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Questions tagged [dice]

For questions on dice, small throwable objects with multiple resting positions, used for generating random numbers.

Traditionally, dice are cubes, with each of its six faces showing a different number from 1 to 6. When thrown or rolled, the die comes to rest showing on its upper surface a random integer from one to six, each value being equally likely.

A variety of similar devices are also described as dice; such specialized dice may have polyhedral or irregular shapes and may have faces marked with symbols instead of numbers. They may be used to produce results other than one through six.

Loaded dice are designed to favor some results over others for purposes of cheating or amusement.

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D20 probability question

How does one calculate the possibility of rolling a 20 between multiple people? My friends claim that between the four of us, if we each roll 1 d20, we have a 20 percent chance of getting a 20, i dont think this is right but i cant prove why. I…
Derelicta
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Possibilities of rolling 15 with top 3 six-sided dice

There are $7776$ possible outcomes of rolling $5$ six-sided dice, of this total there are $651$ possible outcomes where the $5$ dice equal exactly $15$. How could you calculate the number of possible outcomes where the top three dice equal $15$?
danny
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Three fair dice are rolled one time. What is the probability of at least one $6$?

I think the answer is $10/216$, but I am not sure. I did it by brute force though, and would like to know the background, as well as knowing if $10/216$ is correct. Edit: now i think via brute force, the answer is 93/216. if you roll a 1 on any dice…
nate958
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Die Roll Probability with 8-sided Die

What is the probability of rolling an "8" on an 8-sided die four times out of nine attempts? My friends and I were playing a game where one player could only succeed by rolling an 8 with an eight sided die. He rolled nine times, and got an 8 on four…
Chris
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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 between 1-5 dice to roll. If you select n dice, all n…
user157902
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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?
swe
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Five dice vs. five dice; each set can have variable sides; odds for each of winning consecutive rolls?

Situation: There's a game where each player rolls five dice, comparing totals. They do this until one player rolls the higher number twice in a row. That person wins. This is a Discord game, so although all the dice one player rolls have the same…
Spiffy McBang
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Create un unbalanced polyhedron dice

I need a dice with a strange number of faces (Eg. $7,9,11,13,14$) that is totally unbalanced (each side has a different area), but with the ratio of the largest and smallest face area not too big (say between $2$ and $3$). How should I approach this…
Aurelian Florea
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Determining Chances of Last Digit Matches in a Polyhedral Dice Pool

In a pool of polyhedral dice (made up of $4$ to $6$ $2$-sided, $4$-sided, $6$-sided, $8$-sided, $10$-sided, and $12$-sided dice) how do you determine the chances of matching the last digit rolled on a $20$-sided die? I am interested in determining…
Mathew Reuther
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How to show all possible ordered outcomes of 4 dice

I'm working on a project that requires I add a unique result for each and every possible ordered outcome of a roll of $4$ dice at one time. I'm stuck on how to show this in Excel or Google Sheets. Any ideas? Really appreciate it.
kvn2
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Three red dice. Sum of any two of them must be 2,3 or 4. What is the probability of that?

I have a boardgame call Enemy Coast Ahead: The Dambusters in which enemy FLaK poses a major problem. Under some circumstances the game "AI" throws three instead of two dice and if the sum of any two of them is within a certain interval a hit is…
Peter Lageri
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Rolling $N$ indistinct dice and $1$ distinct die, what is the chance that the distinct die is part of the Top 3?

Rolling $N$ indistinct dice and $1$ distinct die, what is the chance that the distinct die is part of the Top 3? Ties favor the distinct die being included over an indistinct die. I'm at the point where I think I know the answer, but I definitely…
Axoren
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What is the sum of all the numbers on the opposite faces of numbers obtained in three rows is?

I have this: A person threw a standard dice three times. He obtained two distinct odd prime numbers in two throws and an even number which is not a factor of 18 in the third throw. The sum of all the numbers on the opposite faces of numbers obtained…
yena shah
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Probability question - clueless about math

We have a die. Success event (S) is 1-4, failure event (F) is 5 and 6 (in other words chances for success are ~0.67 or 2/3 for one roll). We roll the die, say, a billion or n times. What is the probability of the success events number being higher…
Mystic_Quest
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Dice Rolling (Math Game)

You wager an amount W on the roll of two die. Any 1's win 100 dollars, and any 5's win 50 dollars each, otherwise you lose. For what value of W would this be a fair game? I'm not so concerned with the answer, mostly I just want to know how to set…
Jon Jones
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