Skip to main content

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.

Filter by
Sorted by
Tagged with
0 votes
0 answers
24 views

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 ...
shabbychef's user avatar
  • 14.9k
1 vote
1 answer
60 views

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 $ ...
robertspierre's user avatar
9 votes
6 answers
2k views

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. ...
Ria's user avatar
  • 511
2 votes
1 answer
30 views

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 ...
Flo's user avatar
  • 21
6 votes
2 answers
81 views

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 ...
Ria's user avatar
  • 511
0 votes
1 answer
78 views

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 ...
Bovard's user avatar
  • 103
4 votes
2 answers
164 views

Expected value for a fair die game

You roll a fair die until the cumulative sum rolled so far is a multiple of 3. You get $1 for each roll. What is the expected amount you will get? I started by finding the probability of the game ...
gaganso's user avatar
  • 183
1 vote
2 answers
554 views

Dice rolling problem

A game is played with $n$ dice, and an additional parameter $r<=6$. The game has one player who must throw all $n$ dice on each round and add the score to the total. The game works as follows: The ...
Zhihao Xu's user avatar
1 vote
0 answers
183 views

Comparison of Squared Dice Loss vs. Standard Dice Loss

I've been diving into segmentation tasks and came across two variations of the Dice Loss that I'm considering for my neural network: the standard Dice Loss and the Squared Dice Loss. The Standard Dice ...
mutli-arm-bandit's user avatar
2 votes
1 answer
422 views

Interview Question: Expected value of dice game where each subsequent roll determines number of dice sides

Consider the following game: You are playing a game where you roll a die and earn $1 each time you roll higher than 1. For the first roll you get a 4 sided die, and for each subsequent roll you get a ...
Ria's user avatar
  • 511
0 votes
1 answer
85 views

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?
jkj's user avatar
  • 1
3 votes
1 answer
105 views

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 ...
Francesco's user avatar
0 votes
0 answers
88 views

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 ...
AMAS AL's user avatar
  • 33
3 votes
4 answers
668 views

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 ...
Cel's user avatar
  • 275
5 votes
2 answers
137 views

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 $N \gg 6$ ...
Codename 47's user avatar
2 votes
1 answer
116 views

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?
user379945's user avatar
1 vote
1 answer
84 views

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 ...
Pim's user avatar
  • 13
0 votes
1 answer
78 views

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 ...
ezrix's user avatar
  • 3
1 vote
1 answer
423 views

Roll 4 Dice, What's the Expected Value of the Sum of the highest 3?

After writing a simulation in python (code at bottom) I realized my calculations are incorrect but can't figure out where I went wrong. Let {$D_1$, $D_2$, $D_3$, $D_4$} be the ordered dice rolls. Let $...
Samuel Nelson's user avatar
2 votes
1 answer
463 views

Pseudo-dice probability distribution

Given the following data, is there an algorithmic way to generate a probability distribution? Data: min, max, and average results of "die". Known Trend: results will always be weighted ...
Learn34's user avatar
  • 21
2 votes
1 answer
66 views

Probability of same outcome for a pair of dice/urn draws with correlation $\rho$

This is surely a simple problem, but there are so many probability questions with dice, urns, etc. that I have not been able to find an answer to this specific problem. Say you have a pair of $n$-...
virtuolie's user avatar
  • 642
2 votes
1 answer
50 views

Is there a formula for finding the number of ways 3 dice throws can add to 6?

Consider 3 dice throws: t1,t2,t3 Let E be the event that t1+t2+t3 add up to 6 What is the probability of event E? I know the denominator is an example of ordered repetition. So with n=6 and k=3 there ...
Kirsten's user avatar
  • 803
1 vote
0 answers
313 views

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 ...
Aziz Hammou's user avatar
0 votes
0 answers
142 views

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 ...
Estimate the estimators's user avatar
1 vote
0 answers
16 views

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 ...
Frank Patton's user avatar
0 votes
0 answers
50 views

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? ...
MrChair549's user avatar
0 votes
1 answer
410 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[...
Steve's user avatar
  • 3
1 vote
1 answer
199 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 ...
Isaac's user avatar
  • 113
57 votes
12 answers
12k 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 ...
Theguy Whatguys's user avatar
2 votes
2 answers
145 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 ...
Tommy McGuire's user avatar
5 votes
1 answer
162 views

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 ...
Fabian Allendorf's user avatar
1 vote
1 answer
575 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 ...
ee8291's user avatar
  • 207
0 votes
0 answers
38 views

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 ...
Michael Latter's user avatar
9 votes
2 answers
1k 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: ...
Stack Danny's user avatar
-1 votes
1 answer
465 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 ...
Ema's user avatar
  • 1
1 vote
0 answers
60 views

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 (...
banikr's user avatar
  • 116
1 vote
1 answer
79 views

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 ...
Bob Robertson's user avatar
0 votes
1 answer
151 views

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 ...
user avatar
0 votes
2 answers
40 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 ...
Tim Richards's user avatar
3 votes
0 answers
102 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 ...
CidTori's user avatar
  • 181
0 votes
1 answer
268 views

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 ...
user17130's user avatar
  • 101
3 votes
1 answer
124 views

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 ...
ConfusedGachaGamer's user avatar
3 votes
1 answer
467 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{...
dmccaul's user avatar
  • 33
1 vote
1 answer
690 views

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 ...
Ele975's user avatar
  • 217
4 votes
1 answer
75 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-...
kjetil b halvorsen's user avatar
2 votes
2 answers
208 views

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 ...
augeaufdiewelt's user avatar
0 votes
1 answer
59 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 ...
Adam Michael Wood's user avatar
1 vote
2 answers
128 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 ...
Peyman's user avatar
  • 23
2 votes
2 answers
649 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 ...
Jase's user avatar
  • 23
0 votes
0 answers
143 views

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 ...
Adam Jenssen's user avatar