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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2
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1answer
57 views

Die that never rolls the same number consecutively

Suppose we have a "magic" die $[1-6]$ that never rolls the same number consecutively. That means you will never find the same number repeated in a row. Now let's suppose that we roll this die $1000$ ...
4
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1answer
38 views

Special dice generating non-decreasing sequence

Suppose that, when rolled for the first time, a special 6-sided dice shows $1,\ldots, 6$ with probability $\frac{1}{6}$ each, and then, upon rerolling, shows with equal probability a number greater or ...
4
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2answers
58 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 ...
0
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1answer
31 views

Calculating probability that 5 dice rolls will produce an average of 3.5

We are carrying out a dice game which involves 5 people rolling dice and passing buttons equal to the number rolled . We have to work out the probability that we will get an average of 3 .5 items ...
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2answers
50 views

Dice probability, Heaven or Hell [on hold]

You're at the gate of Heaven and St. Peter asks you to play Dice with him. If you roll a 5 or 6, he'll let you into Heaven. However, if you roll a 2,3 or 4, you'll be sent to hell. If you roll a 1, he ...
0
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2answers
34 views

Find dependent event when two dice are thrown simultaneously.

Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If $E_1$ is the event that die $A$ shows up four, $E_2$ is the event that die $B$ shows up two and $E_3$ is the event that the sum of ...
0
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0answers
41 views

Roll dice and get score except when you get 6 where you lose everything [on hold]

At what score to stop when you roll a dice under these conditions: -if you get 6 you lose all your score -You score is the add up of all rolls
2
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0answers
27 views

Can someone help me balance this game (probability question) [on hold]

A team of 9 vs a team of 1. Each round each of "the 9" roll a die to "attack" and "the 1" rolls 9 dice to "defend", the nine dice are preassigned to attackers before the roll, "the 1" cannot choose ...
0
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1answer
701 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 ...
0
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1answer
29 views

Given three six-sided dice, what is the probability that the value of the third will be greater than the sum of those of the first two?

A die is rolled three times, or three dice are rolled. What is the probability that the third die values greater than the sum of the first two? (assuming six-sided dice, but I would be interested in ...
0
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1answer
29 views

Creating $Y \sim U[1, \dots, 6] + U[1, \dots, 6]$ as a function of $X_1, X_2, X_3 \sim U[1, \dots, 6]$

The Three Indistinguishable Dice Puzzle from standupmaths The problem therein can be summarized as follows: You have three dice rolls. Each die is indistinguishable from the others. However, using ...
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4answers
1k views

Rolling a die until two rolls sum to seven

Here's the question: You have a standard six-sided die and you roll it repeatedly, writing down the numbers that come up, and you win when two of your rolled numbers add up to $7$. (You will ...
3
votes
3answers
530 views

You cast a pair of dice. If you get a 6 and an 8 before 7 comes up twice, you win. What is the probability of winning?

You cast a pair of dice. If you get a 6 and an 8 before 7 comes up twice, you win. What is the probability of winning? What I tried was \begin{align*} P(X=6) & = \frac{5}{36}\\ P(X=8) & = ...
0
votes
1answer
643 views

How to use N indistinguishable dice to simulate 1 roll of N-1 dice? [closed]

If I use 3 indistinguishable dice to simulate 1 roll of 1 die. I can use this formula "(SUM % 6) + 1". There SUM is the total amount of the three indistinguishable dice added together, 6 is the max ...
1
vote
2answers
36 views

What is the probability of these questions?

What is the probability of throwing $2$ dice, and the first one is a $6$? (Given that one of them is a 6.) My solution says that it's $\frac{6}{11}$, but I have no clue why. The other one is: What ...
5
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1answer
195 views

Expected outcome for repeated dice rolls with dice fixing

Here is another dice roll question. The rules You start with n dice, and roll all of them. You select one or more dice and fix them, i.e. their value will not ...
5
votes
2answers
449 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 ...
6
votes
2answers
75 views

Rolling a certain total with a dice

Suppose you roll a $k$-sided die repeatedly, totaling your scores as you go, until you reach or surpass $n$. (For a real-world usage ... if you have a non-looping game board and only move forward, ...
2
votes
2answers
94 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 ...
8
votes
3answers
1k views

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 ...
2
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0answers
42 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 ...
1
vote
1answer
48 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. ...
13
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4answers
13k views

On average, how many times must I roll a dice until I get a $6$?

On average, how many times must I roll a dice until I get a $6$? I got this question from a book called Fifty Challenging Problems in Probability. The answer is $6$, and I understand the solution ...
0
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2answers
35 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 ...
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2answers
28 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 ...
8
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2answers
110 views

Three equal die rolls in a row in a $3\times 3$ array

If 9 six-sided dice were rolled consecutively and displayed in a $3\times3$ format, what is the probability of a line of 3 of the same number occurring? Considering the 8 ways that are possible; 3 ...
1
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1answer
50 views

How can I convert [number of expected success per try] into [probability of succeeding N times without failing]?

There's a push-your-luck dice game called Can't Stop where you roll four six-sided dice, group the dice into pairs of your choice, then advance tokens along paths corresponding to the sums of your ...
0
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1answer
79 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 ...
6
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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 ...
0
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0answers
26 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 ...
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3answers
83 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 ...
5
votes
1answer
51 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 ...
0
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1answer
49 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 ...
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1answer
22 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
62 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 ...
1
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1answer
57 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') ...
40
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2answers
31k views

Expected time to roll all 1 through 6 on a die

What is the average number of times it would it take to roll a fair 6-sided die and get all numbers on the die? The order in which the numbers appear does not matter. I had this questions explained ...
2
votes
1answer
37 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
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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 ...
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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 ...
14
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2answers
235 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 ...
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0answers
36 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? ...
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1answer
62 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
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 ...
20
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4answers
31k views

The expected payoff of a dice game

There's a question in my Olympiad questions book which I can't seem to solve: You have the option to throw a die up to three times. You will earn the face value of the die. You have the option ...
0
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2answers
44 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 ...
0
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2answers
99 views

Probabilities of Dice Pools

Given 5 fair, 6-sided dice, calculate the probability of an equal or greater number of dice showing 1 appearing than the number of dice showing 4,5, and 6 combined. For example: if 5 dice are rolled ...
2
votes
3answers
4k views

Solve for numbers to appear on two six-sided dice

I have a small wooden calendar that uses two six-sided dice to display day of month. One die carries numbers 0, 1, 2, 6, 7, 8 and the other carries 0, 1, 2, 3, 4, 5. The six of course doubles as the ...
13
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4answers
879 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 ...