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. P

    Newtons laws on car fuzzy dice

    Homework Statement You have a fuzzy dice with mass .2kg hanging from the rear view mirror. When you step on the gas the dice makes an angle of 25 degrees. what is car's acceleration? Homework Equations F=ma...? Fr=mac..? The Attempt at a Solution Im really not sure where to start...
  2. T

    Probability Two tetrahedral dice are thrown

    Homework Statement Two tetrahedral dice (four-sided dice) are thrown. What is the probability that the sum of the scores is: a) even b) prime c) even or prime? Homework Equations The Attempt at a Solution a) P(even) = 1/2 b) P(prime) = 9/16 c) c for confused :confused: Can...
  3. C

    Angle of fuzzy dice when moving Just want to check

    Homework Statement a pair of fuzzy dice hang from your mirror. While you accelerate from a stop on a horizontal surface to 28 m/s in 6 s, what angle θ does the string make with the vertical? Homework Equations tan θ = Y/X a = ΔV / Δt The Attempt at a Solution Just want a double...
  4. J

    MHB Dice Probability: 5 Rolls, Increasing Number

    A Dice is Rolled $5$ times. The Probability of Getting a higher number then the previous number each time is
  5. N

    How to verify dice by statistic means ?

    Hello all, I got stuck with some problem of probability What I understand is how to verify by statistics, that a die (is that really the singular of dice ??) is crooked: - cast it a number of times, say twenty - count the number that shows most, say we find eight times the six -...
  6. L

    What is the probability of rolling a 7 with two dice?

    I have a basic probability question - say you throw a dice, probability of 'x' occurring is 1/6 Say you throw two dice, probability of 7 occurring is more than others. But how do you prove this experimentally? Throw a dice? how many times?
  7. G

    Optimizing Dice Game Strategy Against Automated Players - Any Tips?

    You play against three automated players who’s dice and actions are independent from you. You start with six randomly rolled dice. Rules: -You MUST keep at least one die, but can keep as many as desired. -A (1) and (4) are qualifiers, without both qualifiers you cannot score. These do not...
  8. S

    Give that two six sided dice are rolled once

    1. Given that two six sided dice are rolled once, what are the odds against rolling a sum that is a multiple of 3 3. The answer I got was 2:3 Was just wondering if this is correct.
  9. M

    Making equations with six six-sided dice

    Suppose I am playing a game where I roll some dice, and must use only combinations of elementary operations (addition, subtraction, multiplication, or division) to make an equation using each number rolled exactly once. For example, if I roll four six-sided dice, and get this: 2, 3, 3, 4 A...
  10. P

    The probabililty of 3 rolls of dice and get two 6's

    I was asked to help someone to work out the probability above. It was more than a year since I done similar questions and thing do get rusty... So I hope to work it out here and get point out where I did wrong before I show that person the correct answer. Intuitively there is three ways I...
  11. K

    Understanding Two Dice Events: EF, E U F, FG, EF^(c), and EFG

    I have a problem that is suppose to be very basic, but it's hard for me to understand. Problem: Two dice are thrown. Let E be the event that the sum of the dice is odd; let F be the event that at least one of the dice lands on 1; and let G be the event that the sum is 5. Describe the events EF...
  12. I

    Probability : Rolling Dice, Flipping Coins, etc.

    The easiest way I can explain this is russian roulette. You have a six-sided die, and I need to find out the probability of the other person rolling a 6 before me, or dying in russian roulette with a 6-chamber revolver. I know it's different depending on who goes first, so for my example, I...
  13. P

    Estimating n for 90% Confidence Interval of Dice Roll Summing to 117

    Homework Statement (I translated this from french) Some n dice are thrown and the sum of all their face values is 117. Estimate n through a confidence interval of 90%. In other words, of all the possible rolls of n dice that sum up to 117, find a range in which n should be located 90%...
  14. S

    Probability of Even Score with 2 Tetrahedral Dice

    Hi, im trying to figure out how to solve the following question and any hints would be greatly appreciated. Question: Two tetrahedral dice, with faces labelled 1,2,3,4 are thrown and the number on which each lands is noted. The score is the sum of the two faces. Find the probability that...
  15. C

    Rolling a dice many times.

    I know how to calculate the probability of getting a 1 and then 2 or 1 and 1 and etc, that's just 1/6 * 1/6 Now what if I ask, what is the chance of getting a 6 from 3 rolls? Let's say I roll the dice 3 times and all I want is just a 6 from anyone of these roll? I just want one 6 from any...
  16. S

    Understanding - how universe/reality plays dice

    According to the more popular interpretations of (parts of) QM: photon (properties) are in an indeterminate state prior to measurement. the outcome of the photon properties, upon measurement, is totally random however after measurement the photon has definite/fixed/deterministic properties...
  17. G

    Probability of 20 dice being divisible by 6

    Homework Statement 20 dice are rolled what's the probability that the sum will be divisible by 6? Homework Equations Law of total probability The Attempt at a Solution The possibilities are between 20x1 and 20x6: 24,30,36,42,48,54,60,66,72,78,84,90,96,102,108,114,120 In...
  18. A

    Probability sum of 4 dice rolling greater than

    Homework Statement What is the probability of 4 independent dice summing to 20 or more? Homework Equations N/A The Attempt at a Solution I am not too sure how to approach this in an exam. I have attempted to do it this way but it would be easy to miss out a term: (I have put...
  19. T

    Rolling Dice and Probability

    Homework Statement The Attempt at a Solution The Fundamental Rule states that, given the six choices of value on a die, the number of possible outcomes for rolling three dice is: (6)(6)(6) = 6^3 = 216. Of these 216 possible outcomes, however, there is only one event that has a sequence...
  20. T

    Calculating Probability of Increasing Dice Rolls

    Homework Statement A die is rolled three times. What is the probability that you get a larger number each time? The Attempt at a Solution So I observed that the total number of possibilities for rolling the three dice is, by the Fundamental Rule: (6)(6)(6) = 6^3 = 216. I also thought...
  21. M

    Calculating Angle of Swing for Fuzzy Dice on a Hill

    Homework Statement A sports car is accelerating at a rate of 4.23m/s^2 up a 14 degree hill. If there are dice hanging from its rear-view mirror, what angle will they swing on? Homework Equations ƩF = ma Kinematic Equations The Attempt at a Solution Well, I'm thinking that I need to...
  22. N

    Number of combinations of 30 dice rolls

    You roll thirty dice. How many different possible combinations can be rolled? Order does not matter I think it's 6^30 choose 30, so: \frac{(6^{30})!}{(6^{30}-30)!(30!)} Also, perhaps the more important part of my question - any idea how to approximate this? The numbers involved are very...
  23. A

    Probability of 6 or 1 with Two Dice: An Infinite Experiment

    Suppose I throw a dice and want either 6 or 1. The probability for that is obviously 1/3. Now suppose instead, that I throw two dices but only want 6 this time. Then the probability of getting 6 is a bit lower than 2/3, but instead there is of course also a probability of getting for instance 6...
  24. A

    Converting Binomal cpk to a fair dice deviation.

    Converting Binomal cpk to a "fair dice" deviation. Hi, I would like to detect low probability in a "fair dice" problem being used for graphing of outliers. The actual data is binned into cells of 1% probability which form a histogram of the dice faces can be drawn. (The original data...
  25. X

    Probability of Rolling at Least One Six with Two Dice

    Homework Statement Two dice are rolled. What is the probability that at least one is six? If two faces are different, what is the probability that at least one is six? Homework Equations The Attempt at a Solution I have no clue. Although the first one shouldn't be that hard, but...
  26. K

    Creating a Dice Game in a Casino: An Analysis

    Hello everyone, I want to ask questions about my task. Below are the description. Thank you in advance. Kind regards, Kirman. The aim of this task is to create a dice game in a casino and model this using probability. It is important to examine how best to run the game from both...
  27. S

    Bar dice: six-of-a-kind out of nine in one shake

    What are the odds of getting six-of-a-kind out of nine dice in one shake? This is the shake of the day at a tavern near me. I know the odds of six-of-a kind-in one shake given six dice; the three extra dice have me bumfuzzled. I have been unable to plug the numbers into the equations I...
  28. P

    Calculating probability distribution for rolling 4 dice plus reroll lowest die

    Hi, I am trying to figure out what the probability distribution is for the following: 1. Roll 4 dice. 2. Take the lowest die and re-roll it. 3. Take the sum of the three highest dice. The result will be between 3 and 18. I know how to figure out the probability distribution for...
  29. P

    Chances of getting one particular number one or more times in 6 dice rolls.

    Its something I've been asking myself. I am studying physics, but I haven't studied anything related to probability since before high school I mean, for example, the chance of getting tails after one throw is 50%, after two throws 75%, after three throws 87,5% and so on... (right?) Say...
  30. S

    Markov chain, sum of N dice rolls

    Question : Let Xn be the maximum score obtained after n throws of a fair dice a) Prove that Xn is a markov chain and write down the transition matrix Im having a problem starting the transition matrix im assuming the states are meant to be the sum. then do you write out the transition...
  31. W

    Zero-modified geometric dice problem

    Hi, I'm trying to come up with a probability for a game I play with a friend of mine. In the game, units "attack" by rolling six-sided dice; either 2 or 4 sides of the die count as a "hit" when rolled, depending on certain circumstances. The specific situation I am trying to figure out the...
  32. S

    Roll 2 fair dice, find pdf and cdf

    Hi guys. I have a test tomorrow and I am trying to work out the problems on the review sheet, but I can't figure out this one dealing with pdf and cdf. Roll 2 fair dice and call each outcome (i,j) where i,j = 1,2,...6. Define: X= {i+j if i+j ≤ 6 ; abs.value(i-j) otherwise} A) Find...
  33. O

    Formula for dice probability where numbers have different values

    Hi all Im hoping someone here can help me out. I'm developing a game and I have a dice system I'm using but I am having trouble mapping the probabilities. I should state that I know very little about such things and my maths is basic but a reasonably explained answer should cause me no...
  34. D

    Probability when rolling 6 true dice

    Hello, So the question is: You have 6 true dice and you want to find the probability of rolling exactly two aces (im assumming ace means 1). I tried using the binomial theroem: P = (6!/(2!4!)) (1/6)^2 (5/6)^4 = 0.2009 But the answer is 0.040..So where did I go wrong? Thanks DoubleMint
  35. C

    Two fair dice are thrown, with the scores (X1, X2).

    Need help with this problem, please! Two standard, fair dice are thrown, and the scores (X1, X2) are recorded. Find the expected value of each of the following variables: (a) Y = X1 + X2 (b) Z = X1*X2 I don't even understand what it's asking! :( Any help is appreciated.
  36. Z

    Coin flip and dice roll question (check my answers?)

    Homework Statement Hi, I just wanted to check my answers for this question: Q: Suppose that we flip a coin six times and roll a 6-sided die once. Suppose also that all outcomes of this experiment (consisting of an ordered sequence of results for the flips (heads or tails) and the number...
  37. Q

    Multiplicity of Macrostates, involving dice

    I didn't really know where the proper place was for this, but this is an intro thermodynamics class and I'm really confused over this math question (it's not strictly physics-related). Homework Statement Consider rolling N six-sided dice. Define a microstate as the number showing on...
  38. D

    Rolling Dice Problem: Win 99% Probability with 5 Fair Dice

    Consider the experiment of rolling 5 fair dice. You “win” if all the dice show different numbers. I have to decide in advance how many times to repeat the experiment. I will be very happy if I win at least once. What is the least number of times I need to plan to repeat the experiment so that...
  39. Char. Limit

    Probability question: n-sided dice

    Homework Statement Two n-sided dice, with numbers ranging from 0 to n-1, are rolled. The first die represents the first digit of a base-n number, and the second represents the second digit of said base-n number. (In other words, the two dice rolls, if they are a and b, give the number a+b*n)...
  40. ArcanaNoir

    How Many Ways Can You Roll Six Dice with Repeating Numbers?

    Homework Statement How many ways can you roll six dice so that at least 2 numbers are the same? At least 3? At least 4? At least 5? Homework Equations The Attempt at a Solution :cry: I've used every equation in the chapter and filled page after page with numbers all moved around. I'm...
  41. F

    Two dice problem, a lot of questions

    Suppose you are going to a night festival and you see a vendor who is willing to double your money. So he explains the game. He has two dice, they are numbered from 0 to 9. He will roll them together in a slot such that they will make a two or one digit number. If he happens to roll a number...
  42. B

    Throwing a die 7 times: Probability of specific outcomes

    Throwing a die 7 times Homework Statement Throw a die 7 times. i) What is the probability that you get number 6 twice and all other outcomes once. (e.g. one possible set of outcomes would be 6, 6, 5, 4, 3, 2, 1) ii) What is the probability that you get all the numbers of a die? (e.g...
  43. S

    Dice probabilities on opposed sets of 10-sided dice

    Hi, I was wondering if anyone might want to help me with some less common dice probability. The dice mechanic is similar to the board game Risk (two sets of dice being compared), but the dice pools are varying numbers of 10-sided dice on either side (2 pools compared of a varying number)...
  44. T

    Probability of Sum of Dice Rolls 10-15 Inclusive

    Homework Statement There is a 5-sided fair dice with faces showing 1, 2, 3, 4, 5 dots. The dice is rolled four times. Find the probability of getting a total score between 10 and 15 (inclusive). Homework Equations If X is the score from one roll, then it follows a discrete uniform...
  45. A

    Probability Distribution of Random Variable X from a Double Dice Roll Experiment

    The question is "An experiment in which a dice is tossed twice. Let X be the random variable defined by recording the higher of the 2 values obtained in the experiment. Determine the probability distribution of X." I know that the range of this distribution is {1,2,3,4,5,6}. For P(X=1) both...
  46. M

    Standard deviation of a dice roll?

    Let's say I have a big, 50-sided die, with values ranging from 1-50. I want to find the exact standard deviation of the dice roll by hand. I would like to avoid subtracting the mean from each possible value, if at all possible. How do I do that?
  47. dkotschessaa

    Roll a 13 using 2 ordinary dice

    Originally posted on another forum with the title "are some things impossible?" The question was more of a philosophical one, but it got me thinking mathematically. I thought I had a solution like this: Put die #1 in a base 5 numbering system, you get the following values for the 6 rolls...
  48. R

    A Dice is rolled til we get two 6

    we roll a fair dice until we get a 6 twice in arrow what is the expectation of numbers of rolls we have to through the dice until we get 6 twice in arrow ? hint : it's not 36 I'll appreciate it if you help me with this question. Thanks
  49. B

    Determining Optimal Strategy for Rolling Dice

    Hi All, I was wondering if anyone could give me a suggestion to solve this "With one die, suppose in a round, you earn the amount of dollars equal to the value of the upwards face of the die. (eg. you earn $6 if you roll a six.) Now also suppose after your first roll, you are given the...
  50. D

    Understanding the Odds of Rolling 4 Dice Together

    Hi guys, I have a very simple but confusing problem that I have with die. It's not a homework problem, more a general understanding question. Now, question (im my own words) Four six-sided die are rolled together and independently to each other. Is the chance to roll a sum of (even) or (odd)...
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