# 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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### Lower threshold for Sequential Probability Ratio Test on Contingency Table testing

For testing whether a die is fair, we have the log likelihood ratio: $$\Lambda = \frac{1}{2} \sum_{i} \mathrm{observed}_i \log\left(\frac{\mathrm{observed}_i}{\mathrm{expected}_i}\right).$$ Suppose ...
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1 vote
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### Probability to get a 1 in 5 rolls 3 or more times

If I roll a dice 5 times, what is the probability to get 3 or more ones? That is, to roll a one three or more times? Because I think it's near 0.05: $\binom{5}{3} \left(\frac{1}{6}\right)^3 = 0.046$ ...
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### Infinite dice roll probability

The following is an interview question: Two players A and B play a game rolling a fair die. If A rolls a 1, they immediately reroll, and if the reroll is less than 4 then A wins. Otherwise, B rolls. ...
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### Formula to find percentage of winning between two different numbered dice

Lets say I have a dice with the numbers from 1 to 10 and another one numbered from 1 to 7. I roll both dices once. Whats the chances in percentage that the 10 numbbered dice will win in terms of ...
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### What is the probability a difference of two appears before 3?

Given a sequence of trials, where each trial is rolling two dice, each trial's outcome is the absolute difference between the values on the die. What is the probability that the outcome of 2 occurs ...
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### How to graphically show how "normal" a collection of dice rolls are in a game

I was trying to think of a way to show how "normal" a set of dice rolls are in a game like catan. In Catan, each turn you roll 2d6 and the sum of those 2d6 dictate game outcomes. A game can ...
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### Why is the distribution of the sum of the values on two dice bell-shaped and symmetric if two uniform dist is triangular distribution?

Why is the distribution of the sum of the values on two dice bell-shaped and symmetric if two uniform dist. sum is triangular distribution via Irwin-hall distribution?
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### Number of configurations in which you can roll 2 6's in a row

A colleague at work gave me a problem to think about. If you throw $n$ dice, how many configurations are there where you get at least 2 6's in a row? I worked a lot with Pascal's triangle and in the ...
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### Hausdorff and IoU are stopped changing while dice metric is decreasing

I am facing a problem in Hausdorff and IoU, where they stop learning when reaching a specific value! While the loss and dice metric keeps changing. surface_distance also has a problem since it is ...
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### Probability of a given result with multiples of mixed dice with different number of faces

What is the formula to calculate the probability of getting 41 when I throw two 10-sided dice and four 8-sided dice? I’m looking for an algorithm for the general case of throwing multiples of two sets ...
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### Quantifying the confidence that the most sampled outcome is the most probable outcome

Let us say we have a cheater's six-sided die, which we can assume to be unfair with an unknown probability distribution. We want to know the most likely roll with this die, and so we roll it $N \gg 6$ ...
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### Is it possible to generate a Pareto distribution with dice?

So I know that there's a really easy way to generate a normal distribution with dice (simply add them). Is there a way to generate a Pareto distribution?
1 vote
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### What are the odds for winning this drinking game?

Out of pure boredom during the corona period back in 2020 I 'invented' a drinking game which seemed to have a fair outcome, but I am not sure. We were sitting on the couch and after a lot of beer, and ...
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### Non-transitive dice probabilities

I got the following question on non-transitive dice, as shown in the following picture. Suppose you roll two white dice against two red dice. What is the probability that the sum of the white dice is ...
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1 vote
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### 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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### 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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### 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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### 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 ...
1 vote
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### 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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### 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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### 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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1 vote
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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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### 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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### 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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### 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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### 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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### 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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### How many unique values can you expect after throwing a die 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 die but it does not solve ...
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### 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 ...
1 vote
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### 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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