For questions on dice, a small throwable object with multiple resting positions, used for generating random numbers. This makes dice suitable as gambling devices for games like craps, or for use in non-gambling tabletop games.

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Suppose you roll two dice. Find the probability that you roll an 8, provided you roll a 7 or 8 first?

In the gambling game "craps," a pair of dice is rolled and the outcome of the experiment is the sum of the points on the up sides of the six-sided dice. The bettor wins on the first roll if the sum is ...
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53 views

Expected number of dice rolls of an unfair dice to roll every side equally many sides

I am having trouble with solving the following problem: The probability that a $d$-sided dice lands on its $k$th side is equal to $p_k$ for $k\in \{k\in\mathbb{N},k≤d\}$ and $p_1+p_2+p_3+...+p_d=1$. ...
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Number of ways a dice can roll every side equally many times for the first time after x rolls

This problem is best viewed as a walk on a $d$-dimensional integer lattice with integer steps corresponding to various results of a dice roll. For a normal 6-sided dice, these would be ...
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1answer
25 views

Can you create non transitive dice for any finite graph?

Let's say you have a finite directed graph, with no two nodes that point at each other. Can we assign each node a dice, so that each node beats the node it is pointing at. This is easy for acyclic ...
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1answer
631 views

Probability of dice roll (board games)

Assume that we have $n$ six-side dices. We will roll all the $n$ dices.What is a probability of getting at least $r$ ones, $s$ twos , $t$ threes and $u$ fours? Number $6$ can be used instead of any ...
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Probability of Rolling a Pairwise Seven rolling $4$ Dice

My friend posed this problem to me. He wrote a computer program to generate all possible combinations of dice and counted the cases with pairwise $7$'s. I thought that the problem had a simpler ...
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1answer
43 views

Number of tosses until 3 consecutive results using conditions

What is the expected number of tosses such that there are 3 consecutive sixes. Denote the event $T$=number of tosses until first non-six Let $X$ be the event of getting $3$ consecutive sixes ...
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61 views

What is the probability that a person wins the game on the first roll?

I can't seem to find an answer for the title/question above and so I thought I'd ask. The aim of the game is to get a higher number than your competitor using only one dice. If two people (For ...
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1answer
3k views

Probability of rolling 3 sixes in 6 rolls [closed]

I roll a die six times. What is the probability of rolling at least 3 sixes? Please share the formula as well, so I can figure it out myself in future.
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1answer
33 views

How to calculate number of dice needed to reach total y with probability z [closed]

I am writing an excel sheet to help with planning for a game I am playing. In this game, you have units which produce 1d10 points per round. Each goal is measured against a target. I am trying to ...
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1answer
46 views

The expected value of the greater and smaller of the two rolls of a die

Rolling two four-sided (tetrahedron) dice, what is the expected value of the higher and of the smaller of the two numbers shown? Partial Solution: $$EX = 1 \cdot 1/16 + 2\cdot 3/16 +3\cdot 5/16 +4 ...
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1answer
37 views

Throw a dice 5 times. what is the probability that you get 4 or 6 in two throws, and 1 or 3 in 3 throws. combinations like 13461 are included.

Now normally, I have 8 (111,113,133,131,311,331,333,313) combinations along with 3 ways to obtain it(4 4, 4 6, 6 6) , so 3/24 would be the answer according to my logic, but I am not sure that this is ...
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1answer
35 views

Calculating probility of dice rolls with conditional rerolls for specific target numbers

I have searched for an answer but quite frankly, I am not sure what to even search for. As such, I apologize if this has already been asked and answered. Given a single die with 10 sides labeled 0-9, ...
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1answer
81 views

Playing a dice game, where the winner is determined when the first 6 appears

I did a course on probability in undergrad, and I felt like brushing up on it by working out some problems a colleague gave me: "Two siblings are playing a dice game, where the winner is determined ...
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2answers
28 views

Dice throw, joint distribution.

The two dice were thrown. $X$ is random variable of the amount of 5 in throw. $Y$ is a random variable of 6 in throw. Compute $\mathrm{cov}(X,Y)$. I suppose, that for $E(X)$ and $E(Y)$ we should use ...
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2answers
411 views

Probability of winning blackjack dice game?

I know a little bit about probability but I am not sure how to calculate this: In a dice game of blackjack, there are two parties. The player and the dealer. The aim of this game is to get as ...
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1answer
32 views

Get dice from matrix of win chances. Is it always possible?

As an example, consider a set of nontransitive dice $D_1: 2, 2, 4, 4, 9, 9$ $D_2: 1, 1, 6, 6, 8, 8$ $D_3: 3, 3, 5, 5, 7, 7$ On the long run D1 wins vs D2, D2 wins vs D3 and D3 wins vs D1. ...
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2answers
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how to calculate the P(the sum of upward face after 7 dice rolls <= 30)

I'm new to the stackexchange math community so forgive me if there are problems with the question format or the question itself. I'm new to probability and is trying to learn the concept of ...
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1answer
32 views

Do d20 dice with different number arrangements have the exact same probability for each value?

I have three d20 dice with the following number arrangements: Each pair of opposite sides add up to 21. 1 shares edges with (clockwise) 2, 5, and 8, and shares vertices with (clockwise) 2, 3, 4, 5, ...
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4answers
351 views

A die is rolled 6 times; what is the chance that the first roll is a one or the last roll is a one.

This question appears on page 244 of "Statistics, 4th ed" by David Freedman. The text of the question is: A die is rolled 6 times. The chance that the first roll is an ace or the last roll is an ...
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2answers
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Optimal Strategy for Bar Dice

This game is played in bars in Wisconsin, USA, but I'm sure variations are played many places around the world. The game has practical value, since once mathematicians figure out the best strategy, ...
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1answer
31 views

Do we need to find an upper bound for the expectation of this stopping time?

From here: It looks like: It is supposed to say 'different from six' rather than 'different from three' $T = \inf\{m: X_{m} = X_{m+1} = X_{m+2} = 6\}$ In every triple $P(all \ 6) = 1/216$ ...
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0answers
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Dice rolls - Combinatorics with limitations

Given 2 players, one rolling $x$ d6 dice and the other rolling $y$ d6 dice, what is the probability of a match between the two players? I'm getting stuck on the sub-set comparisons - I can calculate ...
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2answers
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Poker dice probability

I am working on a maths excersice and got stuck on this question where I need to calculate the probability of poker dice. The game poker dice is played with 5 dice. It's possible to get one of the ...
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1answer
56 views

The probability that the product of 100 die rolls $\le$ $a^{100}$ for $1 < a < 6$

Suppose that a fair $6$ sided die is rolled 100 times. Let $X_i$ be the value obtained on the $i$th roll. Compute an approximation for $ P\left(\prod X_i \le a^{100}\right)$ for $1 < a < 6$. ...
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1answer
40 views

Dice probability

I had a rather interesting yatzee experience. This is Maxiyatzee, 6 dice game. He had 13 throws. All together 78 dices. He only managed to throw one 2 on all those throws. And I am trying to find out ...
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1answer
23 views

Find the joint PMF of X and Y, are they independent?

A fair die is rolled, and then a coin with probability $p$ of Heads is flipped as many times as the die roll says, e.g., if the result of the die roll is a 3, then the coin is flipped 3 times. Let $X$ ...
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0answers
24 views

Trickster and dice

Suppose a trickster has three six-sided dice all of which evenly weighted (so each face is equally likely). One has all 6s, one has half 6s and half 1s, and one is a normal die. The trickster randomly ...
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1answer
29 views

Choosing dices out of a box

In a box we have 5 dices, 3 of them are proper, one has two sixes, second has six sixes. Given the events A - after first throw we have a six, B- after next two throws we have six and something else. ...
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1answer
55 views

“Exploding Dice” vs. “Non-Exploding Dice”

For a roleplaying game I'm designing, I'm using a core resolution mechanic that comes down to counting "successes" on rolled dice. Characters roll a handful of dice (six-sided) and count each die that ...
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2answers
86 views

Proving pairwise independence and mutually independent

I have this problem that states: A = {red die is 3, 4, or 5} B = {blue die is 1 or 2} C = {sum is 7} Both the red and blue die are under equally likely probability. I need help ...
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3answers
614 views

Independence intuition

Toss two fair dice. There are $36$ outcomes in the sample space $\Omega$, each with probability $\frac{1}{36}$. Let: $A$ be the event '$4$ on first die'. $B$ be the event 'sum of numbers is $7$'. ...
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1answer
72 views

Given a biased die, what some of the probabilities

I recently asked this question: Roll a fair 6 sided die twice, What is the probability that one or both rolls are 6? And that makes sense, however, the reason I was confused in the first place is ...
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3answers
189 views

Roll a fair 6 sided die twice, What is the probability that one or both rolls are 6?

Roll a fair 6 sided die twice, What is the probability that one or both rolls are 6? This question is confusing me on a conceptual level, specifically the "or both rolls." With out that, the ...
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1answer
235 views

(CLT) Number of rolls of two fair dice to be 90% certain that the percentage of times they show the same face is between 5/36 and 7/36

How often do you have to roll two fair six-sided dice to be 90% certain that the percentage of times they show the same face is between 5/36 and 7/36? I was thinking, to apply the central limit ...
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1answer
61 views

The difference of two fair dice rolls

If you roll a dice twice, and subtract $ Result_1 $ from $ Result_2 $, in what interval with 97% probability will lie number of all zeros, if we will do this experiment 1200 times. I assume, I ...
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0answers
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Probabilities in a dice game (Ashens' game)

This question relates to a card/dice game by Stuart Ashen which unfortunately I cannot name here because its name is Norfolk slang for male genitalia. This game is played in several phases, but the ...
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1answer
82 views

Expected number of rolls when repeatedly rolling an $n$-sided die

Suppose I roll an $n$-sided die once. Now you repeatedly roll the die until you roll a number at least as large as I rolled. What is the expected number of rolls you have to make? I know the answer ...
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1answer
32 views

We throw $2$ dice, a Red and Yellow one.

A is the event that Red rolls $1, 2,$ or $3; B$ is the event that Red rolls $2, 4, or 6;$ and C is the event that the sum of the two rolls is 5. (a) Find $p(A|B)$, $p(B|C)$, and $p(C|A)$ (b) Find ...
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1answer
53 views

Throwing the dice - wrong interpretation still yields correct result

Imagine the following game: You are throwing two fair dice and you will be awarded with the sum of the points in cents. How much should participants of this game pay so that the game itself is ...
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3answers
53 views

Probability of getting a certain number: rolling a die with x number of sides, with advantage

In D&D when you have advantage or disadvantage you roll your die twice (ex 3&7), and pick the higher number($7$). When you have disadvantage you pick the lower($3$). I want to know how to ...
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1answer
19 views

You roll 3 dices with 6 sides each - Three “0”, Two “1” and One “2” - what are the percentages of each (0-6) result?

I'm making a game based on Dice Rolls, and I need some percentages based on the results of these rolls. The situation: You roll 3 dice and get points based on the results. Each die has 6 sides - ...
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3answers
38 views

Throwing 8 sided dice 3 times with the sum of the throws being 6, whats the probability that the first throw was 3?

We already threw the 8 sided dice 3 times. The sum of these 3 throws was 6. Whats the probability that in our first throw we got 3? I am a little lost on this one, but I would probably do it ...
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4answers
127 views

What is the probability of getting exactly 3 two's OR three's when a die is rolled 8 times?

What is the probability of getting exactly $3$ two's OR three's when a die is rolled $8$ times? I know that $P(E) = |E| / |S|$. I believe that $|S| = 36$, since there are $36$ different ...
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1answer
33 views

SR5: Chance of rolling 2 dice with a result of 5 or 6 and 4 dice with a result of one out of eight dice total

This question is regarding calculating probability for the SR5 role-playing game. The setup: a number of d6, $n$, are rolled. Any dice that come up as a 5 or a 6 are considered ‘hits’, and they add ...
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2answers
37 views

Rolling and rerolling dices

I roll 10 initial dices. Whenever I roll a $6$ I roll 5 more dices. What's the expected number of dices I'm going to throw? I was thinking about it when trying to create a die system, but can't ...
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7answers
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We roll a six-sided die ten times. What is the probability that the total of all ten rolls is divisible by 6?

So the question is really hard I think. I tried using a simple way by calculating the probability of each combination that makes a sum divisible by six, but it would take forever. Does anyone have any ...
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1answer
31 views

The probability of success if rolling two dice and taking the lower result

My question is more for my own knowledge, and is based off of a board game I'm playing. I'm rolling for an event and I'm rolling 2d10 (two 10 sided dice). The chances of succeeding on a roll if I ...
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2answers
172 views

Probability for the occurrence of each outcome in dice game

For a fictitious dice game, there is the following rules: Rules ...
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4answers
10k views

How many rolls do I need to determine if my dice are fair?

Roughly how many times do I need to roll a 6-sided die to feel confident that it's giving "fair" results? What about a 10-sided or 20-sided die? Note that I will be actually manually rolling physical ...