Questions tagged [dice]

Dice (singular: die) are typically small cubical objects marked with spots, numbers (1-6 usually) or symbols to generate random outcomes, particularly in games. Other polyhedral dice are also used in games.

Dice (singular: die) are typically small cubical objects marked with spots, numbers (1-6 usually) or symbols to generate random outcomes, particularly in games.

Other polyhedral dice are also used in games, and may have 4,8,10,12,20 or many other numbers of faces. When dice have some unusual number of faces, a common notation places the number of faces after the letter "d", so "d12" means a die with 12 faces.

Usually dice are constructed such that (via symmetry considerations) each face has an equal probability of occurring; for example, Platonic solids (e.g. d12), Catalan solids (/Archimedean duals, e.g. d30), trapezohedra (suitable for dice with 4k+2 sides, e.g. d10) and dipyramids (suitable for dice with 4k sides, e.g. d16) are all used as fair dice.

Dice used in games are often used in combinations where many dice are rolled at once; their values may be summed, or other calculations performed on the numbers (such as counting the number faces with a particular outcome that are rolled, for example)

Dice are often used as probability models, when sampling with replacement, usually with equally likely outcomes, by contrast with urns and cards when sampling without replacement.

You would use this tag when asking statistical or probability questions about dice, such as the probability of certain outcomes or when asking about testing dice for fairness.

Reference: Wikipedia Dice

163 questions
55
votes
11 answers

Is there a 1 in 20 or 1 in 400 chance of guessing the outcome of a d20 roll before it happens?

My friends are in a bit of an argument over Dungeons & Dragons. My player managed to guess the outcome of a D20 roll before it happened, and my friend said that his chance of guessing the number was 1 in 20. Another friend argues that his chance of…
Theguy Whatguys
  • 633
  • 2
  • 7
42
votes
7 answers

How often do you have to roll a 6-sided die to obtain every number at least once?

I've just played a game with my kids that basically boils down to: whoever rolls every number at least once on a 6-sided die wins. I won, eventually, and the others finished 1-2 turns later. Now I'm wondering: what is the expectation of the length…
Jonas
  • 1,578
  • 1
  • 13
  • 16
38
votes
2 answers

A fair die is rolled 1,000 times. What is the probability of rolling the same number 5 times in a row?

A fair die is rolled 1,000 times. What is the probability of rolling the same number 5 times in a row? How do you solve this type of question for variable number of throws and number of repeats?
Teodor Dyakov
  • 615
  • 5
  • 9
29
votes
6 answers

How can I test the fairness of a d20?

How can I test the fairness of a twenty sided die (d20)? Obviously I would be comparing the distribution of values against a uniform distribution. I vaguely remember using a Chi-square test in college. How can I apply this to see if a die is…
25
votes
11 answers

How to easily determine the results distribution for multiple dice?

I want to calculate the probability distribution for the total of a combination of dice. I remember that the probability of is the number of combinations that total that number over the total number of combinations (assuming the dice have a uniform…
C. Ross
  • 645
  • 1
  • 7
  • 11
23
votes
1 answer

How many times must I roll a die to confidently assess its fairness?

(Apologies in advance for use of lay language rather than statistical language.) If I want to measure the odds of rolling each side of a specific physical six-sided die to within about +/- 2% with a reasonable confidence of certainty, how many…
Dronz
  • 333
  • 3
  • 8
22
votes
10 answers

How do we know that the probability of rolling 1 and 2 is 1/18?

Since my first probability class I have been wondering about the following. Calculating probabilities is usually introduced via the ratio of the "favored events" to the total possible events. In the case of rolling two 6-sided dice, the amount of…
elmo
  • 559
  • 1
  • 3
  • 16
20
votes
5 answers

Roll a die until it lands on any number other than 4. What is the probability the result is > 4?

A player is given a fair, six-sided die. To win, she must roll a number greater than 4 (i.e., a 5 or a 6). If she rolls a 4, she must roll again. What are her odds of winning? I think the probability of winning $P(W)$, can be expressed recursively…
tronbabylove
  • 303
  • 2
  • 5
19
votes
4 answers

Draw integers independently & uniformly at random from 1 to $N$ using fair d6?

I wish to draw integers from 1 to some specific $N$ by rolling some number of fair six-sided dice (d6). A good answer will explain why its method produces uniform and independent integers. As an illustrative example, it would be helpful to explain…
Sycorax
  • 76,417
  • 20
  • 189
  • 313
17
votes
1 answer

What are the difference between Dice, Jaccard, and overlap coefficients?

I come across three different statistical measures to compare two sets, in particular to segmentation on images (e.g., comparing the similarity between the ground truth and the segmented result). What are the differences between these measurements…
17
votes
6 answers

What is the distribution for various polyhedral dice all rolled at once?

Take the 5 Platonic solids from a set of Dungeons&Dragons dice. These consist of a 4-sided, 6-sided (conventional), 8-sided, 12-sided, and 20-sided dice. All start at the number 1 and count upwards by 1 to their total. Roll them all, and take…
Marcos
  • 523
  • 1
  • 5
  • 14
16
votes
4 answers

Is there a law that says if you do enough trials, rare things happen?

I'm trying to make a video about loaded dice, and at one point in the video we roll about 200 dice, take all the sixes, roll those again, and take all the sixes and roll those a third time. We had one die that came up 6 three times in a row, which…
16
votes
5 answers

Probability that number of heads exceeds sum of die rolls

Let $X$ denote the sum of dots we see in $100$ die rolls, and let $Y$ denote the number of heads in $600$ coin flips. How can I compute $P(X > Y)?$ Intuitively, I don't think there's a nice way to compute the probability; however, I think that we…
user239903
16
votes
2 answers

Expected rolls to roll every number on a dice an odd number of times

Our family has recently learned how to play a simple game called 'Oh Dear'. Each player has six playing cards (Ace,2,3,4,5,6) turned face-up, and take turns to roll the dice. Whatever number the dice rolls, the corresponding card is turned over. The…
Peter Prescott
  • 380
  • 2
  • 13
14
votes
3 answers

Formula for dropping dice (non-brute force)

First of all I'm not sure where this question should be posted. I'm asking if a statistics problem is NP-Complete and if not to solve it programmatically. I'm posting it here because the statistics problem is the center point. I'm trying to find a…
SkySpiral7
  • 253
  • 2
  • 8
1
2 3
10 11