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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3answers
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Probability of three dice falling in the same quadrant of a box

This is surely really basic for most people here but it's tripping me up. You get a box and draw lines to split it up into 4 parts. I got asked what the probability was that when rolling three dice,...
2
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0answers
52 views

Roll two fair dice, what is the expected value of rolls such that the sum of the two faces is the multiple of 6.

I was thinking that there were 2 cases: (1) $\\$ $X_{1}+X_{2}=6$, and the probability would be $\dfrac{5}{36}$. (2) $\\$ $X_{1}=X_{2}=6$, and the probability would be $\dfrac{1}{36}$. I am now ...
2
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1answer
51 views

Probability of being able to make a given number with two out of xd6

I'm an amateur games designer, and am working on a mechanic which involves rolling on a table with numbers running from 2-12 - the full range of possibilities from adding together two six-sided dice. ...
0
votes
2answers
43 views

Rolling dice against each other?

After doing some research, I found that the probability of rolling an n-sided die against another, equivalent die and landing a higher number on the first rolled dice to be ((n−1)/2)/n, where n is the ...
1
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2answers
29 views

Probability of Rolling a $1$ on an $n$-Die in $r$ Attempts

I roll an $n$ sided die, numbered $1 \to n$. If I roll a $1$, I walk away; otherwise, I roll the die again. This process could repeat indefinitely. What is the probability, $P(n,r)$, that I will roll ...
0
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0answers
33 views

7th Sea 2e: Grouping dice results into sets of 10 vs doing the same with Tarot cards.

Note: While an interesting problem on its own, it also struck me as an excellent example of how marvelous the human brain is, as it is able to almost effortlessly negotiate a task that (at least to ...
6
votes
4answers
1k views

Probability of obtaining a heads on the coin before a 1 or 2 on the die?

I came across this question recently and can't seem to find the correct approach. Any help would be appreciated! An experiment consists of first tossing an unbiased coin and then rolling a fair ...
5
votes
1answer
88 views

Probability of rolling dice twice

Did I calculate the correct probability for these simple scenarios: 1: What is the probability of rolling 3 and 4 with two dice in two rolls? If you roll either 3 or 4 in the first roll, you put ...
1
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1answer
78 views

If you roll four dice what is the probability of getting at least two sixes?

First of all, I know there are a lot of these and similar questions already online but I am trying to solve this on my own and I need you to tell me what I am doing wrong. So, in class we solved ...
1
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1answer
24 views

Probability of $3$ doubles when two dice roled $4$ times

I thought that when rolling two dices to get only pairs is for a single roll $\frac{1}{6}$ for two $\left(\frac{1}{6}\right)^2$, and for three $\left(\frac{1}{6}\right)^3$. But since I have 4 rolls ...
2
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0answers
80 views

How to statistically beat this dice game?

There is a dice game on this site where you can bet a video game's currency in games. I was wondering if any of the more statistically minded could come up with a way of beating the system? The game's ...
0
votes
1answer
87 views

Dice probability with limited reroll

What is the probability of getting 2 successes when 3 dice are rolled once, and then one die is optionally rerolled? $$ n = \text{Number of dice} = 3 $$ $$ p_s = \text{Single die success probability (...
1
vote
1answer
65 views

Rolling a biased dice, Multinomial probability

What is the easiest way to answer this question. Lets say you had a biased 6-sided die P(rolling '1') = P(rolling '3') = 0.1 P(rolling '2') = P(rolling '4') = P(rolling '6') = 0.25 P(rolling '5') =...
1
vote
2answers
37 views
2
votes
1answer
47 views

How many rolls of two dice are needed so that the probability of rolling a double six within this number of rolls is at least $50\%$?

My approach: How many rolls of two dice are needed so that the probability of rolling a double six within this number of rolls is at least $50\%$? Let $X$ be the number of required rolls. ...
0
votes
2answers
31 views

Rolling the results at the same time as the check

I was in a roll playing game last night. In combat we throw 3 six sided dice when we attack and roll some amount of dice if we hit our target by rolling high enough on the attack (for example the dice ...
0
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0answers
46 views

Most Probable Sum for Dice Rolls

Hey so I discovered this formula for finding out the most probabble result when rolling a certain number of f-sided dice. Could you check it and tell me why it is so? ...
0
votes
1answer
21 views

Probabilities of reoccuring draws in a stack of cards

Let's say I have a stack of $12$ cards where only one card in the set is a golden card. The cards are displayed face down on the table in a $3\times4$ pattern and I can choose one card at the time. As ...
14
votes
2answers
246 views

Rolling $n$ $k$-sided dice and discarding the lowest $m$ of them.

In this question I will use the notation $\Bbb{E}(n,k,m)$ to refer to the expected average of rolling $n$ $k$-sided dice and discarding the lowest $m$ of them. The most trivial response happens ...
0
votes
2answers
47 views

Rolling four dice and the difference between predictions

Four standard dice are rolled. What are the chances of: 1.) Rolling three sixes and one five? 2.) Two sixes and two fives? 3.) Exactly one six? 4.) Four different numbers? Here is my thought ...
14
votes
4answers
915 views

On the probability of getting the same number for three dice

I found the probability of having the same number when throwing 3 dice to be $1\times\left(\frac16\right)^2$. In addition, I don't understand how do people get the equation $\left(\frac16\right)^3\...
2
votes
1answer
41 views

Comparative Dice Statistics

I am part of a role playing game where we roll dice to set our statistics. Our current system is to roll 4d6, reroll the lowest of the 4, then keep the highest 3 out of the original 3 and the new one ...
0
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1answer
38 views

Odds of Winning a Scratch Card

I have a scratch card that has 36 spaces that can be scratch. 9 of the spaces have a winning symbol and 27 spaces have an "X". I am allowed to scratch as many spaces until I either get the 9 winning ...
0
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0answers
53 views

Alternate Answer for a probability fair dice game using conditional probability

The problem: In this game, if two dices give: \begin{cases} 7 \text{ or } 3, \text{ then the player wins} \\ 2,\space 11 \text{ or } 12, \text{ then the player loses} \\ \text{else, then the game ...
4
votes
2answers
90 views

Probability of winning dice roll-off with a re-roll

I am looking to find the probability of winning a basic dice roll-off using a 6 sided die if one of the players can re-roll their die. The main thing that is throwing me off is that player 2 can re-...
2
votes
2answers
99 views

Probability of rolling a sum of at least 18 with 10 6-sided dice

I'm trying to work out how to do this, and I'm very stuck. My grasp of probability is shaky to begin with, and generally with probability questions, I list out cases. Due to the number of ...
0
votes
1answer
81 views

Probabilities for rolling multiple dice and getting one number or greater

I am interesting in producing a table of probabilities for dice rolls. These are standard 6 sided dice. What is the probability that for rolling X dice, Y dice will roll (hit) at least number Z or ...
2
votes
1answer
74 views

probability of not getting same number twice in a row after n die rolls

Having rolled a die $n$ times, I want to determine the probability of not getting any number twice in a row. If I wanted the probability of not getting any number three times in a row, I could use the ...
1
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1answer
68 views

Probability of rolling higher than $N$ by summing the highest $X$ number of dice out of a set $Y$ number of dice, each with $Z$ sides.

I'd like help finding a formula for the probability of rolling higher than a target number, $N$, by summing the highest $X$ number of dice out of a set $Y$ number of dice, each with $Z$ sides, ...
0
votes
2answers
52 views

Expected payment of a roll of dice with rerolls

We've got the following game: You roll two dices. You get paid equal to the number rolled. Additionally, if you roll doubles, you reroll (Same rules apply to that roll. That means there's not limit ...
1
vote
1answer
41 views

Three fair dice are rolled one time. What is the probability of at least one $6$?

I think the answer is $10/216$, but I am not sure. I did it by brute force though, and would like to know the background, as well as knowing if $10/216$ is correct. Edit: now i think via brute force, ...
2
votes
3answers
127 views

Distribution of the sum of $N$ loaded dice rolls

I would like to calculate the probability distribution of the sum of all the faces of $N$ dice rolls. The face probabilities ${p_i}$ are know, but are not $1 \over 6$. I have found answers for the ...
7
votes
3answers
314 views

Exploding (a.k.a open-ended) dice pool

Say we role $n$ identical, fair dice, each with $d$ sides (every side comes up with the same probability $\frac{1}{d}$). On each die, the sides are numbered from $1$ to $d$ with no repeating number, ...
0
votes
1answer
32 views

Covariance of dice tosses that result in 1 or 2 (fake proof)

Question: Consider n independent tosses of a $k$-sided fair dice. Let $X_i$ be the number of tosses that result in $i$. What is the covariance $\mathrm{cov}(X_1,X_2)$ of $X_1$ and $X_2$. \begin{...
0
votes
2answers
214 views

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 ...
2
votes
1answer
69 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 $p_1+p_2+p_3+...+p_d=1$. ...
0
votes
0answers
37 views

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 (1,0,0),(-1,0,0)...
3
votes
1answer
47 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 ...
3
votes
3answers
42 views

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 ...
1
vote
1answer
50 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 in $...
0
votes
3answers
69 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 ...
0
votes
1answer
47 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 ...
0
votes
1answer
38 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 ...
0
votes
1answer
91 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, ...
1
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1answer
67 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 \...
0
votes
2answers
38 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 ...
0
votes
2answers
65 views

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 ...
2
votes
1answer
51 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, ...
2
votes
4answers
457 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 ...
1
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1answer
38 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 $P(all \ 6) = 1/216$ ...