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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2answers
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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 ...
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1answer
23 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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2answers
32 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 ...
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0answers
21 views

Probability and order

5 standard dice are rolled one at a time. What is the probability that the first two show ones and the next three do not? How do I distinguish the first two from the rest?
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0answers
41 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 ...
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1answer
12 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: ...
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1answer
23 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 ...
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1answer
24 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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2answers
55 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 ...
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2answers
41 views

Probability I am first person to roll a six [closed]

If I take turns rolling a die with a friend and I roll first, what is the probability I roll a 6 first?
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0answers
46 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
15 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 ...
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0answers
25 views

Probability of rolling one die by two persons 3 times each [closed]

So suppose you have one die. Person A rolls one die 3 times. Person B does the same after A is finished. What is the probability that person A's smallest number (of his/hers 3 rolls) is greater than ...
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2answers
31 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 ...
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1answer
24 views

How to win at a dice game using Central Limit Theory and Binomial Probability? [closed]

I'm not too savvy in the way of statistics, so please keep this in mind with the answer. There is a dice game where a person will bet money on rolling equal to or above this number. The die rolls to ...
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1answer
34 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 ...
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2answers
153 views

How Many Permutations of Die Rolls Add Up to a Fixed Total?

I'm toying around with the idea of designing a board game. I like the idea of a hexagon-tile setup (a la Catan). There would be some number of different resource categories; I'm trying to determine ...
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1answer
38 views
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1answer
40 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 ...
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1answer
23 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 ...
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2answers
181 views

Continuous Dice rolls

A dice is being rolled continuously. Suppose you roll a 3 ( or any number ). What is the probability that you will get the next "3" exactly after n rolls?
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1answer
45 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) ...
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1answer
27 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 ...
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0answers
39 views

If you roll a dice twice, and substract result of

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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2answers
42 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 ...
66
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10answers
19k views

Given a die, what is the probability that the second roll of a die will be less than the first roll?

If you are given a die and asked to roll it twice. What is the probability that the value of the second roll will be less than the value of the first roll?
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3answers
81 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 ...
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1answer
34 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 ...
4
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1answer
70 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 ...
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2answers
31 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
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2answers
25 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 ...
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1answer
345 views

Probability in Rolling dice 6 times

If I have one die and I'm rolling the dice $6$ times. What is the probability that in the all $6$ times the result will be the same? I know that the probability for each number in $6$ sides dice is ...
2
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2answers
6k views

Probability of rolling the same number twice

Math novice here. With a 10-sided die, the probably of rolling '1' is 10%. I'm tempted to think the probability of rolling '1' with two consecutive rolls is 20%. Would I be correct? Not sure if I ...
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3answers
585 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 ...
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2answers
26 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 ...
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2answers
66 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 ...
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3answers
42 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? ...
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3answers
2k 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 the ...
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3answers
38 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, ...
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1answer
41 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. ...
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2answers
57 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 ...
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2answers
31 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 $3.5$. ...
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1answer
44 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 ...
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2answers
69 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 ...
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2answers
42 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 ...
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1answer
137 views

Probability of a result from 3d6, lowest to highest

I have a fascination with tabletop sports games, and through that, I've developed an interest in probability. That said, it's not my strong suit, so I wanted to pose this question because I think ...
2
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1answer
65 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 ...
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1answer
45 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 ...
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2answers
179 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 ...