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.

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what is the probability of this event?

given this outcome of the dice {2, 3, 4, 6, 6}. You decide to re-roll both sixes. What is the probability that you roll either a small straight (four dice are in a row) or a large straight (all five ...
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Difference between geometric distribution expectation and 1 - failure with Binomial

I'm trying to understand a simple problem: How many times you'd need to roll two dice to get two ones in a single roll. One way I see this is as a problem the geometric distribution describes. You ...
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Super noob requesting help testing dice balance [duplicate]

So, I have a few sets of polyhedral dice (77 individual dice) that I'd like to try to test for balance. I'm thinking a decent sample size is to roll each of them 100 times, then plot the proportional ...
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How much compensation is needed to take on risk?

We roll three, 8 sided dice. If same face appears 3 times we win 80 dollars. We have a bank of 10,000 dollars. How much are we willing to pay to play? What if we increase the prize to 80,000 dollars? ...
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1 answer
41 views

Covariance between two binomial RVs

Suppose we toss a fair dice $n$ times. For $i=1,\dots,6$, let $X_i$ denote the number of times the dice comes up with value $i$. Find the $\textrm{cov}(X1, X2)$. By definition, $\textrm{cov}(X1, X2)=E[...
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1 vote
1 answer
180 views

D&D Probability question: why am I wrong?

In Dungeons and Dragons, the primary die used for success or failure is the D20, or 20 sided die. A 1 is a critical failure, and a 20 is a critical success. When one has advantage, one rolls 2 dice ...
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56 votes
11 answers
9k views

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 ...
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2 votes
2 answers
136 views

A method for simplifying manual random number generation? [closed]

Is there a good way to take a more complicated dice-rolling mechanism and create a simpler dice-rolling mechanism that gives roughly similar results? Example 1: Say you have a game where both sides ...
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2 votes
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Probability that sum of x dice greater than sum of y dice

If I roll a 6-sided die x times (or roll x 6-sided dice at once), what is the probability that the sum of the result is greater ...
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1 vote
1 answer
187 views

Probability - How to approach Unfair Dice Problem?

I am working on a problem to use probabilities for a game with 2 dice. I have researched many methods (Bayesian, etc.) but I am not sure what the right path would be to answer these questions. Here is ...
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How to test for significance for binomial count data where the expected outcome is unknown?

Description of the data: The study is investigating whether conversations on a messaging app are greater or less than 8 words long. The variable is the count of messages that contain more than 8 words ...
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8 votes
2 answers
936 views

How can I simulate the frequency of each face for N die rolls? [duplicate]

I want to simulate a fair die roll N times without actually rolling a die. To be clear, I want to achieve something like this: ...
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Cumulative sums of two competing multinomial distributions

Related to this: https://math.stackexchange.com/questions/1977628/dice-roll-cumulative-sum Take an example of turn-based RPGs. $A$ and $B$ are two competing game entities, with hit point totals $n_A$ ...
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-1 votes
1 answer
190 views

Dice roll question [closed]

Suppose you roll a fair die two times. Let A be the event "the sum of the throws equals 5" and B be the event "at least one of the throws is a 4 ". Calculate p(A|B)? How to ...
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1 vote
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Fluctuating loss curve/ steady dice score. Why? And How to improve? [duplicate]

I am training 3D data with multi-class 3D target ground truths(9 tissue labels) for segmentation. Using dice Loss and focal dice loss as loss criterion. Updating optimizer every second batch (...
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Have I found something new? (a formula for the odds of rolling at least one 1 when rolling an n-sided die n times)

The formula First, the formula I found for the odds of rolling at least one 1 when rolling an n-sided die n times: Math.round(1 - ( ((n-1)/n)^n -1 )*(n^n-1) )/n^n ...
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Uniform distribution or Poissonian distribution?

Suppose I take a 6-sided dice and roll it N=1000 times; then I organise the measures in a histogram whose bins are the 6 faces and each of them contain the number ...
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1 answer
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Combined probabilty for 1 to 6 between a cube and a dodecahedron, not counting 7 to 12

We have two dice, one with six sides (a cube) and one with twelve (a dodecahedron) The cube bears the numbers 1 to 6. The probability for each number is $\frac{1}{6}$. The dodecahedron bears the ...
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0 votes
2 answers
33 views

Interpreting chi-squared value returned by Excel 2010

I'm trying to assess whether the number of doubles (dice) being rolled by my opponents on a backgammon website are fair; to the naked eye they most definitely aren't but I need some science to back up ...
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3 votes
0 answers
37 views

Mean number of throws to exceed a threshold [duplicate]

Say that you have a die with n faces, and you need to throw the die until the sum of your results exceeds a given threshold. What is the average number of throws needed? I think that to compute that ...
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1 answer
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Distribution of sums with multiple dice of differing sides for a probability of success. Why do distributions vary with probability?

Intro I have been looking into dice distributions within the context of rogue-like or D&D type games. I found this question. In lots of these types of games you will be attacked by something with ...
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3 votes
1 answer
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How do I find the probability of getting specific, distinct, dice rolls on an unfair die in the same group of trials?

I play gacha games, and recently I've wanted to compare the rates of the one that I play compared to competitors in the market to warn some friends of mine from starting one with rates that I feel are ...
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3 votes
1 answer
117 views

Trouble finding var(ax)

So the variance of a 6-sided (1,2,3,4,5,6) die is $291.6$ using the formula: $$ \text{Var}(X) = \frac{(b-a+1)^2}{12} $$ Also, $\text{Var}(10X) = 10^2 \cdot \text{Var}(X)$, so that would mean $\text{...
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1 vote
1 answer
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What is the probability that in 3 rolls of a pair of six-sided dice, exactly one total of 7 is rolled?

I tried to solve the exercise and it seems meaningful, but the problem is that in the book the result is $25/72$, while mine is $1/7776$. I don't know if maybe I didn't understand the problem, but by ...
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4 votes
1 answer
60 views

Halving time for a population of dice

The following question arose today on a Norwegian facebook forum for math teachers, with some unclear definitions and a lot of simulation. We have a population of $K$ (regular, 6-sided, equal-...
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0 votes
2 answers
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How many unique values can you expect after throwing a dice with k sides?

I ended up asking here. My Problem might be familiar with the Coupon collector's problem and related to this post Probability of throwing n different numbers in m throws of a dice but it does not ...
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0 votes
1 answer
46 views

How far from "even" is (or is not) significant?

If a six-sided die is rolled 600 times, an even distribution would be 100 rolls for each number. If I actually rolled 600 times and tallied the results... How far away from 100 would a count need to ...
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1 vote
2 answers
101 views

Generalization of a boy or girl paradox with die!

Here is the link to the boy or girl paradox Wikipedia page. The question I have is: Let's say you have two fair 6-sided dice and you roll them simultaneously. If at least one is 6, what's the ...
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2 votes
2 answers
246 views

How many rolls required for 90% chance to reach expected values of consecutive dice rolls in tabletop game?

I'm trying to work out if random variance in dice rolls is more likely to influence a given situation in a game rather than the overall expected values of those dice rolls being significant. The game ...
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0 answers
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Variance of one die with binary result

I have a task that is worded: "You have a deciding die-throw ahead of you in a game (using a fair 6-sided die) and you realize that you will win if you get a 4 and lose in every other case. You ...
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39 votes
2 answers
8k views

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?
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3 votes
0 answers
27 views

10-faces dice "emulation" from N 6-faces dices [duplicate]

I want to play a game which uses one 10-faces dice, but I only have 6-faces "classic" dices at my disposal. Is it possible to approximately recover, to an arbitrary precision, a 10-faces ...
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18 votes
5 answers
3k views

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 ...
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0 votes
1 answer
126 views

What is the probability of getting exactly doubles when rolling N number of dice

For example if i roll 2 dice the probability of getting exactly doubles is 6/36. similarly if i roll 3 dice the probability of getting exactly doubles not considering triples is 90/216. How can i ...
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3 votes
1 answer
173 views

How many flips are needed to confirm a coin's intentional bias?

I've made some 'special' coins and I know for a fact that they have a very small but known/designed bias $\epsilon$. I define bias as the probability $(\frac{1}{2} + \epsilon)$ towards heads and $(\...
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9 votes
6 answers
5k views

What are the chances rolling 6, 6-sided dice that there will be a 6?

More generally, what is the probability that n n-sided dice will turn up at least one side with the highest number ("n")? My crude thinking is that each side has 1/6 probability, so that 6 ...
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3 votes
3 answers
3k views

Calculating the variance of dice rolls?

I am having trouble understanding how to find the variance for the proportion of times we see a 6 when we roll a dice. The question is below: Suppose we are interested in the proportion of times we ...
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4 votes
2 answers
100 views

Expected number of rolls until a number appears $k$ times

Roll a fair die, what is the expected number of rolls until a number appear $k$ times? Not necessarily consecutive. Let $N$ be the number of rolls until a number appear $k$ times. For $k=2$, we know ...
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16 votes
2 answers
1k views

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 ...
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1 vote
2 answers
200 views

Calclulating Probability of a Distribution of a set of Two-Dice rolls

I was calculating the odds of a set of dice rolls in a game of Catan recently. In 35 rolls, we rolled 0 3's, and 0 5's. To calculate the probability of this, I calculated the probability of rolling 0 ...
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1 vote
1 answer
121 views

Calculating the probability that one distribution is greater than another

I have a problem which I think should actually be really simple, but I can't see the solution and either it's more complicated than I realize or I just cannot figure out how to word it for Google. I ...
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2 votes
1 answer
120 views

How many rolls of sum of 6d6 for an expectation of 90% chance of hitting three consecutive 6d6 totals each less than or equal to each other?

each Roll is the sum of six six-sided dice ( therefore a value of 6 to 36). How many times would I have to roll (and take the sum of 6d6) before I would have a 90% expectation of seeing three 6d6 ...
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0 votes
0 answers
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Cracking a safe: matching $n$ unique numbers with $d$ dice. What is the expected number of rolls?

This problem is inspired by the board game Burgle Bros. In the game there are safes to crack. You have to match $n$ unique numbers with $d$ dice, where $n = 1,...,6$ and $d=1,2,...$. For example, ...
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1 vote
1 answer
66 views

Which game is more advantageous?

I got a pretty simple problem but I'm not sure about my solution. Game $A$: We roll a fair die 4 times. If we get the "6" at least one time, we win. Game $B$: We roll a fair die 8 times. If we get ...
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4 votes
1 answer
145 views

What is the probability of getting three pairs that makes up seven when six dice are rolled?

Stumbled upon this question in a game of dice where a point is dealt for each pair that makes seven. In the game there were a total of six dice that were to be thrown up to three times. Each time a ...
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2 votes
1 answer
211 views

Expected Return of Die Game

The game is as played: To preface you can roll a die at most three times. You roll the die the first time, if you get a six you get \$6 and you roll the die again, if you don't get a six the game ...
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2 votes
1 answer
138 views

Interpreting frequency statistics to find fair dice

I was just in a lecture where my (bayesian evangelist) professor claimed that for questions like 'Is this a fair die?', frequency statistics gives an answer of {0, 1}, meaning that the probability is ...
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1 vote
1 answer
103 views

Probability of getting a 6 on at least one die from a pair of dependent dice

I am stuck on this particular question: Suppose you have two dice. These dice however are not independent: the probability that both dice will roll a 6 is 0.29. What is the probability that at least ...
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6 votes
2 answers
106 views

How to win this dice probability game?

The game is a variation of Pig. Here is how the game works: There are about 20 players. Each round, a single six sided die is rolled. All players add that rolled number to their "bank." However, if a ...
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0 votes
1 answer
797 views

Calculate Probability of 50 different Dice Roll to Same Number

The Problem: Provided there are 50 different dice with 50 sides. What is the probability any two dice or more will roll the same number? My Attempt: So, I know the probability of two different dice ...
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