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 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 ...
3
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1answer
222 views

The math behind generating Dungeons & Dragons ability scores: roll 4d6, toss lowest

D&D 5th ed. gives the following instructions for determining your “ability scores.” Roll four 6-sided dice and record the total of the highest three dice If I repeat the ...
3
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1answer
138 views

Dice: Expected highest value with a tricky condition

I know how to calculate the expected value "E" of a roll of n k-sided dice if we are supposed to keep the highest number rolled. If I am not wrong, the formula is: E = k − (1^n + 2^n + ... + ...
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1answer
337 views

Best strategy for rolling 20-sided and 10-sided dices

There are a 20-sided (face value of 1-20) dice and a 10-sided (face value of 1-10) dice. A and B respectively roll the 20 and 10-sided dices. Both of them can roll the dice twice. They may choose ...
3
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1answer
131 views

Dice probability of a winning more than $X\%$ of the time over $Y$ Throws

I have a die with three possible outcomes. The three outcomes are win (+1), draw (0) and lose (-1). $P(w) + P(d) + P(l) = 1$. (1) If I throw the die Y times, what is the probability I will win $X$ ...
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1answer
2k views

Roll 5 dice and find the probability that at least 3 dice are 4

My approach is find P that exactly 3 dice are 4 + exactly 4 dice are 4 + exactly 5 dice are 4. $(5C_3 * (1/6)^3 * (5/6)^2) + (5C_4 * (1/6)^4 * (5/6)^1) + (5C_5 * (1/6)^5)$ = 276/6^5 Is my ...
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1answer
65 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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1answer
47 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 ...
2
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1answer
119 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
63 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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1answer
35 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
51 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 ...
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1answer
25 views

$n$ dice, finding $\operatorname{var}(X)$

If we throw $n$ dice. And $X$ is the total number of eyes. Find $\operatorname{var}(X)$. My idea was to label $X=X_1+\cdots+X_n$ where $X_1$ is the outcome of die $1$ etc. And because $X_1,\ldots, ...
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1answer
38 views

Approximation of distributions with dice

I want to know what dice to roll to get a given probability distribution(mainly normal distributions but exponential distribution would also be helpful). I want a function $f$ so that ...
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1answer
42 views

Optimal strategy in the following game:

In this game, 12 hidden D6s are rolled and summed. The player is given the total of the rolled dice. The player will then guess a number from 1 to 6. If there is a unrevealed dice with that number, ...
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1answer
48 views

Finding an $f(x,y,n)$ such that $round[f(x,y,n)] = \lfloor\frac xn \rfloor + \lfloor\frac yn \rfloor$

Problem: I have an equation: $$\left\lfloor\frac xn\right\rfloor + \left\lfloor\frac yn\right\rfloor$$ I need to find an equation that does NOT use the floor function, but will take those same two ...
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1answer
53 views

Probability of hitting a certain sum with dices

Using $5$ $6$-faced dices, what's the probability of hitting a cumulative sum $S$, on a particular roll (each roll incorporates all $5$ dices ), if $15 \leq S\leq 20$? I reckon this particular ...
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1answer
66 views

Conditional Expectation of Two Dice Roll?

A is the first roll of the dice, B is the second. The question is to find the expected value of A given A + B = 7; E(A|A+B = 7) Since A can be any number between 1 and 6, is this as simple as ...
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1answer
46 views

Can a biased physical random source be post-processed to control the bias?

Let $X_i$ with $i\in\mathbb N$ be a sequence of independent 6-ary random variables with distribution $\operatorname{Pr}(X_i=e)=p^e_i$ where $e\in\{1,2,3,4,5,6\}$ and $\sum_{e=1}^6p^e_i=1$. Let's ...
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1answer
201 views

$95$ percent confidence interval for roll of two dice

Given a roll of two fair six-sided dice, we know the expectation for a specific result (e.g. a $4$ and another $4$) is $\frac{1}{36}$. But with what certainty could you expect that result in $N$ ...
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1answer
70 views

The difference of two fair dice rolls

If you roll a dice twice, and subtract $ Result_1 $ from $ Result_2 $, in what interval with 97% probability will lie number of all zeros, if we will do this experiment 1200 times. I assume, I ...
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1answer
221 views

Calculate Probability that X amount of N die are equal to Y?

Update --- I think I see my problem... in the example at Stack Exchange Question it shows 5C3 5C4 and 5C5... if I have researched this out, this means 5 combinations choose X. If so, what is that ...
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1answer
38 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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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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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
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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1answer
30 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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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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66 views

Progressive Dice Game

You have a fair, regular 6-sided dice. The game is played for $n$ turns. Each turn you make a roll and gain that many points the rolled side is showing, then do one of the following: ...
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0answers
50 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 ...
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0answers
68 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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0answers
105 views

Simulating dice by coins

Suppose you have a fair n-sided die $D_n$ - or rather suppose you don't have a $D_n$ but want to simulate one by repeatedly (but finitely many times) throwing a single (possibly biased) coin $C_p$ ...
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51 views

Dice throwing probability : at least one success

What would be the function for calculating the probability of at least one success of $n$ $10$-sided dice thrown, if success is $9$ or $10$, but $1$ is counted as negative success (or failure). In ...
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0answers
38 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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0answers
78 views

Probability dice game, multiple turns

Alice and Bob are playing dices, Alice begins. If the current player gets a 6, he wins. If he gets 4 ou 5, he plays again. Else, the other player plays. Let $p_n$ (resp. $q_n$) be the ...
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49 views

How good of an approximation is a normal probability distribution for sum of dice rolls?

I want to know how well the normal distribution explains the sum of rolls with n dice with s sides. The mean value and the variance of the dice rolls are $$\mu=n\frac{s+1}{2}$$ and ...
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0answers
233 views

Probability of rolling n dice to match another set of dice, d, given r rolls (like yahtzee)

(Note: I will eventually code this, but i'm primarily interested in the math behind it) I'm trying to create a function in Java to calculate the probability of getting a desired outcome from n rolled ...
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0answers
368 views

Two dice are rolled. If the sum is greater than 8, what is the probability that it is 11?

Two dice are rolled. If the sum is greater than 8, what is the probability that it is 11? I'm not sure if this question is asking for conditional probability or just 2/10...
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0answers
115 views

Probability of consecutive row of at least $m$ by $n\leq2m$ events. Is there a shorter route?

Inspired by this I started to generalize it. Go out from independent events $E_{1},E_{2},\cdots$ that succeed or fail. This with $p$ as probability of succes, and $p+q=1$. Event $A_{m,n}$ occurs if ...
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53 views

Generalization of classic 3 roll die game to $n$ rolls

I am trying to generalize the following well-known 3 roll die problem: "We roll a single die no more than 3 times. We can stop immediately after the first roll, immediately after the second roll, or ...
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20 views

Probability of the n-th dice matching in 2 groups of sorted random numbers

Say we have 2 groups of 6 6-sided dice. Each group of dice is rolled and then sorted so we have 2 groups of sorted numbers. What is the probability of each die in the group matching the corresponding ...
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28 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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0answers
38 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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50 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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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 ...
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28 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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56 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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110 views

Probability of Sequential events on a die roll

If a person were to roll two dice and have to get a 9 or below for success. But if you fail the first time, you have the opportunity to roll it one more time for success, what is the probability of ...
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68 views

probablity question related to 2 die and the classic monopoly game.

While playing monopoly I accidentally figured out that probability for landing on Illionis Avenue is most in the whole game and for landing on orange colored group ...
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97 views

On an average How many times must I throw $r $ die with $N$ faces, such that I see all $N$ faces?

For an $n$-sided die, the number of rolls needed, on average $n\log n$ for large n. For one die the question is here: "A Collection of Dice Problems" by Matthew M. Conroy. What about $r$ dice?