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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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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1answer
54 views

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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1answer
86 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 $1 < a < 6$. I'...
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1answer
58 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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0answers
30 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
30 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
81 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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1answer
139 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
727 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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0answers
63 views

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
33 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 $p(...
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1answer
258 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
62 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 fair. ...
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3answers
94 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
20 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
43 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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1answer
34 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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2answers
38 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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4answers
264 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
83 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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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
54 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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1answer
185 views

Product of numbers is even , when an unbiased die rolled?

An unbiased die is thrown $n$ times. The probability that the product of numbers would be even is $1/(2n)$ $1/[(6n)!]$ $1−6^{−n}$ $6^{−n}$ None of the above. My attempt : we have $3$ even ...
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1answer
33 views

What is the average number of rolling 4 six-sided die and choosing the 2 higher rolls( which will be added)?

As an example, if you roll 6,5,3,3 you will have 11 as the sum of 6 + 5. The average is obviously higher than 7 but i have no idea how to calculate it other than by brute force.
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2answers
55 views

Craps Two Dice Question

In the game of craps, a player throws a pair of dice. The game ends with the first throw if a 2, 3, 7, 11, or 12 is thrown. Otherwise, the player throws the dice repeatedly until either the number ...
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2answers
187 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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2answers
87 views

Probability of Exactly X Successes with Variable Success Dice

I am interested in finding the probability that on any single roll of dice you can have an exact number of successes. However, depending on the particular dice success is a different probability and I ...
3
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1answer
49 views

Probability of rolling n times 3 dices with a specific sum

Imagine we're rolling 3 dices. How many times do we need to roll them so we get a sum of 15 with a probability of 0.6. What I got so far: We're throwing the dices n times (this hints at bernoulli ...
2
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1answer
141 views

Probability of hitting a target number on x number of dice with y number of sides

I have a complicated probability question. I want to know how to calculate the probability of reaching a target number (or greater) on a variable number of dice with each die having a variable number ...
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2answers
59 views

I rolled a 6, what is the probability of having chosen a manipulated dice?

I have two dice, $F$ and $M$. $F$ is a fair die and thus $P_F(6)=\frac{1}{6}$. $M$ is manipulated and $P_M(6)=\frac{1}{2}$. I randomly choose a die and throw it. I already know $P(6)=\frac{1}{2}*\...
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1answer
95 views

Probability n Dice Results are subset of m Dice Results

Let D(n,m) be the probability that a multiset of n dice results will be a submultiset of m dice results. Multiset indicates repeats are counted: If n=3, {3,3,4} is a submultiset of {3,3,4,5,6} but ...
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2answers
118 views

What is the pmf of rolling a die until obtaining three consecutive $6$s?

I am trying to find the pmf of rolling a die until 3 consecutive 6s turn up. I am able to find the expected value using a tree diagram, but the pmf is not obvious to me. Let A be the event of not ...
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2answers
87 views

Game probability

I hope you could help me with this problem... The game goes this way: There are 6 players, numbered 1 to 6. Player 1 starts the game, he rolls a die with six faces. If the result (x) of rolling ...
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1answer
42 views

Probability game problem

I hope you could help me with this problem... The game goes this way: There are 6 players, numbered 1 to 6. Player 1 starts the game, he rolls a die with six faces. If the result (x) of rolling ...
0
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3answers
136 views

Probability six game player [duplicate]

The game goes this way: There are 6 players, numbered 1 to 6. Player 1 starts the game, he rolls a die with six faces. If the result ($x$) of rolling the die is 1 then Player 1 wins. Else the player ...
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2answers
336 views

Is rolling a dice a Gauss distribution?

I'm in an argument with a friend over rolling a dice several times, for example rolling 5 times. His argument is, that is far more difficult to roll out 1-1-1-1-1 than any other combination (for ...
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1answer
72 views

Probability of getting at least 4 numbers by rolling dice n times

I want to compute probability of getting at least 4 numbers by rolling dice n times. Now my formula is $$ P = \frac{6^n - 2^n * {6 \choose 2} + 4 * 1^n * {6 \choose 1}}{6^n} $$ But by principle of ...
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2answers
534 views

Probability of rolling a 6 before an odd number [closed]

A dice is rolled many times. What's the probability of rolling a 6 before an odd number? I'm unsure of where to start with this, please help.
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2answers
69 views

Loaded die probability

The loaded die has the following probabilities: $0.3,0.2,0.1,0.1,0.2,0.1$ for $1,2,3,4,5,6$ respectively. The question asks What is the probability of rolling at least one $1$ and no $2's$ in $4$ ...
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1answer
55 views

Probability's Game

The game goes this way: There are 6 players, numered 1 to 6 (Player 1, Player 2,...,Player 6). Player 1 starts the game, he rolls a dice with six faces. If the result (x) of rolling the dice is 1 ...
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1answer
132 views

Puzzle on rolling dice game

A gambler goes to bet. The dealer has 3 dice, which are fair, meaning that the chance that each face shows up is exactly 1/6. The dealer says: "You can choose your bet on a number, any number from 1 ...
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1answer
136 views

Roll dice, high number wins.

Me and my brothers (3 of us) decided to roll a single dice to see who would get to have my fathers old pocket knife. The guy who rolled the highest number would win. So I rolled first and got a 6, ...
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2answers
232 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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2answers
67 views

If I do not know how much sides a dice has, how often should I throw it to know the number of sides?

Lets say we have a dice with an unknown number of sides, and we are only allowed to see the results of the rolls. How often do I have to throw the dice to know the number of sides?
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8answers
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Probability that the sum of 6 dice rolls is even

Question: 6 unbiased dice are tossed together. What is the probability that the sum of all the dice is an even number? I think the answer would be 50%, purely by intuition. However, not sure if ...
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1answer
106 views

Use any dice to calculate the outcome of any probability

While looking at this question, I had a gut feeling that you can use any fair, single die with any number of sides to calculate the outcome of any probability. Assuming we express the probability as ...
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3answers
738 views

One die probability questions [closed]

I was given this exercise: If a standard die has twice the probability of rolling an odd number than an even number. Find the probability of rolling a non-prime number with this die. My attempt: P(...
3
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3answers
81 views

Statistics dice question

$6$ people, $A, B, C, D, E, F$ sit in a circle to play a dice game. Rule of game: as you roll a die and get a number which is a multiple of $3$, give the die to the person on the right(...
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1answer
50 views

two rolls of a die. independent.

for two rolls of a die, the dice fall independently. an even number shows on the first die and the event that an even number shows on the second die? this is what i got= the probability that the ...
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3answers
47 views

Probability. Fair dice with $n>6$ sides. Who wins?

I am fairly new to statistics so bear with me. Two players are playing a game with a fair dice that has $n>6$ sides. The sides are labeled $1,2,3,..,n$. The one who throws a larger number wins but ...