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
2answers
474 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 ...
0
votes
3answers
137 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 ...
1
vote
2answers
86 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 ...
3
votes
3answers
147 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 ...
1
vote
2answers
102 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 ...
2
votes
2answers
3k 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 ...
0
votes
3answers
2k 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 ...
0
votes
3answers
408 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 ...
3
votes
1answer
126 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, ...
0
votes
2answers
76 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 ...
1
vote
0answers
87 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 ...
3
votes
1answer
111 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 ...
8
votes
2answers
147 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 ...
1
vote
2answers
546 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 ...
1
vote
1answer
124 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
2answers
81 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 ...
0
votes
3answers
5k 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 ...
1
vote
3answers
151 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?
3
votes
5answers
413 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 ...
3
votes
2answers
731 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 ...
2
votes
2answers
477 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 ...
3
votes
1answer
100 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. ...
3
votes
1answer
179 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 ...
3
votes
1answer
389 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 ...
0
votes
1answer
115 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 ...
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 ...
1
vote
1answer
124 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, ...
3
votes
3answers
284 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 ...
3
votes
2answers
110 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 ...
3
votes
1answer
84 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 ...
2
votes
1answer
499 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.
5
votes
2answers
748 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 ...
1
vote
2answers
73 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 ...
2
votes
1answer
3k 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 ...
1
vote
2answers
280 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 ...
0
votes
1answer
88 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?
14
votes
2answers
267 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) ...
1
vote
1answer
69 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 ...
1
vote
1answer
101 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 ...
4
votes
1answer
100 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: ...
3
votes
1answer
238 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 ...
1
vote
2answers
103 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 ...
0
votes
4answers
76 views

Probability of $X$ out of $N$ dice landing on $M$

The problem is as follows: We have $N$ dice and we throw them on a table. What is the probability that $M$ will fall $X$ times? Specific example: We have $10$ dice and we throw them on a table. What ...
0
votes
2answers
213 views

Probability of gaining more than $\$20$ in a two person die game

Jack and Jill gamble on a roll of a die, as follows. If the die shows $1$ or $2$ spots, Jack gives Jill $\$1$. If the die shows $5$ or $6$ spots, Jill gives Jack $\$1$. If the die shows $3$ or $4$ ...
1
vote
1answer
41 views

Determining the probability of throwing $8$ with two dice

Suppose we have two dice. Now we are imposing a condition that the two dice are independent of each other and when we throw, we must have $8$ (that means $6+2 , 5+3$ or $4+4$ etc). Therefore we are ...
3
votes
1answer
189 views

How do you calculate the probability of army loss in Risk, but with modifiers to dice?

I was wondering how you can calculate the outcome of dice rolls in the board game Risk, but with modifiers, assuming 3 attackers and 2 defenders. In Risk the attacker rolls 3 dice, and the defender ...
3
votes
1answer
181 views

30-sided die, 2-player game

Two players play a game. Player 1 goes first, and chooses a number between 1 and 30 (inclusive). Player 2 chooses second; he can't choose Player 1's number. A fair 30-sided die is rolled. The player ...
5
votes
2answers
1k views

100-sided die probability

The question is as follows: You are given a 100-sided die. After you roll once, you can choose to either get paid the dollar amount of that roll OR pay one dollar for one more roll. What is the ...
4
votes
2answers
173 views

3 Die Probability

The number of times you have to roll a set of 3 die to see a 6 on each die appears to be around ~10.555 according to a implementation of this in c++ and c#. How would this be statistically proven as ...
2
votes
2answers
313 views

The Carnival Dice game

I was reading through an elementary mathematics book lately. The author claims that every probability question, no matter how intimidating it may look, can be solved using a four-step method: ...