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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How do I go about solving this probability question?

I was playing around with dice this morning and flipping them, when a problem suddenly hit me. If I roll $n$ normal six-sided dice, and flip every single dice, what is the probability that the ...
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2answers
47 views

100-sided dice was rolled 98 times, how do you choose next numbes to bet, based on current outcomes.

100-sided dice was rolled 98 times, Numbers form 1 to 50 were rolled exactly once, except number 25, which wasn't rolled yet. Number 75 was rolled 49 times You can only bet if the next roll result ...
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2answers
317 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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1answer
31 views

How can I convert [number of expected success per try] into [probability of succeeding N times without failing]?

There's a push-your-luck dice game called Can't Stop where you roll four six-sided dice, group the dice into pairs of your choice, then advance tokens along paths corresponding to the sums of your ...
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2answers
47 views

conditional probability of coming up 3 at least in one dice

Sorry for the simple problem, but I wanted to make sure that my idea is right (this is is the problem 1.8.50 from Rice's book) Two dices are rolled and the sum of the face values is six. What is the ...
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4answers
93 views

Roll summing over a long stretch

Say I roll a 6-sided die until its sum exceeds $X$. What is E(rolls)?
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1answer
44 views

Probability Dice and Expected Value

You are rolling a fair 30-sided die. (a) What is the expected number of rolls required to get a 27? (b) What is the expected number of rolls required to get a 27, followed later by a 28? For example, ...
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1answer
25 views

Probability of Sequential events on a die roll

If a person were to roll two dice and have to get a 9 or below for success. But if you fail the first time, you have the opportunity to roll it one more time for success, what is the probability of ...
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2answers
27 views

Having a value, calculating the probability of the number of times a die has been rolled

If I enter a friend's house and he has rolled a dice (d6) on a table which has a value $1$, he asks me the following, "Do you think I rolled this dice once and got $1$ or do you think I rolled it ...
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1answer
113 views

Dice: Expected highest value with a tricky condition

I know how to calculate the expected value "E" of a roll of n k-sided dice if we are supposed to keep the highest number rolled. If I am not wrong, the formula is: E = k − (1^n + 2^n + ... + ...
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2answers
229 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 ...
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1answer
49 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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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 ...
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3answers
100 views

Can we simulate a biased coin with fair die? [closed]

Given a fair 6-sided die, how can we simulate a biased coin with P(H)= 1/$\pi$ and P(T) = 1 - 1/$\pi$ ?
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1answer
43 views

Monopoly dice probabilities, including doubles

According to Monopoly, when you roll a set of doubles, you get to roll again. So if we get 6;6, 5;5, 4;4, 3;3, 2;2, 1;1, we will roll again. However, Monopoly has the "speeding" rule, this means that ...
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1answer
51 views

Probability of succesful rolls of different sided dies

This seems so simple, but I'm not sure how to calculate it. I have one six-sided die and one 12-sided die. What is the probability that, on a roll of both dice, that the six-sided die will win? ...
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1answer
47 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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3answers
537 views

How Many Permutations of Die Rolls Add Up to a Fixed Total?

I'm toying around with the idea of designing a board game. I like the idea of a hexagon-tile setup (a la Catan). There would be some number of different resource categories; I'm trying to determine ...
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2answers
43 views

Dice Probability (increasing numbers)

If I have 6 regular dice, (each numbered 1-6): What is the probability that when rolled that each will be a different number.(each individual di is a different number from 1-6, but a random order) ...
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1answer
157 views

The math behind generating Dungeons & Dragons ability scores: roll 4d6, toss lowest

D&D 5th ed. gives the following instructions for determining your “ability scores.” Roll four 6-sided dice and record the total of the highest three dice If I repeat the ...
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1answer
90 views

Probability of a rolling a dice $n$ times with $k$ faces

I need help calculating the probability of rolling $n$ dice with $k$ faces. So you have multiple dice, all with $k$ faces (number of sides on a dice) and you want to calculate the probability of a ...
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1answer
22 views

Given Nd6, what is the probability that the two highest are minimum 4?

So, my statistics knowledge is rather poor, so I would welcome a formula explanation to the question: given Nd6 (6-sided dice) what is the probability that the two highest numbers are at least a 4? ...
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1answer
480 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
42 views

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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31 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
56 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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3answers
86 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
81 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
25 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
66 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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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
23 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
52 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
176 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
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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
103 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
57 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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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
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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
116 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
104 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
77 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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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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247 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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2answers
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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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60 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
55 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
70 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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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 ...