Questions tagged [dice]

For questions on dice, small throwable objects with multiple resting positions, used for generating random numbers.

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Finding the median of the total number of die rolls

Question A fair die is to be rolled repeatedly until a six comes up. Find the median of the total number of rolls given that five comes up on the first roll. My working Clearly, this follows a ...
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1 answer
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Calculation of probability for the game

There is a game on which I am working now and I need to balance it. There are N=10 dices and K=3 attempts for throw them simultaneously. If a 6 comes up on any die, then this die is transferred to the ...
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What are odds of rolling a 7 three times before rolling a 12 one time? All other rolls do not matter.

Since other rolls do not matter, I thought I could consider there are only $7$ possible outcomes for each roll, 6 for 7 (1/6, 2/5, 3/4, 4/3, 5/2, 6/1) and 1 for 12 (6/6). So the odds of getting 3 7s ...
4 votes
1 answer
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How do I find the probability distributions for multiple dice rolls for dice with a differing number of sides?

I have been learning how to play Dungeons and Dragons recently, and have bought my first set of dice. The standard DnD dice are: 1d4 1d6 1d8 1d10 1d10 × 10 [10, 20, 30... 90, 100] 1d12 1d20 I was ...
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Is the chi squared goodness of fit test valid for the multinomial distribution if the outcomes are unlabeled?

I'm investigating Sketchy Dice Inc. for purportedly selling unfair dice with the following probability distribution: \begin{align} p(1)&=0.1 \\ p(2)&=0.3 \\ p(3)&= 0.2 \\ p(4)&= 0.15 \\...
4 votes
0 answers
47 views

Calculate probability of flipping coins with probabilities dependent on previous results

Let's say I have a biased coin that has a probability of 0.2 for heads and 0.8 for tails. If you flip it 6 times without getting a heads however, the probability of heads increases by 0.2 per non-...
0 votes
1 answer
45 views

Odds of rolling 3 or more consecutive numbers on n number of dice

I'm searching for an answer to the above problem - how to calculate the probability of getting 3 or more sequential numbers on n number of dice. I found this formula for 6 six-sided dice here (What ...
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Throw three dice such that at least two $3$'s shows up with $0.25$ probability

We consider three fair dice which are thrown simultanously. In other words, one repetition of the experiment means that we have thrown three dice. Use Chebyshev inequality $P(|X-\mathbb{E}(X)|\geq \...
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4 votes
5 answers
259 views

Dice, conditional probability - where am I wrong?

There is a problem which I solved wrong. I know the correct solution from the book, but I cannot find the gap in my reasoning. The problem is: three fair dice are rolled at the same time. What is the ...
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1 answer
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How to calculate the probability spectrum for a 'super roll' with all seven DnD dice? [closed]

I'm trying to calculate the probability distribution for what I'm calling a 'super roll'. A super roll is made by throwing all seven of the standard DnD dice and adding up their values. The standard ...
-1 votes
0 answers
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I found a way to beat my simple dice game with dice 6 sides and option to select 3 sides to win

This problem was probably addressed but I am not sure how to correctly find the problem here or find a solution. I am not mathematician so I apologise if it's not described properly. I wrote I simple ...
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Four fair dice are rolled, we count (6,6,6,5) and not (6,6,5,6), why ? And when two dice are thrown simultaneously we count (5,6) and (6,5) both, why? [duplicate]

Four fair dice are rolled, we count (6,6,6,5) and not (6,6,5,6), why ? And when two dice are thrown simultaneously we count (5,6) and (6,5) both, why? Is it because we throw simultaneously or there is ...
2 votes
2 answers
140 views

Why selecting 2 numbers is different from rolling 2 dice simultaneously?

I have a maths exam tomorrow and this these questions are bugging me. Question 1: Two numbers are randomly selected from set of first 6 natural numbers, find probability that selected numbers are co-...
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Expected number of dice rolls to see each number twice [duplicate]

In one version of this question, it is required to compute expected number of rolls to see each side of a dice. In that case, the answer is $$\frac{6}{6}+\frac{6}{5}+\frac{6}{4}+\frac{6}{3}+\frac{6}{2}...
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2 answers
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What's the explanation for the distribution of this kind of dice roll?

Consider the following type of dice roll for the attack damage in some tabletop RPG: Roll three six-sided dice. Pick two of them that have a sum greater six. The remaining die is the attack damage. ...
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Probability of 4 state system probabilities

In thermodynamics we had exercise to determine witch probabilities $p_1, p_2, p_3, p_4$ (we call it 4-sided dice, in english it would be loaded dice, I guess) would be if we know following: $$p_1=2p_2$...
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Statistics of dice

To keep up my (very basic) python skills and just generally as a hobby I programmed a program that takes a dice input and rolls in a bunch of times. As a case study, I took how a friend of mine ...
-3 votes
1 answer
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Four dice are thrown (6 faces). What is the probability of getting at least three 6s on them? [closed]

I dont know, how to count this with formulas, but i run the program, and answer was ≈ 0,15.
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2 answers
96 views

What is the most likely set of scores produced by rolling 3d6 six times?

In the original Dungeons & Dragons game (D&D), each character has six ability scores determined by rolling three six-sided dice and taking the sum (i.e., 3d6 taken 6 times). What is the most ...
2 votes
1 answer
65 views

Suppose three fair dice are rolled. What is the probability at most one six appears?

From Ross, Intro to Probability Models - Chapter 2. Suppose three fair dice are rolled. What is the probability at most one six appears? Attempted Solution The total amount of combinations are 216. ...
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2 answers
107 views

If a die is rolled $10$ times, what is the probability that the number of even results differs from the number of odd results by at most $2$?

Here is the problem: A fair die is thrown independently $10$ times. What is the probability that difference between the amount of obtained even results and amount of odd results is lower than or ...
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2 answers
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How much does rerolling improve your odds

I have been playing a lot of dice based games and re-rolling has been a major mechanic in a lot of them. knowing when to re-roll and just keep what is currently face up seemed like a basic stats ...
2 votes
1 answer
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Is it better to bet on a d12 or on the sum of two d6?

The game is simple we throw a $d12$ and two $d6s$. We sum the value of the outcomes of the two $d6$ and compare it with the outcome of the $d12$. If the sum of the two $d6$ is higher, $d6$ wins, if ...
3 votes
3 answers
143 views

20-sided dice 100 rounds game

In a game there is a 20-sided die. At the start of the game it is on the table and the 1 face is facing upright. In each of the 100 rounds you have 2 options: you can either roll the dice or you can ...
4 votes
2 answers
214 views

Boxes and dice game

You have $9$ boxes numbered $1$ through $9$ and then you have two $6$-sided dice. Each turn you roll the two dice and deduct the sum of the dice from the boxes by removing the number itself or any ...
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3 votes
4 answers
320 views

What is the probability that the sum of 6 four-sided dice is less than or equal to 14?

The solution given is shown below. My question is how did they count the numerator like that? What is the explanation for it please? $$\begin{align} \frac{C_6^{14}-C_1^6\times C_6^{10}+C_2^6 \times ...
2 votes
1 answer
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The expectation of a Dice game

Let's assume there is a $n$ faces fair dice with face value as $1, 2,...,n-1, n$. Player return would be the value of throwing result, i.e. if player throw once and the result face is $m$, then player ...
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1 answer
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Joint probability function of a fair dice where one random variable is geometric and the other is counting all 1s until 6 is achieved

A fair dice is been tossed until "6" is achieved. Let Y be the random variable stating the number of tosses required. Let X be the random variable stating the number of tosses where "1&...
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1 answer
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Probability - Expected value of a geometric R.V. which connects to a result of a dice roll

A fair dice is rolled and the result and written down, Then the dice is rolled repeatedly (independently) untill the first occurence of a result bigger or equal to the result we've written down. Find ...
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2 votes
1 answer
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Probability question from 2000 STEP III Exam (Question 13)

I got on the first part of the question fine but I'm really confused about the expression "the last of the dice to show a six does so on the $r$th roll" in the second part of the question. I ...
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1 answer
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Number of throws where each face appears at least once.

Given $10$ distinct dice I want to know the number of throws where each one of the $6$ faces appears at least once. First I approached the problem by puting all the $6$ faces and there are $\dfrac{10!}...
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1 answer
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$100$-sided die probability follow-up: Why doesn't the maximizing EV strategy change?

This is a follow up to the question here: 100-sided die probability The question is as follows: You are given a 100-sided die. After you roll once, you can choose to either get paid the dollar amount ...
3 votes
1 answer
129 views

How does rerolling one of two dice affect the expected value?

This problem came to my head this morning and now I've just been curious since. Say you have two fair dice and you roll both of them after you must reroll the lowest die, if the dice are equal one ...
1 vote
2 answers
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Deriving the probability of winning a dice game with two different sets of dice?

Purely out of curiosity, I wanted to determine the probability of winning a dice game when each set of dice is not the same. For example, Player 1 has a dice set of $[d_{20}, d_{4}]$, and Player 2 has ...
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Probability with dices involving colored sides

We have three colored symmetrical dices each having 3 red sides 2 yellow sides and 1 green side. If they are rolled simultaneously what is the probability that. a) Each dice show the same same color. ...
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3 votes
2 answers
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Optimal stategy for 2-players d6 game? [closed]

I came across the following problem when preparing for an interview: Two players each roll a d6, and are not able to see each other's rolls. The player with the higher value wins 1\$ (no win in case ...
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1 vote
1 answer
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What are the limiting probabilities for this silly dice game?

The game works as follows: Two $n$-sided dice are rolled. If the dice show unequal numbers, then the higher number is rerolled. If the dice show equal numbers, then that is the final result of the ...
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2 votes
3 answers
60 views

Fair Value of a Dice Game [duplicate]

1 die. Up to 3 rolls. Your winnings are equal to the value of a single roll. You can stop after roll 1 or roll 2. If you proceed to the next roll (i.e the 2nd or 3rd), you forfeit the previous value (...
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2 answers
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Probability of dice pool throw >= than given dice pool (ordered, unsorted)

Assume we have a game with two dice pools. Each dice pool consists of k n-sided dices (all dices are fair, i.e. each side has the same probability to show up). The first dice pool is rolled once and ...
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Probability of taking an odd number of throws to get 6 [duplicate]

Throw a dice until get 6.What's the probability that total number of throw is odd? My approach: throw 1 time : $1/6$ throw 3 times : $(5/6)^2*1/6$ throw 5 times : $(5/6)^4 * 1/6$ ...and sum them up.It ...
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5 votes
2 answers
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Dice game: bidding for sum

Consider the following two-player game. Both players roll a fair die. They can see their own roll, but not their opponent's roll. Then, both players simultaneously choose a (possibly fractional) ...
1 vote
1 answer
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Probabilty of throwing a select number from 2 dice or a pair from 2 dice

We have 5 dice, 3 outside of a cup, 2 inside of a cup. The three outside are number 6. We only throw the ones inside the cup. What’s the probability of throwing a poker (4 dice with 6s) or a full ...
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Revisit: Probabiity of X dice results in a row

This is a revist of this question, which was closed because the posting was of low quality. The original question is : A (fair) 6 sided die is tossed $10$ times. What is the probability that ...
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4 votes
2 answers
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EV of a strictly increasing sequence of n-sided dice rolls

You roll a fair, $n$-sided die. If its value is higher than that of your previous roll (or this is your first roll), you add it to your score and roll again. If not, you keep any banked points and ...
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Probability of getting a total p from rolling $\{c_1,c_2,\dots,c_n\}$ dice with sides $\{1,2,\dots,n\}$

Using dice notation to denote the total (i.e. xdy means the total of x dice with y sides) my question would be finding the probability of the following statement to be true (I am not sure if there is ...
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Whether or not to pay for a boost in die playing game

You and an opponent play a game by rolling a fair 6 sided dice- the one who gets the higher number wins 1\$. If you lose you get nothing. If you tie you both just roll again. (a) What are the expected ...
3 votes
1 answer
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What is the dice result probability curve of 4d6kh3r1, but with an exception rule?

So the equation is four 6-sided dice, keep the highest three results of the four results, and reroll any ones rolled. However the exception comes in where the reroll won't happen if there are already ...
1 vote
0 answers
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Probability of rolling consecutive fours after a specified roll [duplicate]

We roll a regular and fair die repeatedly until two fours in a row come up, then we stop. What is the probability of halting after n rolls? My attempt at solution: Let $A_n$ be the event that the $n^{...
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Why does successive rolls on a die increase probabilty?

So in my maths textbook the questions asks: "What is the probability of rolling at least one 5 in 6 rolls". So of course the probability of rolling a 5 is 1/6. Supposedly rolling the die 6 ...
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How much must the casino charge for this game for a non-negative expected profit?

St. Pete's Casino is introducing a new dice game called "Guess and Win." After paying (not betting) a fixed ante of $x$ dollars, the player guesses what the next roll of a fair six-sided ...

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