What is Dice: Definition and 228 Discussions

Dice (singular die or dice) are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random numbers, commonly as part of tabletop games, including dice games, board games, role-playing games, and games of chance.
A traditional die is a cube with each of its six faces marked with a different number of dots (pips) from one to six. When thrown or rolled, the die comes to rest showing a random integer from one to six on its upper surface, with each value being equally likely. Dice may also have polyhedral or irregular shapes and may have faces marked with numerals or symbols instead of pips. Loaded dice are designed to favor some results over others for cheating or entertainment.

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  1. R

    B Calculating Probabilities of a dice roll

    I'm trying to figure out how to correctly workout the probability of rolling 3 6's if I roll 4 dice at a time. If I roll 3 sixes in a row, I don't bother with the last roll The order in which I roll them doesn't matter So here are my potential combinations Combination 1 => x 6 6 6 Combination 2...
  2. S

    Roll 5 Dice Simultaneously: Probabilities and Conditional Probability

    Homework Statement Calculate a) P(exactly three dice have the same number) b) Calculate the conditional probability P(three of the dice shows six|two of the dice shows 5) Homework EquationsThe Attempt at a Solution a) Say we have 1 as the number we get for three dice. There is 1/6 chance of...
  3. A

    Can I Predict the Correct Dice Using Probability Distributions?

    Say I have two dice which have different probability distributions but I don't know which probability distribution belongs to what dice. I now throw one of them exactly one time and the result is x. I know that die A has probability pA(x) for rolling x and die B has probability pB(x). I want to...
  4. G

    Throw of a die: Dependance on initial conditions and chaos

    Hi, We normally use a simple symmetry argument to show that the probability of each outcome of a throw of a fair, cube-shaped die is 1/6. However, is it possible to actually model the physics of the throw and show that the probabilities are 1/6? Since this is classical physics, the outcome can...
  5. C

    MHB Dice rolls: Counting number of rolls that equals 6 or 7

    The following calculates the number of times the sum of two dice (randomly rolled) equals six or seven. #include <iostream> #include <cstdlib> using namespace std; int main(){ int i = 0; // Loop counter iterates numRolls times int numRolls = 0; // User defined number of rolls int numSixes =...
  6. S

    PDF of open ended double dice rolls

    In many games a pair of standard six sided dice is used. I denote this 2d6. In this particular game, if a die is rolled the result is registered. If it returned a 6, it is re-rolled while a 5 is recorded. So it's basically a 2d5+1 open ended roll, which in theory could end up with very large...
  7. C

    C/C++ C++ Dice rolls: Counting number of rolls that equals six or seven. ()

    1) Calculates the number of times the sum of the randomly rolled dice equals each possible value from 2 to 12. 2) Repeatedly asks the user for the number of times to roll the dice, quitting only when the user-entered number is less than 1. Hint: Use a while loop that will execute as long as...
  8. E

    Probability problem -- Number of throws of a pair of dice to get a 7

    Homework Statement The minimum number of throws of a pair of dice so that the probability of getting the sum of the digits on the dice equal to 7 on atleast one throw is greater than 0.95, is n. Find n. Homework EquationsThe Attempt at a Solution There are 6 possible ways of getting a sum of...
  9. P

    MHB What are the odds of rolling 4, 5, 6, and 7 of a kind with 7 dice?

    Could somebody please tell me, in layman's terms, the answer to the following: When 7 standard six sided dice are thrown what are the odds of 4 showing the same number, 5 showing the same number, 6 and 7. Also the odds of 7 sixes being thrown. This is all to do with a game used to raise money...
  10. F

    Combination formula on dice and bit errors

    When the learning combination formula the formula nCr is usually derived using a deck of cards. There are n=52 different card. If you choose r number of cards, each is different so you basically start with n!/(n-r)! , then because the order is unimportant multiply by 1/r!. This explanation is...
  11. E

    MHB Just need a little explanation. Dice Problem

    I know this should be easy to understand but I just need a little clarification on the last part of my answer for this problem: If three distinct dice are rolled, what is the probability that the highest value is twice the smallest value I started this problem with the understanding that there...
  12. C

    MHB Dice Probability (5 Sided Dice and 6 Sided Dice)

    hi I am stuck on a question and was wondering if anyone could help me out (show a working solution/steps) to the problem. here's the question: Las Vegas Casino has introduced a new gambling game. A five-faced die A has numbers 1, 2, 2, 2 and 5 on its faces. This die and a normal die B (i.e...
  13. A

    Number of Macro-States w/ 2 6-sided Dice: Formula

    If there are 2 6-sided dice. What is the formula used to calculate the number of macro-states where a micro state is the sum of the two dice? I know there are 11 macro-states but I was curious if there was a formula for calculating this.
  14. Lenus

    Enumeration of increasing sequences of 2 dice sums

    I tackle the following game analysis: 2 players, two 6-sided dice. Bigger sum of points win. First roller has an advantage, as he wins even if 2nd player's dice sum equals to his. As the game is played with doubling cube (potentially increasing the odds before any roll), I tried to enumerate...
  15. P

    MHB What is the Probability of Winning a Dice Game?

    Hi There! This is my first time posting on this forums, so I hope I am following the right etiquette. Im having some severe difficulties with the problems under Question 3 in this past exam paper. http://www.nzqa.govt.nz/nqfdocs/ncea-resource/exams/2014/91267-exm-2014.pdf Can someone please...
  16. A

    Probability after Rolling Dice

    How does one calculate the probability of a sum of r in the dice rolls of n dice? Can a probability distribution be written for something like this, to calculate the probability of a sum greater than r, greater than or equal to r, equal to r, less than or equal to r, less than r, etc.? I do not...
  17. ZetaOfThree

    Entropy of a loaded dice throw

    Homework Statement A 6 sided dice is loaded such that 6 occurs twice as often as 1. What is the total probability of rolling a 6 if the Shannon entropy is a maximum? Homework Equations Shannon Entropy: $$S=-\sum_i p_i \ln{p_i}$$ where ##p_i## is the probability that we roll ##i##. The Attempt...
  18. P

    Probability of Rolling 7 with Loaded Dice: A Homework Solution | 11/56 Odds

    Homework Statement A pair of dice is loaded. The probability of 4 appearing on the first die is 2/7. and the probability of a 3 appearing on the second die is thrice as much as the other numbers on the die. If the rest of the numbers are equally likely events in both dice, what is the...
  19. D

    MHB Two Dice Toss: Outcomes & Plotting

    Two dice are tossed. The number of dots observed on the dice are added together to form the random variable \(X\) and also difference to form \(Y\). Determine the possible outcomes of the random vector \((X, Y)\) and plot them in the plane. How many possible outcomes are there? Solved
  20. J

    Unique Dice Throwing Probability Question

    G'day, I've recently been given a probability question to solve and I'm not 100% on my approach towards it. It goes as follows; A dice is found to be weighted so that the chance of throwing a 6 is four times the chance of throwing a 1. Chances of throwing numbers other than 6 are equally...
  21. S

    How many ways can you roll a four of a kind and a two of a kind with 6 dice?

    Homework Statement Hello, thank you in advance for help here. I am just trying to figure this out for my own edification. If I took 6 dice, each a regular 6 sided cube, how many possibilities are there of me rolling a four of a kind and a two of a kind? In other words, rolling a 646646...
  22. Z

    MHB How can I maximize my points when rolling multiple dice with different options?

    Hi, i was wondering how to calculate this problem: Rolling a 5 or a 6 on a dice means you score a point. You are given x dices. You have 2 options: Either you add y dices to your dicepool and can roll dices that show a 6 again (still gaining a point) or you can reroll your dices not showing a...
  23. gfd43tg

    Dice Rolling probability (matlab)

    Homework Statement In this problem, we will demonstrate the Central Limit Theorem by a virtual test that involves rolling of dice. To this end, you will create a function, with the following declaration line function [avgDice, histDice] = rollDice(NumDice, NumRolls) ##\bullet## NumDice: the...
  24. 1

    Ratio of Dice Rolls: A/B Dependency & Expectation Values

    Consider two independent random events A and B. Is the event A/B independent from event B? My real problem stems from a debate between myself and a colleague dealing with using the arithmetic mean vs. the geometric mean. My colleague used an example of rolling dice to discredit arithmetic...
  25. D

    What is the Probability of Throwing Two Dice and Getting Specific Numbers?

    Homework Statement A pair of dice are thrown. If a die show number 6 , what is the probability of (a)another die show number 2? (b) total score for both number greater than 8 ? for part (a) , my working is 1/6 x 1/6 = 1/36 but actual ans is 2/11 for part (b), the ans is 7/11...
  26. K

    Possible outcomes of rolling dice

    for second group, why the set of numbers of ( 132, 152, 153, 154, 213, 214 , 215, 216, 231, ...) is not included? since they are all three different numbers. https://www.flickr.com/photos/123101228@N03/14323629833/
  27. F

    [Statistical Physics] No. of dice rolls so prob of getting a 6 is >90%

    This question is really wearing me out, any ideas? Homework Statement How many times must I throw a fair dice in order to make the probability of getting at least one ‘6’ greater than 90%? With this many throws, what is the probability of getting three ‘6’s? It's the first part I'm...
  28. R

    Probability 2 Dice Question

    Homework Statement A pair of dice is rolled once, what is the probability that neither a doublet nor the sum of 10 will appear Homework Equations P(A) = 1 - P(A') Demorgans law (AUB)c = Ac ∩ B c The Attempt at a Solution I know how to do the solution through brute force and...
  29. Spinnor

    Fair and unfair N-sided dice in principle.

    In principle does classical physics allow us to make a fair N-sided die where N ≥ 3? If I give you a set of N positive numbers n_i whose sum is 1 can a N-sided die be made in principle such that each face of the N-sided die comes up on average with a probability n_i? Can N above be reduced to...
  30. B

    MHB Solving Dice Throwing Problem: Is Shared Outcome Higher/Lower Than Expected?

    Hi,I have the following problem that i don't know how to start solwing. I want to know if an occurence of my dice throwing outcomes is higher or lower then expected. I'll try to describe the problem as much as i can but if i miss something please feal free to ask. All I am looking for is a kick...
  31. U

    Probability question related to dice

    Homework Statement A die is thrown n times(n being odd). The probability that even face turns odd number of times is Homework Equations The Attempt at a Solution The probability that even face appears is 1/2 and odd face appears is 1/2. From any of the n throws, the even face can appear...
  32. N

    Rolling Two 3s: Probability & Combinations

    Say you roll a dice twice.You want to calculate the probablity of getting both dice to land on 3. Using the formula for combinations: the total number of combinations is 21. so is the probabilty of getting a 3 on both dice 1 /21 ?
  33. veronica1999

    MHB Rolling 5 Dice: Probability of At Least 3 Sixes

    Five standard 6-sided dice are rolled. What is the probability that at least 3 of them show a six? I am surprised my answer is wrong. First the total outcomes are 6x6x6x6x6=7776 Successful outcomes 10x6x6=360 There are 10 ways to choose 3 from 5 and then the remaining 2 can be any number...
  34. P

    Calculating E(X+Y+Z/X) and E(W/X+Y)

    we throw three ordinary dice and X,Y,Z their results and W=X+Y+Z how many differents values have the random values E(W/X) and E(W/X+Y)? can anyone explain me how to beggin because i am confused.. i will use E(X+Y+Z/X)=E(X/X)+E(Y/X)+E(Z/X)=? for the first one?
  35. P

    Estimating Expected Value of a Random Variable X from 129 Rolls of a Dice

    Pour an ordinary dice 129 times and let X the sum of all indications that it brings. Let p=P(X<=12) What is the minimum upper bound for the probability p resulting from inequality of Chebyshev; Note: The probability density of X is symmetric about the mean value of X how i can find...
  36. S

    Rolling a pair of dice 20 times

    Homework Statement I have math experiment where I roll a pair of honest dice 20 times. The results are: 2,3,4,4,5,5,6,6,6,7,7,7,7,7,9,9,9,10,10,11 write a frequency table of the outcome of the dice roll with respect to size: 2,3,4,5,6,7,8,9,10,11,12 Firstly there must 36...
  37. P

    Probability dice and coin

    Throw a dice and record the result. After flipping a fair coin. If it comes letters repeat. If it comes up heads stop. (In other words, throw the dice continuously until we crown the currency immediately after throwing the dice.) What is the probability that the maximum effect of the dice...
  38. W

    MHB Combinatorics question involving 6 6-sided dice

    When rolling 6 6-sided dice, how many different ways can you have exactly 4 different numbers? I tried solving this like so, the first dice has a possible 6 numbers, the second has a possible 5, the third has a possible 4, and the fourth, 3. Then there are 2 remaining dice of which each has...
  39. Saitama

    What is the probability of getting a sum of 10 when rolling two unfair dice?

    Homework Statement (see attachment) Homework Equations The Attempt at a Solution The sum of the probabilities of each number on the dice is 1, i.e \frac{1}{6}+\frac{1}{6}+\frac{1}{9}+x+\frac{2}{9}+y=1 where x and y are the probabilities of number 4 and 6 respectively. Solving...
  40. G

    Probability in a Dice Game?

    In this game you roll six dice. After each roll you must take at least one die but you can take more than one as well. After you take a die you have the ability to roll again. In order to score you must have the qualifying die rolls of (4) and (1). The four other spots compromise your scoring...
  41. U

    Probability question considering 6 dice throws

    Homework Statement Dice is thrown 6 times. What's the probability of numbers 5 and 6 showing up at least once.Homework Equations This ought to be basic probability calculus but i just can't get my head around this. Some kind of attempt(ish) below. THe answer ought to be 0.418 or 41.8%.The...
  42. L

    Chance of rolling at most one six with two dice in 20 rolls.

    Homework Statement Well as I said what is the chance of getting at most one six when rolling two dice twenty times? Homework Equations I know the probability of getting one six in one roll with two dice is: 11/36 And not getting one is: 25/36 The Attempt at a Solution...
  43. N

    Which Dice Is Best for Highest Mean Value?

    Hey! :-) I have got question about verisimilitude. I have got classic one dice. The dice can have 2-20 walls, where is numers from 1, 2, 3, ...20 (two-walls: only 1, 2; seven-walls: 1,2,3,...,7). You can throw with dice. When you have got largest number on dice (two-walls: 2...
  44. N

    Probability question with dice

    Two dice are rolled. What is the probability that the first die is a perfect square and the second die is a 4? First die : 2/6 Second die : 1/6 Won't the probability be just (2/ 6) * (1 / 6) = 2 / 36 = 1 / 18 My answer says 3 / 6 but aren't these events not mutually exclusive? :|
  45. M

    What is the probability of getting 1,2,3,4 when 5 dice are thrown and

    What is the probability of getting 1,2,3,4 when 5 dice are thrown and one of them is not 5.(the order of 1,2,3,4 doesn't matter) I am really confused: So I computed chances of getting correct numbers that is 1/6^4 times 5/6,then I multiply this by 4 times 5! Am I right?
  46. E

    So, does God play dice with the Universe or not?

    Hi. I'm currently reading 'The Goldilocks Enigma' by Paul Davies. In it he attempts to explain some areas of Quantum Mechanics in laymans terms and writes... "Quantum randomness, by contrast, is irreducible, which is to say that quantum processes are in some sense genuinely spontaneous -...
  47. M

    Probability dice roll questions

    Homework Statement A player rolls a fair die and receives a number of dollars equal to the number of dots appearing on the face of the die. What is the least a player should expect to pay in order to play the game? Homework Equations I don't really understand the question?? can...
  48. mishima

    Help change 6-sided dice circuit to 20-sided

    I'm looking for input as to how I could modify this: http://www.electronicdesignworks.com/circuits/electronic_dice/electronic_dice.htm so that it does a 20-sided dice instead of a 6. Thanks.
  49. C

    What Is the Probability A Rolls a Winning Sum in Dice Game?

    Homework Statement A and B alternate rolling a pair of dice, stopping either when A rolls the sum 9 or when B rolls the sum 6. Assuming that A rolls first, find the probability that the final roll is made by A. The Attempt at a Solution A rolls a sum 9 on each roll with prob 1/9 B rolls a...
  50. I

    Solve Dice Probability Homework - Mean, Standard Deviation

    Homework Statement Well I need to design a program that simulates rolling 2 dice. After the dice have been rolled 100 times, I need to find the mean and standard deviation of each (from the data that I get from the simulation). I can't seem to figure out how to do this.. Seems simple right...
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