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.

learn more… | top users | synonyms

4
votes
1answer
65 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, ...
4
votes
1answer
162 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 ...
4
votes
1answer
186 views

What is the probability of rolling a 1 on the Catenative Doomsday Dice Cascader?

As seen here. Assume that each cascader bubble begins with a d6, as opposed to being determined by the prime bubble along with the number of cascader bubbles; the scene makes it ambiguous. ...
3
votes
1answer
87 views

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
votes
1answer
199 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
votes
1answer
134 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 + ... + ...
3
votes
1answer
305 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
votes
1answer
129 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 $X$ ...
3
votes
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 ...
2
votes
1answer
53 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 $p_1+p_2+p_3+...+p_d=1$. ...
2
votes
1answer
35 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
votes
1answer
74 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 ...
1
vote
1answer
32 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. ...
1
vote
1answer
48 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 ...
1
vote
1answer
24 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, ...
1
vote
1answer
32 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 ...
1
vote
1answer
41 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, ...
1
vote
1answer
38 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 ...
1
vote
1answer
49 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 ...
1
vote
1answer
63 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 ...
1
vote
1answer
45 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 ...
1
vote
1answer
153 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 $N$ ...
1
vote
1answer
61 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 ...
1
vote
1answer
201 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 ...
0
votes
1answer
37 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
37 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, ...
0
votes
1answer
32 views

We throw $2$ dice, a Red and Yellow one.

A is the event that Red rolls $1, 2,$ or $3; B$ is the event that Red rolls $2, 4, or 6;$ and C is the event that the sum of the two rolls is 5. (a) Find $p(A|B)$, $p(B|C)$, and $p(C|A)$ (b) Find ...
0
votes
1answer
31 views

What is the average number of rolling 4 six-sided die and choosing the 2 higher rolls( which will be added)?

As an example, if you roll 6,5,3,3 you will have 11 as the sum of 6 + 5. The average is obviously higher than 7 but i have no idea how to calculate it other than by brute force.
0
votes
1answer
41 views

Probability game problem

I hope you could help me with this problem... The game goes this way: There are 6 players, numbered 1 to 6. Player 1 starts the game, he rolls a die with six faces. If the result (x) of rolling ...
0
votes
1answer
75 views

Roll dice, high number wins.

Me and my brothers (3 of us) decided to roll a single dice to see who would get to have my fathers old pocket knife. The guy who rolled the highest number would win. So I rolled first and got a 6, ...
0
votes
1answer
26 views

Goodness-of-Fit tests for Multinomial and Binomial Data

A box has 4000 red, 5000 blue and 1000 orange balls. A selection of 70 balls is made, with 25 reds, 35 blues, and 10 oranges being observed. Can one essentially prove that the selection was NOT a ...
0
votes
1answer
103 views

Probability of multiple dice rolls with decreasing amounts of dice

Calculating probabilities over multiple dice rolls is easy, but what do you do if the amount of dice decreases (dependently) from roll to roll? This is a common feature of many games, including Risk, ...
0
votes
1answer
91 views

How do I calculate the adjusted percentage of dice out comes.

What I’m attempting to do is construct a spreadsheet to calculate the number of wounds and kills for a tabletop board game I play. To give everyone an idea of the situation. You have figure A shoots ...
0
votes
1answer
62 views

Probability of succesful rolls of different sided dies

This seems so simple, but I'm not sure how to calculate it. I have one six-sided die and one 12-sided die. What is the probability that, on a roll of both dice, that the six-sided die will win? ...
0
votes
1answer
119 views

The name for predicting future rolls of dice based on the past

My friends and I were playing a game where you roll dice and you bet money on what picture it's going to land on and I began reasoning with myself that if I tallied up what pictures the dice landed on ...
2
votes
0answers
101 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 $C_p$ ...
1
vote
0answers
74 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 ...
1
vote
0answers
47 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 ...
1
vote
0answers
192 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 ...
1
vote
0answers
302 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...
1
vote
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 ...
0
votes
0answers
30 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 ...
0
votes
0answers
36 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 ...
0
votes
0answers
24 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 ...
0
votes
0answers
44 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 ...
0
votes
0answers
84 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 ...
0
votes
0answers
54 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 ...
0
votes
0answers
60 views

Multiple Dice Roll Probability (With Forumla)

I'm having the trouble of determining probability over multiple die rolls. I'm working with this formula. $$\frac{d20+d(\textrm{skill}) - \textrm{difficulty}}{d20+d(\textrm{skill})}$$ Basically, you ...
0
votes
0answers
94 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?
-1
votes
0answers
55 views

50% Probability of N-Sided die rolls every number at least once.

First part: If i have 116 sides equally weighted how many rolls must be thrown to have 50% of the population get every number at least once. Sorry don't know mathjax formatting. 116 over ∑ under k=1 ...