolling a $9$ is $\frac{4}{36}$, that is ...
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4answers
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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 ...
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0answers
44 views

Expected number of rolls on a 200 sided die to roll a 1? [duplicate]

We have a 200 sided fair die with faces numbered 1 through 200 and want to know how many rolls are expected to roll a 1. How would I go about calculating this?
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1answer
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Optimal strategy in the following game:

In this game, 12 hidden D6s are rolled and summed. The player is given the total of the rolled dice. The player will then guess a number from 1 to 6. If there is a unrevealed dice with that number, ...
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1answer
55 views

What's more likely with 7 dice - Straight, Full House, or 3-of-a-Kind

Here's a problem I'm having. I have 7 dice. I want to rank the difficulty of achieving a particular 5 dice combination after all 7 dice have been rolled. A straight is when at least 5 of the seven ...
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14answers
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Simulate repeated rolls of a 7-sided die with a 6-sided die

What is the most efficient way to simulate a 7-sided die with a 6-sided die? I've put some thought into it but I'm not sure I get somewhere specifically. To create a 7-sided die we can use a ...
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1answer
46 views

Dice Probabilities - How often does 3, 4, 5 show up in 5 dice on one roll?

I want to find out the probability for rolling 5 dice and the result containing at least 3, 4, and 5 without caring what the other 2 numbers are. I'm not very familiar with this kind of probability so ...
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1answer
38 views

Is this Event Mutally Exclusive?

I am trying to calculate the following, however I'm unsure on whether this event would be Mutally Exclusive or Independent. Can someone help with finding the probability of the Intersection? P(A) ...
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3answers
52 views

How to handle dice probability? ie, how much more likely would 3 six sided dice give a higher sum than 3 four sided dice?

I am playing at making my own table-top gaming system/rules and I wanted to have a better handle on how likely different dice combinations will give a higher result than one another. I know that a six ...
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1answer
73 views

Normal distribution with dice

I'm wondering how to control the normal distribution that comes from summing dice rolls only using different numbers of dice, different combination of types of dice (d4, d6, d8, d10, d12, d20) and ...