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 of a dice game with an emphasis on the number $4$

If I were to roll a set of $4\,$ four-sided dice $4\,$ times, what is the probability that on each of the $4\,$ dice rolls, the sum of the dice will be divisible by $4\,$?
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1answer
32 views

3 dices probability that number 5 comes up on exactly two of the three dice?

I roll three different loaded dice. For the first die the probability of getting a 5 is 0.7, for the second die the probability of getting a 5 is 0.48, and for the third die the probability of getting ...
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3answers
706 views

Throw 10 dice, probability of getting 6 identical numbers?

I got this result when I threw a set of 10 dice (btw. for the first with this set): What is a probability of getting 6 identical numbers (any) with 10 dice, with no particular order?
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1answer
129 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 ...
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4answers
205 views

Expected number of tosses before you see a repeat.

Suppose we roll a fair die until some face has appeared twice. For instance, we might have a run of rolls 12545 or 636. How many rolls on average would we make? What if we roll until a face has ...
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2answers
118 views

Probability of getting Required Sum

What is the probability of when four dice rolled together once,and getting a sum of Thirteen If we do by just calculating all possible values of sum, then it will take more time; so we can solve ...
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2answers
74 views

Probability theory - Dice

Two guys are playing dice with each wagering $50. Player 1 chooses 2 as his lucky number, and Player 2 chooses 6. Every time their lucky number appears as a result, the player gets one point. The ...
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3answers
131 views

Expected number of sixes tossed before success

Given a fair dice, what is the expected number of sixes that get tossed before throwing 2 sixes in a row? Would I start by finding all possible sets that occur without two sixes in a row and multiply ...
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2answers
667 views

Combinatorial probability of multiple dice rolls

I am trying to come up with a probability for a combinatorial problem that I'm working on and I'm stuck. I've managed to distil it down to a toy dice-roll problem: What is the probability of any two ...
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3answers
161 views

Probability of rolling unique sides on a bias die

If you have a six-sided die labeled 1-5 with two sides labeled 5, what's the probability of rolling the die five times and getting a unique side that you haven't previously rolled? I've been mulling ...
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2answers
97 views

Rolling a die, expected number of coins won

So this is a problem I'm stuck on, You roll a fair 4-sided die and with probability 1/3 you get to roll once more, and with probability 2/3 you have to stop. Assume that you get as many coins as the ...
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3answers
182 views

Trying to work out the probabilities of a dice game I used to play

At college, my friends and I would sometimes waste time playing a game with dice. We would roll 25 dice, pick out all the dice that landed on a 6, then roll the rest. This would carry on until all the ...
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2answers
117 views

Likelihood of sum of dice roll is exactly 1 million

A board game is set up such that there is a number line with squares numbered 0..1 million. You roll a standard 6 sided die and move forward the number of spaces that you roll. Eventually you will ...
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2answers
4k views

Probability of rolling 6's on 3 dice - adjusted gambling odds?

I'm struggling to work out odds on a game that were working on. It's probably best if I write an example as I'm really not a mathematician! I'm working on a dice game where the player bets 1 coin and ...
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3answers
3k 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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3answers
699 views

Rolling 6 dice and 4 on the same side

Guys I made myself a question to answer and its this. What is the probability of having 4 dice land on the same side if I toss 6 dice. I got this answer, I don't know if its correct. I dont want to ...
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1answer
133 views

Why Is It Rational to Bet on the Most Probable Event?!

Suppose that someone is going to bet in a game. A dice is rolled, and there are only these two options for betting: Option 1. Give 1 dollar and bet on 6. Option 2. Give 1 dollar and bet on 1, 2, 3, ...
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2answers
79 views

Dice sum probability

Simulate two separate dice (use random numbers with the appropriate range) being rolled 10 times. What are the percentage of rolls that resulted in a sum of 7, a sum of 2 and a sum of 11. I came ...
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0answers
94 views

probability of consecutive row of at least m by n<=2m 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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1answer
127 views

Interesting pattern that I found while finding dice that always roll a prime number

The original puzzle I was trying to solve is to find unique numbers to write on the faces of two dice such that the numbers you see on each dice after rolling sum to a prime. I realized that for this ...
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3answers
221 views

The rotation of dice on a grid

Imagine you have a plane, flat surface with a square grid drawn on it. You have a standard cubic die which is placed flat on the surface. Its length is the same as the length of side of each grid ...
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2answers
785 views

Increasing sequence of dice rolls, explanation of “6 choose 2”

With a 6 sided die, what is the probability of 3 rolls being increasing? I understand from reading other questions that the answer is $\frac{\binom{6}{2}}{6^3}$. The $6^3$ on the denominator makes ...
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1answer
144 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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2answers
82 views

Probability of dice thrown

What is the probability of getting -atleast 1 six when 6 dice are rolled? - atleast 2 six when 12 dice are rolled? - atleast 3 six when 18 dice are rolled? "At least 1 six" is ...
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3answers
8k views

How do i calculate Dice probability

Im trying to learn how to calculate dice probability but all i can finf on the net are the odds of rolling a given number in a single roll. An example of what i am looking of is rolling a 4+ on a D6 ...
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3answers
168 views

Dice probability puzzle

What is the probability of a run of at least 3 sixes when a die is thrown 5 times? I think I have the answer but from what I have been told its not the correct answer. Would someone like to help?
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5answers
447 views

Probability of 1x six from seven dice?

Could someone help me with how the following is calculated: What is the probability of rolling a die seven times and getting at least one six? My instinct told me it would be $1/6+\cdots + 1/6$ but ...
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2answers
789 views

Probability of rolling at least one 6 while rerolling 1's

Scenario: You roll a number of 6-sided dice Success: Roll at least one 6 Conditions: You can re-roll any 1's you get on the first roll What are the odds of success for n dice? Example: 7 dice ...
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3answers
826 views

Dice probability over multiple rolls.

What is the probability of rolling one or more 6's using 3 six sided dice (1...6) that are rolled three times? How does multiple rolls influence the probability, is it simply 3 times the probability ...
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1answer
105 views

How much money should we take?

I'm a new user so if my question is inappropriate, please comment (or edit maybe). We want to define a dice game. We will be the casino and a customer will roll dice. I will assume customer is man. ...
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1answer
190 views

Expected value of getting to plus or minus twenty.

We start with our game in the box number $0$. We throw a die with: "$+1$", "$+2$", "$+3$", "$-1$", "$-2$" and "$-3$" written on its faces. After each throw we move to the right of the number of boxes ...
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1answer
553 views

Calculate probability of obtaining at least a sequence of numbers for a given number of dice rolls

I want to calculate the probability of rolling at least a sequence of values for a given set of dice. This sequence may have duplicate values. I am aware of the Binomial Probability Equation used to ...
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1answer
140 views

Exclusion and Inclusion principle in rolling a dice

A die is rolled $n$ times. The probability for getting "6" is $p$. Use exclusion inclusion principle and find what is the probability getting at least one time "6". First I expect the result to ...
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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
154 views

Yahtzee Bar Game

A bar near where I work has a game where you pay $5$ dollars which gets you two chances of rolling $5$ dice and if roll results in all of the dice having the same number you win the running pot, ...
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3answers
308 views

You roll a die until the sum of all your rolls is greater than 13. What number are you most likely to land on, on the last roll?

So I was thinking of doing this recursively: $f(x,i)$ is equal to the probability of rolling greater than $x$ and landing on $i$ on the last roll. $f(0,i) = 1/6$ for $i = \{1,2,..,6\}$. $f(1,i) = 1/6 ...
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2answers
120 views

Roll dice and ignore worst results

I am at my wits' end with my very basic statistics knowledge. I roll $n$ dice with $k$ sides each (numbered $1$ thru $k$, laplace). I then add the numbers of the $m$ best dice (the higher the roll ...
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1answer
88 views

An asymmetric die game

Suppose there is a prisoner who is being held by a gambling-addicted warden. The warden offers a compromise to the prisoner - if the prisoner can win a certain game of chance, the warden will let them ...
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1answer
627 views

What are the odds of rolling 3 pairs with six dice?

Given a roll of six standard six-side dice, how do you calculate the odds of rolling 3 pairs? This should included non-unique pairs like 2,2,2,2,3,3 or even 5,5,5,5,5,5.
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1k views

Probability of consecutive dice rolls

This is probably quite a simple question but here I go.. Suppose you are going to roll a six-sided (fair) die N times, what is the probability that you will get at least one set of three consecutive ...
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2answers
79 views

Probability of rolling a $6$ between $90$ and $110$ times when rolling a die $600$ times

Show that if you roll a fair die $600$ times, then with probability at least $1/6$ you will get the roll $6$ between $90$ and $110$ times. This is what I have so far Let $E(x) = 100 \Rightarrow ...
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1answer
4k views

Probability Distribution of Rolling Multiple Dice

What is the function for the probability distrabution of rolling multiple (3+) dice. The function is a bell curve but I can't find the actual function for the situation. Example, what is the function ...
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2answers
365 views

Probability question involving colored dice

This question is really getting to me, a friend of mine has suggested a solution but I believe it is incorrect. Anyway here's the question: You throw 9 coloured dice. Every dice has 2 white ...
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1answer
98 views

Probability of rolling three dice without getting a 6 in 8 rolls

I know the propability of rolling three dice without getting a $6$ in $1$ roll is $91/216$, but what about rolling it in $8$ rolls consecutively with three dices?
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2answers
325 views

Generalized nontransitive dice

Let $X_1, \ldots, X_n$ be a collection of random variables. Consider the directed graph with vertex set $\{ 1, 2, \ldots, n \}$ where there is a directed edge $i \to j$ if $\mathbb{P}(X_i > X_j) ...
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1answer
73 views

Dice probability when a number is disallowed in the first round

In the game Settlers of Catan a player starts each turn rolling 2 six sided dice. There's a variation of the game where if a 7 is rolled in the first round of a game (a 'round' is when each player has ...
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1answer
116 views

Dice tracker and roll probability percentage

I have a dice tracker that graphs the combined roll of 2 fair six sided dice (numbers 2 through 12). I want to display the variance percentage that the current number is over/under as a ...
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1answer
125 views

Deduce dice configuration knowing 2 adjacent faces

Let's say I have a die. I know it's up face and right face. I'd like to know what's on other faces, in this configuration. I know the dice configuration: ...
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1answer
301 views

Probability of rolling $n$ successes on an open-ended/exploding dice roll

I'm trying to compute the probability of achieving a certain number of successes when rolling a die pool for both open-ended/exploding and closed tests. Success is defined as a roll above a certain ...
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2answers
132 views

Coinflip statistics

There is a betting strategy for coinflips, called Martingale, in which the player should pick heads or tails and keep betting on it (doubling their bet on every loss) to eventually make a win when it ...