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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Expected number of rolls on a 200 sided die to roll a 1? [duplicate]

We have a 200 sided fair die with faces numbered 1 through 200 and want to know how many rolls are expected to roll a 1. How would I go about calculating this?
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1answer
28 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
49 views

What's more likely with 7 dice - Straight, Full House, or 3-of-a-Kind

Here's a problem I'm having. I have 7 dice. I want to rank the difficulty of achieving a particular 5 dice combination after all 7 dice have been rolled. A straight is when at least 5 of the seven ...
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1answer
301 views

Probability of dice roll (board games)

Assume that we have n * 6side dice. We will roll all n dice. I ask what is a probability of getting at least r * 1(number 1 on a die), s * 2, t * 3, u * 4? Number 6 can be used instead of any of other ...
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Simulate repeated rolls of a 7-sided die with a 6-sided die

What is the most efficient way to simulate a 7-sided die with a 6-sided die? I've put some thought into it but I'm not sure I get somewhere specifically. To create a 7-sided die we can use a ...
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1answer
43 views

Dice Probabilities - How often does 3, 4, 5 show up in 5 dice on one roll?

I want to find out the probability for rolling 5 dice and the result containing at least 3, 4, and 5 without caring what the other 2 numbers are. I'm not very familiar with this kind of probability so ...
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1answer
37 views

Is this Event Mutally Exclusive?

I am trying to calculate the following, however I'm unsure on whether this event would be Mutally Exclusive or Independent. Can someone help with finding the probability of the Intersection? P(A) ...
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3answers
42 views

How to handle dice probability? ie, how much more likely would 3 six sided dice give a higher sum than 3 four sided dice?

I am playing at making my own table-top gaming system/rules and I wanted to have a better handle on how likely different dice combinations will give a higher result than one another. I know that a six ...
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4answers
120 views

Dice roll probability, at least 9 total?

If I have two dice with $6$ sides each, what is the probability of me rolling atleast $9$ total? I think I'm correct when thinking that the probability of rolling a $9$ is $\frac{4}{36}$, that is ...
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1answer
33 views

Normal distribution with dice

I'm wondering how to control the normal distribution that comes from summing dice rolls only using different numbers of dice, different combination of types of dice (d4, d6, d8, d10, d12, d20) and ...
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32 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? ...
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1answer
307 views

Two dice roll questions related to rolling a Yahtzee

I watched a video on youtube which stated the probability of rolling a yahtzee in a single roll (same value on 5 six sided dice) before 1296 rolls is 63%. The probability of rolling a yahtzee on any ...
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1answer
25 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 ...
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2answers
35 views

Expected number of rolls?

Suppose a fair six-sided die has the following sides: 1, 1, 1, 1, 4, 4. The die is rolled twice. The mixed outcomes [1,4] and [4,1] are considered "successes" while the outcomes [1,1] and [4,4] are ...
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2answers
45 views

Probability with a 7-sided dice

I have this : "We roll a 7-sided dice n times. What is the lower value of n to have 60% of chance to have 2 same value" And I don't know how I can resolve this ... I know that the result is 5 but ...
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3answers
4k views

Chance of getting six in three dice

I am having a hard time wrapping my head around this and am sure that my answers are wrong. There are three dice. A. Chance of getting exactly one six on the three dice. (1/6) * 3 = 1/3 B. Chance ...
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1answer
35 views

expected number of gold you can collect.

expected number of gold you can collect. you have a six sided dice and n points 1 to n. there some golds in any points. initially you are in position 1. if you reach any point you can collect all the ...
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1answer
665 views

Probability of rolling 3 sixes in 6 rolls

I roll a die six times. What is the probability of rolling at least 3 sixes? Please share the formula as well, so I can figure it out myself in future.
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2answers
33 views

What are the chances of drawing this unique combination of 3 coloured dice from 6 dice?

I'm having trouble understanding why one (or both) of my methods is wrong. Here is the problem. Let's say I have 6 dice: 2 yellow, 2 green, 2 red. I'm going to draw 3 dice from the 6 dice, and I ...
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2answers
103 views

Why is the sum of the rolls of two dices a Binomial Distribution? What is defined as a success in this experiment?

I know that a Binomial Distribution, with parameters n and p, is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which ...
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1answer
43 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> ...
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2answers
55 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 ...
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4answers
20k views

If I roll two fair dice, the probability that I would get at least one 6 would be…

11 out of 36? I got this by writing down the number of possible outcomes (36) and then counting how many of the pairs had a 6 in them (1,6) (2,6) (3,6) (4,6) (5,6) (6,6) (6,5) (6,4) (6,3) (6,2) (6,1). ...
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2answers
36 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 ...
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2answers
25 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 ...
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1answer
40 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 ...
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0answers
31 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 ...
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1answer
183 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
210 views

Toss a fair die until the cumulative sum is a perfect square-Expected Value

Suppose we keep tossing a fair dice until we want to stop, at which point the game ends and our score is the cumulative sum, or until the cumulative sum is a perfect square, in which case we lose and ...
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2answers
48 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 ...
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2answers
48 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 ...
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1answer
24 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
75 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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24 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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1answer
21 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
35 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
34 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
64 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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0answers
72 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
23 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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2answers
57 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
35 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
319 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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41 views
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1answer
58 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
34 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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188 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
47 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
35 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
42 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 ...