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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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 ...
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71 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 ...
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1answer
81 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 (...
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1answer
60 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') =...
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2answers
37 views
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1answer
46 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. ...
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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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42 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
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 ...
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2answers
241 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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2answers
46 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 ...
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4answers
904 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\...
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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 ...
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1answer
35 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 ...
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0answers
51 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 ...
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2answers
71 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-...
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2answers
97 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 ...
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1answer
72 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 ...
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1answer
67 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 ...
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1answer
67 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, ...
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2answers
47 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 ...
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1answer
39 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, ...
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3answers
108 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 ...
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3answers
313 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, ...
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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{...
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2answers
198 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 ...
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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 $p_1+p_2+p_3+...+p_d=1$. ...
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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)...
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1answer
42 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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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 ...
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1answer
49 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 $...
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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 ...
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1answer
46 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
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 ...
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1answer
72 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
64 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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2answers
37 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
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 ...
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1answer
41 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
449 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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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 $P(all \ 6) = 1/216$ ...
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1answer
37 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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1answer
52 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
85 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
56 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
29 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
75 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
120 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
687 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 ...