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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0answers
82 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 + ... + ...
0
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1answer
143 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
55 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 ...
26
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14answers
5k views

Simulate 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 ...
1
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2answers
72 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. ...
1
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1answer
48 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 ...
2
votes
1answer
27 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 ...
1
vote
1answer
41 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 ...
2
votes
2answers
51 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
votes
2answers
536 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 ...
1
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0answers
18 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
38 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 ...
0
votes
3answers
65 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 ...
1
vote
1answer
67 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. ...
0
votes
2answers
75 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 ...
1
vote
1answer
75 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
votes
1answer
57 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 ...
1
vote
2answers
55 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 ...
1
vote
0answers
39 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 ...
4
votes
2answers
91 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 ...
0
votes
1answer
43 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 ...
6
votes
3answers
62 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 ...
0
votes
2answers
61 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
votes
3answers
102 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
29 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 ...
5
votes
1answer
87 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 ...
0
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1answer
37 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. ...
2
votes
1answer
332 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 ...
1
vote
1answer
49 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
votes
2answers
42 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 ...
0
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1answer
44 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 ...
0
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2answers
130 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 ...
-1
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3answers
37 views

Chance of rolling at least five 3s on fifteen dice [closed]

What is the formula to calculate rolling fifteen dice and at least five of them show 3?
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1answer
34 views

Variance of a modified sum of dice rolls

Suppose one rolls 3 (fair) dice with 20 numbered faces and sum the results. Call that sum $X$. The distribution will resemble a normal distribution with mean $3\cdot 10.5=31.5$ and variance ...
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vote
3answers
48 views

Are the number on the dice placed on these sides for a reason?

To further explain the title: Is there a probabilistic reason as to why a 6-sided die has the opposing sides suming to 7? My argument begun when a friend decided to use this die instead of this die. ...
0
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0answers
57 views

On an average How many times must I throw $r $ die with $N$ faces, such that I see all $N$ faces?

For an $n$-sided die, the number of rolls needed, on average $n\log n$ for large n. For one die the question is here: "A Collection of Dice Problems" by Matthew M. Conroy. What about $r$ dice?
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5answers
144 views

game theoretic die rolls

Suppose player X has a 6 sided die and player Y has a 10 sided die. They each get two rolls and they can each choose to stop rolling on either one of the rolls, taking the number on that roll. Whoever ...
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1answer
112 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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vote
2answers
37 views

Probability of obtaining equal number of each outcome of a fair die at the nth trial

Suppose a fair die is tossed repeatedly. I am concerned in deriving the probability of the occurrence of obtaining equal number of each possible outcome at the nth trial. Clearly this is only possible ...
0
votes
1answer
54 views

What is the chance of this dice appearing twice in a row? [closed]

3 friends roll a 6-sided dice. What is the probability that at least two of them roll the same number?
0
votes
1answer
170 views

Probability of rolling 3 sixes in 6 rolls

I roll a dice six times. What is the probability of rolling at least 3 sixes? Please share the formula as we'll, so I can figure it out myself in future. Many thanks!
0
votes
3answers
62 views

Strange Dice probability

I started a discussion with some friends trying to understand: if I roll 1 dice of 10(1d10) and 1 dice of 4(1d4) 20 times, and do it again 1000 times. Why the d4 have the probability to score the ...
0
votes
1answer
151 views

A fair dice is tossed 6 times. What is the probability that there is at least one pair of identical consecutive face values?

For example, 231146 is a valid sample point but 131213 is not. This is a question on past exam that i have no idea to solve. Please help me!
0
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2answers
71 views

Rolling a balanced die 10 times

A balanced die is rolled 10 times by 5 different people. What is the probability that at least two people rolled exactly 4 twos, 3 fours and 3 sixes? So I know I'm looking for $P(X\ge 2)= ...
0
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1answer
43 views

Expectation of conditional event for throwing a fair dice

A fair die (with face numbered $1,\ \ldots\ ,6)$ is independently rolled repeatedly. Let $X$ denote the number of rolls till an even number is seen and let $Y$ denote the number of rolls till $3$ is ...
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2answers
37 views

Probability of 3 dices

Been looking through past exam papers and came across this question: Three fair dices are rolled. The probability that all three dices show 5 is 1/216. Is this true?
3
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1answer
164 views

Best strategy for rolling 20-sided and 10-sided dices

There are a 20-sided (face value of 1-20) dice and a 10-sided (face value of 1-10) dice. A and B respectively roll the 20 and 10-sided dices. Both of them can roll the dice twice. They may choose ...
0
votes
1answer
89 views

Roll 2 dice adding and rolling one die, probability of being equal

Roll two dice, add the results, call the number x. Roll one die call that number y. What is the probability that x and y are equal? Help please.
0
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1answer
89 views

How many times to roll a die before getting $n$ consecutive sixes given $m$ occurences?

Given a unbiased dice how to find the average number of rolls required to get $n$ consecutive sixes given already $m$ number of sixes occurred where $m\leq n$. I know how to solve using n consecutive ...
5
votes
2answers
111 views

Number of dice rolls taken to reach a certain sum

I was reading about sums of dice rolls and Chernoff bounds, and I thought of a question I couldn't obviously answer with the techniques I know. You're given some number $x$ and told it was generated ...