# 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. ### I Probability to get a certain number or less by throwing two 6-faced die

In a board game, I need to reach a certain place in a board divided into boxes, I move by throwing 2 six-faced dices. If my goal is 4 boxes away I need to obtain at least a combination of numbers that sums to 4, but any higher number is also a favorable outcome. I want to calculate the...
2. ### Probability of getting arithmetic sequence from 3 octahedron dice

I try to list all the possible sequences: 1 2 3 1 3 5 1 4 7 2 3 4 2 4 6 2 5 8 3 4 5 3 5 7 4 5 6 4 6 8 5 6 7 6 7 8 I get 12 possible outcomes, so the probability is ##\frac{12 \times 3!}{8^3}=\frac{9}{64}## But the answer key is ##\frac{5}{32}## . Where is my mistake? Thanks
3. ### B Probability in a roll of dice

I was trying to calculate the probability of throwing only one six when throwing a pair of dice. Using the formula for non-mutually exclusive events : P(A)+P(B)-P(A,B) I get 1/6+1/6-1/36=11/36 but when I count all the 36 possibilities on paper I get 10/36 ways of getting only one 6. What am...
4. ### Probability: Dice Game between 20- and 12-sided dice with re-rolls

Hi, I was reading around and found this problem. I have seen some discussion about the solution (but nothing verified) with some disagreement. Problem: One person has a 12 sided die and the other has a 20 sided die. They each get two rolls and they can each chose to stop rolling on either one...
5. ### Expected value of median of rolling three fair dice

Hi, I was reading this problem and I found a solution on Math Stackexchange which I don't quite understand. Question: Calculate the expected value of the median of rolling a die three times. Attempt: I read the following answer on math stack exchange here "As already noted in a comment, the...
6. ### Game theory: dice game to aim for sum no greater than 9

Hi, I was attempting the following question and would appreciate any insight on how others would approach this game theory/probability-type question. Question: You have been chosen to play a game involving a 6-sided die. You get to roll the die once, see the result, and then may choose to...
7. ### Dice Game: 6-sided die vs 20-sided die

Hi, I was taking a look at the following question. Question: There is a game where one person rolls a 20-sided dice and another person rolls three 6-sided dice. They both roll their dice and whoever gets a higher number (for 20-sided die) OR sum of numbers (for three 6-sided dice) wins the...
8. ### MHB Probability of Rolling Sum > 3 with Two Dice

Two fair dice are rolled. What is the probability of rolling a sum that exceeds 3?
9. ### Probability distributions using 4 dice

Let X denote the largest number shown on the four dice. P(X ≤ x) = (x/6)4 , for x = 1,2,3,4,5,6. Complete the following table: x 1 2 3 4 5 6 P(X=x) 1/1296 15/1296 65/1296 175/1296 369/1296 671/1296 The values in red are the answers, I don't understand how the answers were found. Thanks.
10. ### B Dice calculation of p(7), two different values?

Scenario 1] The dice are rolled out of your sight and you are then asked the p(7), before you are allowed to look at the results. Calculate p(7) by looking at table of 36 possibilities and counting the number of sum cells totals that equal 7, there are six of them, so p(7) = 6/36 = 1/6...
11. ### B Probability in a dice game

We're playing a game with regular, fair, six-sided dice, and we're throwing 14 of them. The "1" is a "joker", which means it can count as any other number. So, for example, if we roll three "1"s and four "2"s, we have seven "2"s. What is that probability that we get exactly seven of any face...
12. ### Calculating the expected value of a dice roll

I write p(k) as: $$p(k) = 1/6, k = 2,3,4,5$$ $$p(k) = 2/6, k = 6$$ Is that wrong? Because then the expected value becomes $$1/6 * 4 + 2/6 * 6 = 8/3$$ While my book says 11/3
13. ### Are these two dice rolls dependent or independent?

Summary:: Roll a dice twice. Event A: First dice roll yield 2 or 5. Event B: Sum of the two results are atleast 7 Is A and B independent? If they are independent then $$P(A \cap B) = P(A) * P(B)$$ P(A) = 2/6 = 1/3 P(B) = 1 - 9/36 = 27/36 $$P(A \cap B) = 7/36 \neq P(A)*P(B) = 1/4$$Yet book...
14. ### MHB Understanding Dice Throwing Probabilities: A Layman's Guide

Hello I am involved with a Rotary Club which uses a dice game to raise funds at various events. We want to look carefully at the probabilities of throwing dice. Can you tell me please in very basic layman's terms the odds on the same number being thrown on 4 out of 7 dice in one throw (which...
15. ### B Calculating Dice Roll Probability: Learn Basics with Frank

Hello, I am trying to learn the basic concepts of calculating probability as it pertains to dice rolling. I have searched the internet and not been able to figure it out. If I have a regular 6 sided dice and I want to know the probability of rolling a 3, I know its 1/6 or 16.6%. This is...
16. ### I Predictive Dice Roll: Physics & Accuracy

Hi, 1. A multi-sided dice - 20 sides for example. Highly accurate each side equal size. 2. Dice dropped from a machine - with same starting orientation. 3. Dropped in a vacuum from same height each time. 4. Dropped onto a very flat surface - 90-degree angle. Now given I have tried to make...
17. ### MHB Find the probability all 5 dice rolls are the same

Given 5 dice rolls that are independent from each other, what is the probability for the following results? (order of roll does not matter) 1. all 5 dice rolls are the same 2. 4 dice rolls are the same 3. the dice rolls are in sequence (1-5 or 2-6) -order does not matter 4. two pairs of dice...
18. ### I Stuck on the probability of rolling 'p' with 'n' s-sided dice

Hi, I've been following the derivation of wolfram mathworld for this problem and I'm running into some trouble regarding the summation indices. Currently I am at the step where we have found that (it's pretty much just binomial expansion and taylor series to get to this point)  f(x) =...
19. ### I God plays dice, stochastically and deterministically.

Seeking to support Einstein, I'd like to know how the above sentence -- from a reading of EPR (1935)* -- sits with physicists, mathematicians and philosophers. * EPR (1935), p.777: "If, without in any way disturbing a system, we can predict with certainty (ie, with probability equal to unity)...
20. ### I Is throwing dice a stochastic or a deterministic process?

As far as I understand it a stochastic process is a mathematically defined concept as a collection of random variables which describe outcomes of repeated events while a deterministic process is something which can be described by a set of deterministic laws. Is then playing (classical, not...
21. ### MHB Probability of AT LEAST 3 6s in 5 Dice Rolls

I've been teaching myself Probability Mathematics, but I'm still struggling. Please help me understand with an example. Say I roll five six-sided dice all at once, with die faces numbered 1 through 6. I want to determine the probability of AT LEAST three 6s occurring. First, is this the best...
22. ### MHB Rolling 20 times a fair dice

Hey! :o Tim rolls $20$ times a fair dice. Calculate the probability to get a "$3$" exactly $8$ times. The probability to get at least $k$ times a "$5$" is equal to $10,18\%$ Calculate $k$. Explain the relation to the term $\displaystyle{\sum_{i=0}^2B\left (10;\frac{5}{6};i\right )}$...
23. ### I Probability of getting a dice value

If I have ten dice and pick one at random, given that I don't know anything about them the probability of getting a dice of value 4 would be 1/6? Given that I know that there is two dice of value 4, the probability of getting a 4 would be 2/10 = 1/5? Which would be correct in repeated trials?
24. ### Number of valid ways to roll M dice with N sides

Homework Statement Suppose we have M dice each with N sides. The dice are ordered, so that rolling (1, 2, ...) is not the same as (2, 1, ...) A valid configuration is one for which each number rolled is at least as large as the previous. (For instance, take M=N=2. (1,1) is valid, (1,2) is...
25. ### MHB Average "Hits" on exploding dice

Hey folks, I've been using a really simplistic equation for this and I'd like to get an actual table/equation/and standard deviations if possible. Here are the rules. roll xd6s (six-sided dice) every die that rolls a 4 or greater is a "hit." 6s rolled count as a hit and then "explode," adding...
26. ### Geometric Law of Probability with Dice

Homework Statement We have a normal 6 sided dice marked from 1 to 6. There is an equal chance to get each number at every roll. Let's put 1&2 as A type, 3&4 as B type and 5&6 as C type. We roll the dice over and over until we get a number of every type. Let X be the number of rolls. We are...
27. ### Probability of Getting a Total of 15 or Higher in Three Dice Throws

Homework Statement If two identical dice are thrown, what is the probability that the total of the numbers is 10 or higher? [Hint: list the combinations that can give a total of 10 or higher.] [2] Two dice have been thrown, giving a total of at least 10. What is the probability that the throw...
28. ### How to Modify Python Dice Rolling Game to Accept User Input for Number of Rolls?

Homework Statement I want to prompt the user to input how many times they want to roll a die, then generate a random number between 1 and 6. I then need to print what their number is and if it is even or odd. The code I posted below is what I came up with for a single die roll that allows...
29. ### MHB Probability of winning dice game

Hey, so I've got this problem that I'm trying to figure out. I've worked out something that I think is probably right through simulation, but I'm not really sure how to tackle it from a purely mathematical probability perspective. So, would anyone know how I should approach this? I've tried a...
30. ### MHB Pr of exactly one dice showing 2

So I ran into this problem: You roll two fair die. What is the probability of one of the dice showing 2 or the sum being at least 8? I thought it should be: 15/36 for the sum being at least 8 and 10/36 for exactly one dice showing 2, but it tells me it is wrong. I got these numbers by...
31. ### Elementary probability question: dice roll

Homework Statement Lets say you role a single honest dice 12 times. Where succes is either if the die shows 4 og 1 eye. My question is what is the probability of sucess or failure? Homework EquationsThe Attempt at a Solution Is it binomial or conditional probability?
32. ### MHB How Many Rolls of Dice to Get Sum 12?

How many times do we need to throw 2 dices to get more than 1/2 probability that at least once the sum of the two dices will be 12.
33. ### How many ways can you roll an 18 from 5 dice?

Homework Statement How many ways can you roll an 18 from 5 dice? Assume the dice are different colors. Homework Equations Factorials The Attempt at a Solution I listed combinations of dice that would add to 18 as follows 66411 65511 55521 44442 33336 66312 65412...
34. ### MHB Dice rolling -Which of 2,6,1006 is more likely to be one of these totals?

A standard six–sided dice is rolled repeatedly and a running total is kept of all the numbers rolled. Which of $2, 6, 1006$ is more likely to be one of these totals? Prove your answer.
35. ### Insights Intransitive Dice with a Twist - Comments

mfb submitted a new PF Insights post Intransitive Dice with a Twist Continue reading the Original PF Insights Post.
36. ### B Simultaneous roll of Non Transitive Dice

So say that we roll three of them and assume that the fates of the roll are all decided simultaneously. I've seen the baysean network analysis for games where one player goes first and another goes second. But what I'm talking about is a roll of three dice such that they have to land...
37. ### B Hawking believes "God confuses us throwing dice....", why?

Hi, I'm trying to understand the QM, I have no background and I can only do some research sometime because I've no time for this. Yesterday I read the quote above. He's talking about black holes and the horizon of events. I read that the microcosm can make indeterminate the macrocosm, for...
38. ### Dice throw, avg.,standard deviation

Homework Statement Homework EquationsThe Attempt at a Solution Let's denote the result of the throw by the variable x. ## <x> = Σ_i P_i x_i , i = 1,2,3,...,6. \\= \frac{1+2+3+4+5+6}{6} \\<x^2> = \frac{1^2+2^2+3^2+4^2+5^2+6^2}{6} \\σ_x = \sqrt{<x^2> - <x>^2} ## Is this correct?
39. ### Probability with two dice problem

Homework Statement If we throw with two dice a and b, than we make two spaces call them space A and B. Space A = a+b and space B = a*b. Next the question there are a couple of questions: 1) What is the probability P(A > 7) 2) What is the probability P(B = odd) 3) What is the probability P( A n...
40. ### B Exploring 120-Sided Dice and Eigenvalues

Here is a picture of a set of 120 sided dice. Each die has 120 eigenvalues. It is easy to see that as the number of eigenvalues increases, the probability of any eigenvalue gets smaller. In the limit where the number of eigenvalues is ##\infty## the probability of anyone eigenvalue approaches...
41. ### Statistics: Pattern present in dice data?

Homework Statement I generated data for a dice experiment. For the first case, two dies were rolled and the minimum number and the sum were recorded. For the other cases with three, four, and five dies, the minimum and sum were also recorded. I attached a picture of the tables with my data and...
42. ### C/C++ Solve C++ Pig Dice Game: Aragorn Wins!

Hello! So for an assignment, we have to write a program for the pig dice game. You are to finish the program below that implements the dice game PIG played by 2 human players. Pig is a dice game where each player during their turn rolls a 6-sided die. If the player rolls a 2 through 6, they...
43. ### Probability of sum is 20 (4 dice are rolled)

Homework Statement 4 dice are rolled. Find probability that sum is 20. Homework Equations If a dice is rolled the outcome can be 1, 2, 3, 4, 5, 6 The Attempt at a Solution Well the combinations for sum to be 20 are: 5, 5, 5, 5 = 20 5, 5, 6, 4 = 20 6, 6, 5, 3 = 20 6, 6, 4, 4 = 20 6, 6, 6...
44. ### How many shuffles are needed for a 50% probability of matching a deck of cards?

Homework Statement The problem I'm having involves looking for a specific formula for the probability of matching a deck of playing cards via the result of a shuffle. I want to know how many times I must shuffle for the probability of the shuffle matching one of the past resulting decks to be...
45. ### Double Dice Probability: Event A and B in Sample Space | Solved

Homework Statement In a probability experiment, a fair die is rolled twice. • If the first roll is odd, the outcomes are recorded as they appear. • If the first roll is even, the recorded outcome for the second die is doubled. For example, if the first die was 2 and the second 4, the...
46. ### The probability of dice coming up 6 twice in twelve rolls

Homework Statement Explain the formulas used to obtain the solution for the question above (What is the probability of two tetrahedral dice landing on a 6 if twelve dice are rolled?) 1 - (3/4)^12 - 12 * ((3/4)^11) * (1/4) = 0.842 Homework Equations If we were looking for one dice landing on 6...
47. ### B A whole bunch of dice -- Statistics riddle

Following the "enormous success" (it received a single like) of the last riddle, I decided to waste some bandwidth with a sequel! This one doesn't have an interesting concept or an unexpected solution, it's just hard to solve, so if you're looking for such a riddle, do yourself a favor and...
48. ### I Probability involving n dice

I'm studying probability and am currently stuck on this question: Let's say we have n distinct dice, each of which is fair and 6-sided. If all of these dice are rolled, what is the probability that there is at least one pair that sums up to 7? I interpreted the above as being equivalent to the...
49. ### B Is it possible that god does not play dice with the universe, as Einstein said?

How could it be tested that there exists true randomness in the universe? One could simply argue that the is information that we do not posses that causes the outcome of a measurement to occur, right?
50. ### Conditional Probability exercise with dice

Hey there community, I have a question on an exercise. Actually it is a general question based on it. Here is the exercise: We throw 3 dice. If we know that the sum of these 3 is 10, then what is the probability of at least one of them being 3? Well now, this exercise is very simple. I mean I...