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

1
vote
1answer
69 views

Propability of M-faced dice rolling a greater result than an N-faced dice ( M<N) and expected value of the absolute difference?

Hello I have a game-mechanic which goes like this: Two-sides are rolling numbers. The defender rolls between [1,Armor_Value] , attacker rolls between [1,Damage_Value]. If the attacker_roll> ...
2
votes
2answers
77 views

4 Sided dice - flawed logic?

If we had a 4 sided dice (numbers 1,2,3,4 on the faces) and rolled it 6 times and recorded the results. What would be the probability that we rolled the same number 3 or more times? (Such as rolling ...
0
votes
2answers
54 views

Chance of rolling one skull with these three dice?

Let's say I have three 6-sided dice. One is red, one is green, one is yellow. The red dice have 3 skulls on 3 of its faces, the other faces are blank. The green dice have 1 skull each. The yellow ...
0
votes
2answers
40 views

What are the chances of drawing 2 shotguns in Zombie Dice in this situation?

I'm rusty on probability and, even so, I don't think I know how to deal with this situation. Here's the problem. Let's say I have a cup of $n$ dice. Each dice face has either a shotgun, a brain, or ...
1
vote
1answer
56 views

Dice rolls probability

Given a six-faced die with six distinctly marked faces, what is the probability that a toss will turn-up any one of the six faces. If three of the six faces are red and three blue, what is the ...
1
vote
1answer
76 views

Estimating the number of sides of a die

A friend of mine inspired this question: Given a fair die, can one accurately estimate (within some margin) the size of the die given enough rolls? For example: If I roll a die 1000 times and all the ...
11
votes
3answers
647 views

Independence intuition

Toss two fair dice. There are $36$ outcomes in the sample space $\Omega$, each with probability $\frac{1}{36}$. Let: $A$ be the event '$4$ on first die'. $B$ be the event 'sum of numbers is $7$'. ...
1
vote
2answers
3k views

Why are the probability of rolling the same number twice and the probability of rolling pairs different?

Two scenarios: 1. Using one die, roll a 6 twice. $\frac16\times\frac16=\frac1{36}$ Rolling two dice roll the same number (a pair). $\frac6{36}=\frac16$ Why are these two probabilities ...
0
votes
2answers
71 views

Probability with 8 number of dice

Eight identical dice are rolled simultaneously. In how many possible outcomes each of the six numbers appears at least once? I got result as $\left(\dfrac 16\right)^8.$ And I think I missed some ...
1
vote
2answers
2k views

4 sided dice rolls - a probability question

If we had a 4 sided dice (numbers 1,2,3,4 on the faces) and rolled it 5 times and recorded the results. What would be the probability that we rolled the same number exactly 3 times? What about 3 or ...
3
votes
1answer
200 views

Sum of resulting values of dice

We have thrown with $n$ dice. The sum of resulting values is $k$. We are looking for a function $f$ which gives the number of throws, with we can construct $k$ with $n$ dice. Some example for ...
1
vote
1answer
51 views

Expected amount of different diced numbers

I roll n regular, d-sided dices. What is the expected amount of different numbers on the dices? Or equivalently: What is the expected amount of numbers that have not been diced at all? Example: ...
1
vote
2answers
201 views

Dice Game - Probability Theory

There are many dice problems on here so there could be duplicate. If there is I apologize. Here is the question. The game is given as follows: you are given 5 dice, and the goal of the game is to get ...
1
vote
1answer
49 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
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 ...
0
votes
2answers
120 views

Regarding combinatorics on dice…

The problem: If you are to roll a die five times, what is the probability the fifth die is not a repetition? Apparently the answer is $$\frac{6\cdot5^4}{6^5}$$ but I don't really see why. What ...
1
vote
0answers
234 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 ...
0
votes
2answers
2k views

Conditional probability rolling two dice

Two fair dice are rolled. What is the conditional probability that at least one lands on 6 given that the dice land on different numbers? I already know the answer, but am having some trouble ...
2
votes
1answer
49 views

Probability that less dice thrown will beat more dice thrown?

I'm trying to figure out a general equation to determine the probability that the sum of $m$ dice will be greater than the sum of $n$ dice, where $m < n$. For example, if I roll $4$ dice, what's ...
0
votes
1answer
200 views

Expected Value question regarding rolling a die multiple times

Let's say we play a game where we can roll a die up to two times. After each roll you may take the value you rolled, or roll again. What is the expected value assuming perfect play? Intuitively (not ...
1
vote
1answer
437 views

probability between two 6-sided dice and a 12-sided die

So if we have a game with player A who roll 2 dice with 6-sides and player B with one 12-sided die what is the probability to win for the player A and the probability to have a draw game. I have make ...
2
votes
2answers
57 views

Why is the probability of a dice being larger then the 2nd roll the same 2nd,3rd?

I understand that the probability of the first die roll being larger then the second is 5/12. I'm having a harder time understanding why, according to a small problem I wrote, the probability of the ...
1
vote
1answer
42 views

Finding solutions to an inequality(releating to statistics)

I am trying to solve the following problem. A person rolls 3 die, what is the probability that the sum of these die is less than or equal to 9? I have built the following inequality model ...
2
votes
1answer
79 views

Probability when two dice rolled. Why am I getting two different answers?

This is a homework problem that I've done two different ways. The question is P(Both dice show 4 or less $\bigcap$ No dice show a 1). I first separated them out to do P(Both dice show 4 or less) ...
0
votes
1answer
95 views

Probability of at least 3 sixes with 18 dice

I am trying to logically think about this, not to just apply formulas that are readily available for similar problems. Can anyone help explain the math behind finding the probability of getting at ...
1
vote
3answers
195 views

If a fair dice is rolled $5$ times, what is the probability that some number appears more than once?

A fair dice is rolled $5$ times. Find the probability that at least one of the possible outcomes $(1,2,3,4,5,6)$ appears more than once. A hint is the Birthday Problem. I keep getting $0.9074$, but ...
0
votes
2answers
40 views

Probability of 5 dices being 6s, given that I know 3 are 6s

Imagine a game with two players who each throw 5 dice and only they can see their own dice. If we roll and I see that I have 3 sixes, what are the probabilities that there are at least 5 sixes in ...
3
votes
2answers
60 views

Variance and expected values by dices, how does addition work?

I have read through some stuff and I am confused now. If we have a fair die and we just roll once, the expected value is going to be 3,5 and the variance is 2,916. Well, it is easy to count by one ...
1
vote
2answers
55 views

How to calculate the probability of a die with a wild side?

So I have a 6-sided die with 5 different values in 5 of their sides. Its sixth side can be treated as any of the other 5 values. So my question revolves around which is the probability of getting any ...
0
votes
2answers
158 views

Expected value problem on dice reroll

The question is here: Roll N* 3-sided dice(0,0,1), roll them twice and choose a better result, what is the expected value? If possible I would also like an answer for dice {0,1,2} or {1,2,3} if ...
13
votes
4answers
14k 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
votes
3answers
152 views

Chance of winning simple dice game

Tossing two fair dice, if the sum is 7 or 11, then I win; if the sum is 2, 3 or 12, then I lose; if the sum is one of rest of numbers then I toss the two dices again. What is probability of winning? ...
23
votes
4answers
629 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 ...
1
vote
3answers
76 views

Determining number of combinations on odd dice

Suppose we had four dice with four sides. Two sides have a $\frac{1}{10}$ chance of being rolled, two sides have a $\frac{4}{10}$ chance of being rolled. The dice score points equal to 1, 3, 4, and 6, ...
0
votes
1answer
148 views

Formula for X “successes” with X 10 sided die.

I am trying to create a formula for the % chance of having Y number of dice hit a number 8, 9 or 10 out of X possible. For example the chance of having 7 dice out of 10 dice be one of the 3 numbers. ...
3
votes
2answers
88 views

combinatorics dice question

There are $10$ identical dice ($1$ - $6$). How many different results can we get so that the set of results will be exactly $3$. for example: $7$ dice will be the number $2$, $2$ dice will be $3$ and ...
0
votes
2answers
47 views

An $m$ sided dice is rolled $n$ times what is the chance of getting an average of $\frac{m+1}{2}$?

If I roll a six sided dice twice there is a $1$ in $6$ chance that the results will sum up to $7$ (giving an average of $3.5$ per dice). And if I only roll it once it is not possible to get a $3.5$. ...
2
votes
1answer
82 views

Tetra Master Dice Rolls

In the game Tetra Master, two players play a card with a number n between 0 and 15, inclusive. Then, both players roll a 16-sided die numbered from 0 to 15. Both players than add up their dice rolls ...
0
votes
2answers
100 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 ...
-1
votes
2answers
52 views

Question about combinatoris of four dice

We have $4$ dice with $4$ different dyes : Green, Yellow, Red and Blue. I need to know how many options do i get so that I'll get the number $3$ at least once. These are 6 sided dice, color does ...
2
votes
1answer
110 views

Derivation of dice-sides polynomial

This question on PPCG.SE fascinated me. In particular @xnor's brilliant answer providing an elegant polynomial to provide the solution. In summary, the question asks for a program that, for an ...
0
votes
1answer
55 views

Four dice showing 3 values

I have 4 different color dice: blue, red, yellow and green. I need to check how many possibilities we get if the set of the numbers that are on the dices consists of 3 distinct numbers. In other ...
8
votes
2answers
321 views

A fair die is rolled $N > 6$ times. What is the probability the last 6 rolls were exactly $1,2,3,4,5,6$?

You rolls a fair die $N > 6$ times and you want to rolls the sequence $1,2,3,4,5,6$ in this order. What is the probability that the last 6 rolls were (in consecutive order) $1,2,3,4,5,6$, (So, on ...
2
votes
1answer
105 views

Probability Sum of One, Two, or Three out of Three Dice

I was given a problem in my stats homework that I had some trouble with. The question is as follows: If three six-sided dice are thrown, what is the probability of obtaining a four when obtaining a ...
2
votes
1answer
180 views

Expected number of moves of a random walk inside a simplex

Few days ago, Roger Blazey, retired head maths teacher, at LinkedIn group told about the following problem: “This problem was raised as part of a lecture at The Biennial AAMT (Australian ...
2
votes
2answers
265 views

Why does it seem to decrease probability to roll more times?

I am looking how to find the probability of rolling 10 sixes in 60 rolls. After reading Calculate probabilities. 40 sixes out of a 100 fair die rolls & 20 sixes out of a 100 fair die roll, it ...
4
votes
2answers
384 views

Probability of rolling a sum of N with up to infinite rolls of a die

I'm trying to figure out if there is some (relatively simple) formula for calculating the probability of rolling a sum of N with as many rolls as needed with a single regular six-sided die. For ...
3
votes
1answer
255 views

Dice 10000 probability of not scoring

There is a dice game I played recently, called "Dice 10,000", that is very similar to Farkle but a little simpler. In the version I played (house rules) a person scores on any given turn if they get ...
1
vote
3answers
198 views

Probability of rolling $111, 222, 333, 444, 555, 666$ in that order

What are the odds of rolling triples with $3d6$ like this: $111, 222, 333, 444, 555$, and $666$ perfectly in a row? I know that the odds of rolling triples in a row without any specific order is $36^3 ...
5
votes
3answers
620 views

Probability of some die face being missed N or more times in a row in M rolls? [Clarified]

2015/01/28 Clarification: Question rewritten to remove ambiguity that elicited (interesting) responses to a different problem (use edit should you wish to view). From Markus' feedback on the earlier ...