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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Chevalier de Méré's Problem Type Question

Is the following argument correct: A double six in a single turn in game B is 1/6 as likely as rolling a six in one turn in game A. But there are 6 times as many turns in game B as game A. Thus the ...
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3answers
518 views

Probably of 2 six in 5 dice rolls

What is the probability of obtaining exatcly 2 six when rolling a dice 5 times? In order to obtain this probability, I will need to devide the number of favorable events by the number of possible ...
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4answers
84 views

Rephrasing die question

Seems I asked my last questions poorly and it got a bad response. Okay so basically here's the problem and I will explain how I am trying to do it. You roll 1 fair die repeatedly until you either ...
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1answer
76 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 $2$? ...
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1answer
125 views

Calculate the Entropy Change if 5 Previously Tossed Dice Are Turned to All “1”

Relevant Equations: S = Boltzmann*ln(W) where S is entropy and W is the number of microstates. I have thought about this two ways. 1 way. Look at each die separately. Let macrostate 1 = number of ...
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1answer
186 views

Three dice rolled

Three indistinguishable (fair) dice are thrown simultaneously at random. Find the probability that the sum of the three dice is less than six and that no two dice show the same face (the same number). ...
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1answer
47 views

Probability of Fair Die

Hi everyone I have a question about probability: Fair die thrown two times, final score is calculated as follows. If the number on the second throw is a 5 he multiplies the two numbers together, and ...
3
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1answer
159 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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2answers
68 views

How to find the probability of a score from multiple dice with varying sides

I'm trying to find a general method for working out the probability of a score from rolling several dice with varying sides. For example, the probability of getting a result of 12 when rolling two ...
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1answer
42 views

Conditional Expectation of Two Dice Roll?

A is the first roll of the dice, B is the second. The question is to find the expected value of A given A + B = 7; E(A|A+B = 7) Since A can be any number between 1 and 6, is this as simple as ...
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4answers
87 views

Simple combinatorics dice problem

How would you explain, how ${5\choose4}$ corresponds to the pattern $6-6-6-6-3$ when throwing five dice. The pattern is meant to form a sum of $27$ in total. What I do understand is that you could ...
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4answers
126 views

Dice rolling probability. [closed]

A die (6 face) is thrown 3 times. What is the probability that the second and third rolls are larger then the first roll. Thank you
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0answers
210 views

Two dice are rolled. If the sum is greater than 8, what is the probability that it is 11?

Two dice are rolled. If the sum is greater than 8, what is the probability that it is 11? I'm not sure if this question is asking for conditional probability or just 2/10...
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5answers
304 views

Expectation and best strategy for a dice game

I am somewhat stuck on this problem, it should be straightforward but I cannot find a clearly explained solution: A single dice is rolled as many times as you want. For each throw, you receive n ...
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3answers
47 views

Die Roll Probability with 8-sided Die

What is the probability of rolling an "8" on an 8-sided die four times out of nine attempts? My friends and I were playing a game where one player could only succeed by rolling an 8 with an eight ...
3
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3answers
117 views

probability rolling a dice 5 times

I can't solve this problem: What is the probability that, when rolling a dice 5 times, the number of times when you get a 1 or 2 is greater than the number of times when you get a 6. any help?
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2answers
694 views

What is the probability of my sum reaching exactly 10? [closed]

I throw a 6-sided dice (with values: 0,1,2,3,4,5) multiple times and add each value to a sum, which is 0 in the beginning. What is the probability of my sum reaching exactly 10, 11, 12, 13, 14? After ...
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1answer
336 views

Fudge Dice: Reroll vs. Bonus

A "fudge die" is a die with equal probability to result in -1, 0, or +1. The commercially produced fudge dice are generally 6-sided dice with two "–", two "+", and two blank sides. In the ...
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1answer
116 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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1answer
505 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 ...
3
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1answer
62 views

Is it absolutely certain that repeated random selection of integers from 0 to 100 will eventually select every integer?

I would like to know if one can be absolutely certain, after a number of trials, to circle every integer from 1 to 100 using the following method: Let's say you write down integers 0 to 100 from left ...
30
votes
14answers
6k views

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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2answers
514 views

How many combinations from rolling 5 identical dice?

Where, for example: (1,3,1,4,6) is considered the same outcome as (1,1,3,6,4) How many total outcomes are there? Edit 1: My hunch is that there are: 6 outcomes from choosing 1 dice to be missing. ...
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1answer
70 views

Rolling 6 dice and 3 on the same side

I found similar answer for 'Rolling 6 dice and 4 on the same side'. Will exactly the same rule apply for 3 dice? Instead of 15000 (according to the above link), I found somewhere 14700. $${6 ...
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1answer
33 views

Probability that theoretical results match experimental results

I am not sure if this can be determined, but I was wondering if there was any way to go deeper into probability to find the odds that your experimental results match your theoretical results. For ...
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1answer
92 views

How to compute of each player winning this sequence of games?

Players A and B play a sequence of independent games. Player A throws a die first and wins on a "six." If A fails, then player B throws and wins on a "five" or "six." If B fails, then A throws and ...
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2answers
83 views

Probability that k is the maximum of n dice throws

Given a dice with $m$ sides that is thrown $n$ times, what is the probability that $k <= m$ is the maximum number obtained? Here is my attempt: In order of $k$ to be the maximum, in at least one ...
5
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2answers
586 views

Throwing dice twice, with unlike probability of occourence?

A loaded dice has the property that when the dice is thrown the probability of showing a given number is proportional to the number. For example $2$ is twice as likely to show up compared to $1$ and ...
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0answers
22 views

Optimal strategy for n consecutive throws of a dice and deciding if the current value is the result [duplicate]

You have a six sided dice. You roll the dice and decide if you want to stop and keep the current value as your result. If not you try again. You can at most throw the dice n times. If you throw it n ...
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1answer
47 views

A question involving the throw of seven dice, which of my answers is correct?

Seven dice are thrown, what is the probability that all numbers show up on the dice? My first answer uses the logic that if all numbers show up and you throw seven dice, then one number is repeated ...
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3answers
72 views

Should I pick the higher dice?

Assuming I start with $n$ dice that have been rolled once, is it beneficial to choose the higher dice when I roll less than $n$ dice again (assuming I want a high roll)? In some board games, dice ...
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1answer
133 views

Expected number of dice rolls to uniquely determine values of the faces

Suppose we have $k$ fair $n$-sided die (so each face rolls with probability $1/n$), with each face of the die labelled as $a_i$ $ (i=1, \ldots, n)$, with the values of the $a_i$ being unknown to us. ...
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2answers
136 views

Expected value and variance of max{x, y}

I've run into this problem while playing a game called Europa Universalis 4. I've done similar maths before in my studies so I'm pretty sure this should have an easy answer but I can't for the life of ...
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1answer
118 views

Calculate single “battle” outcome odds for RISK

I am trying to reproduce the values in this odds ratio table from Wikipedia. For all those unfamiliar with RISK, this is a game where units fight against each other via the roll of the dice: The ...
3
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1answer
73 views

Statistical test for “too perfect” random number generator?

I am attempting to characterize some random number generator programs in a very simple way. Specifically, I'm rolling a simulated 6-sided die $3 \times 10^8$ times and keeping a count of how many ...
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2answers
114 views

Calculating the probability of getting a specific set of dice from a single roll

If I want to create a function $p_{roll}(x_1, x_2, x_3, x_4, x_5)$ that calculates the probability of getting the given dice (order is not important) in a single roll with 5 dice then how would that ...
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1answer
43 views

Can a biased physical random source be post-processed to control the bias?

Let $X_i$ with $i\in\mathbb N$ be a sequence of independent 6-ary random variables with distribution $\operatorname{Pr}(X_i=e)=p^e_i$ where $e\in\{1,2,3,4,5,6\}$ and $\sum_{e=1}^6p^e_i=1$. Let's ...
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2answers
172 views

Biology: How to find the probability of randomly generating multiple, sequentially identical sets

If I randomly generate a substring (example "ATGCAGC") with equal probability (1/X where X=4) for each digit with length (L) digits: What is the formula for finding the probability (P) of randomly ...
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1answer
46 views

Probability of a dice being in a set of dice

I have no formal background in math, statistics, or anything. Just trying to figure out a fun problem with a game of dice. Lets say you have 3 people sitting a table rolling dice (including ...
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3answers
73 views

Probability Puzzle: Mutating Loaded Die

Take an (initially) fair six-sided die (i.e. $P(x)=\frac{1}{6}$ for $x=1,…,6$) and roll it repeatedly. After each roll, the die becomes loaded for the next roll depending on the number $y$ that was ...
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2answers
66 views

What is the best strategy for this dice game?

Given the following game, what is the best strategy to maximize your total score? Each game play starts with a random point value. You are then given a chance to multiply that value by choosing ...
2
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3answers
215 views

Expectations and variance with rolling a dice 10 times

Let's say you roll a fair dice 10 times and X is the number of sides that never show up. (i.e. Roll 1 - 10 = 1424145221, X = 2 because 3 and 6 never show up) Values of $N=0,1,2,3,4,5.\\ P(N=6) = 0$ ...
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2answers
30 views

clarify basic probability question

You have a loaded die. $A =$ even numbers $B =$ odd numbers $P(A)=3/4$ $P(B)=1/4$ $P(\{1\})=1/12$ $P(\{2\})=1/4$ How was $P(\{1\})$ and $P(\{2\})$ calculated? Is it beacuse there are 3 odds ...
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1answer
125 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 ...
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1answer
75 views

Conditional Probability in Dice

Please forgive me if this is an easy question, because I have never had a class in probability. Lets say two people are each going to roll a D6 to determine who is going to go first in a board game. ...
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1answer
461 views

Highest average value when rolling dices

This question is in reference to a game called "Tiny Dice Dungeon." In this game, damage is calculated based on rolling dice. I want to know how I can achieve the highest average damage. This is the ...
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1answer
91 views

What are the chances of getting at least 3 fours when rolling 5 dice?

What are the chances of getting at least three or more "fours" or higher number when rolling a fair six-sided die five times? Actually, this is a problem I am curious about the answer and I can't ...
2
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2answers
62 views

Six dice, six different figures (model problem)

I am thinking about the same problem as posted here: Probability question (Six dice). If one rolls six dice, what is the probability of attaining six different figures. I do understand the solution ...
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1answer
46 views

probabilities for obtaining 3 dice result

I am developing an app that needs a 3 dice result and there are two methods I can use: method a) create a matrix of 216 possible combinations and choose 1 randomly method b) or generate 3 ...
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2answers
348 views

Sum of 3 dice rolls

If we roll a fair dice 3 times, what is the probability that the sum of values of the three rolls is greater than 9? I approached it like this: Let X be the result of a single dice roll. Let Sn = X1 ...