1
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1answer
34 views

Rolling 6 dice and 3 on the same side

I found similar answer for 'Rolling 6 dice and 4 on the same side'. Will exactly the same rule apply for 3 dice? Instead of 15000 (according to the above link), I found somewhere 14700. $${6 ...
1
vote
1answer
35 views

A question involving the throw of seven dice, which of my answers is correct?

Seven dice are thrown, what is the probability that all numbers show up on the dice? My first answer uses the logic that if all numbers show up and you throw seven dice, then one number is repeated ...
1
vote
1answer
59 views

Calculate single “battle” outcome odds for RISK

I am trying to reproduce the values in this odds ratio table from Wikipedia. For all those unfamiliar with RISK, this is a game where units fight against each other via the roll of the dice: The ...
1
vote
1answer
62 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 ...
1
vote
1answer
61 views

Finding the coefficient of a generating function

Given $f(x) = x^4\left(\frac{1-x^6}{1-x}\right)^4 = (x+x^2+x^3+x^4+x^5+x^6)^4$. This is the generating function $f(x)$ of $a_n$, which is the number of ways to get $n$ as the sum of the upper faces of ...
1
vote
2answers
360 views

Rolling two dice 10 times, what is the probability of getting all possible “doubles”?

Rolling two dice 10 times, what is the probability of getting all possibble "doubles": (1,1),(2,2),(3,3),(4,4),(5,5),(6,6) among our rolls? For instance, ...
1
vote
2answers
228 views

Is there a way to simulate any $n$-sided die using a fixed set of die types for all $n$?

I am assuming that we can increase the number of dice based on $n$, but they have to be $k$-sided, $k\ge3$. When I say die types, I mean that we are allowed to use non-standard dice such as ...
4
votes
4answers
505 views

Throwing dice: Probability Total is Divisible by 3

Suppose I throw a fair die $1995$ times. What is the probability that the total is divisible by 3? I tried to attack this problem inductively, storing the total in a variable $t \mod 6$, and ...
0
votes
1answer
68 views

The number of rolls of $6$ dice with exactly $4$ distinct values.

I know the answer is $${6 \choose 4}{5 \choose 3}$$ However, I don't understand why this is true?
0
votes
3answers
118 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 ...
1
vote
2answers
434 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
363 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 ...
1
vote
0answers
86 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
2answers
722 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 ...
1
vote
1answer
117 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
281 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 ...
2
votes
1answer
486 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.
0
votes
1answer
2k views

Dice question: Probability of rolling at least 2 of 3 dice with score 3 or less

my first post here. I've recently gotten back to boardgaming (Labyrinth: The War on Terror in this case) and would like to get clear on the probability of various actions. I've learnt about 'basic' ...
3
votes
5answers
6k views

Probability of rolling three dice without getting a 6

I am having trouble understanding how you get $91/216$ as the answer to this question. say a die is rolled three times what is the probability that at least one roll is 6?
2
votes
2answers
152 views

Yahtzee large straight strategy.

I've recently got into playing Yahtzee with my brother. During a game we had on my first roll for my last round I got (5 4 4 2 1). I only had my large straight left, so naturally I was hopeful with ...
1
vote
3answers
46 views

probability proof requiring conditional probability

Consider the experiment where two dice are thrown. Let $A$ be the event that the sum of the two dice is 7. For each $i\in\{1,2,3,4,5,6\}$, let $B_i$ be the event that at least one $i$ is thrown. ...
3
votes
2answers
83 views

What are the probabilities in this particular spin-off of BlackJack

A few of my friends are playing on a gaming server where this game exists. I was curious about the probabilities in it but i was unable to derive them. Any help would be MUCH appreciated. Note: For ...
4
votes
1answer
214 views

Probability of a certain dice roll sum disregarding lowest rolls

The number of ways to obtain a total of $p$ in $n$ rolls of $s$-sided dice is: $$c=\sum_{k=0}^{\lfloor(p-n)/s\rfloor}(-1)^k\binom{n}k\binom{p-sk-1}{n-1}\;.$$ What I'm interested in is making the $n$ ...
4
votes
1answer
177 views

Probability of a fair die appearing to be biased

I'm interested in the probability of a die appearing to be biased when it is, in fact, fair. I'm trying to derive a result given, without proof, on YouTube: http://youtu.be/6guXMfg88Z8?t=1m29s The ...
2
votes
2answers
179 views

Question about an 8 sided die

I have a question about an 8 sided die problem. I will put up my work what I have if someone can tell me how to proceed I will appreciate it. We roll an 8 sided die numbered 1 to 8 six times and ...
2
votes
1answer
183 views

Three dice having sides labelled 0,1,e,π,i,√2 are rolled. Find the probability of getting the product of the three results a real number.

Three fair 6-sided dice each have their sides labeled $0\,,\,1\,,\,e\,,\,\pi\,,\,i\,,\,\sqrt 2\,$. If these dice are rolled, the probability that the product of all the numbers is real can be ...
6
votes
1answer
351 views

“8 Dice arranged as a Cube” Face-Sum Problem

I found this here: Sum Problem Given eight dice. Build a $2\times 2\times2$ cube, so that the sum of the points on each side is the same. $\hskip2.7in$ Here is one of 20 736 ...
1
vote
1answer
143 views

Probability - Average value of the sum of 3 bigger dices in 4 throws (D&D)

There is a certain game based in a D&D mechanics in which the player throws 4 perfect dices and sums the three bigger values to obtain his score. Which is the average value to be obtained after ...
0
votes
1answer
102 views

Probability - Tales Game

A dice game played by two players is like this: each player throw two dice and sum theier results; that is the number of points the player scored. Whoever scores more, wins. One additional detail is ...
2
votes
1answer
761 views

Probability of predicting, then throwing, a particular multiset for 5 dice.

My friend shared with me a story that after losing to his SO at Yahtzee, before they put the game away he just randomly predicted he would roll four 5's and a 1. He then got that roll and freaked out. ...
2
votes
1answer
113 views

Throwing the dice, sum of the points

We are throwing the die (original cube for the board games). How many are ways to get the sum of the points equal to $n$ ? I've heard this problem today in the morning and still can't deal with ...
3
votes
3answers
293 views

Probability that no side of a dice is rolled more than $k$ times

Suppose, we roll a fair die $n$ times. The expected value of how many times each side of the die will appear is $\frac{n}{6}$. The question is, what is the probability that any side of the die will ...
8
votes
3answers
984 views

“Go-first” dice for $N$ players

I'm interested in sets of dice that can be used to determine who "goes first" (hence the name) in an $N$-player game; more generally, I want to determine a complete ordering of the players with a ...
8
votes
2answers
454 views

“8 Dice arranged as a Cube” Face-Sum Equals 14 Problem

I found this here: Sum Problem Given eight dice. Build a $2\times 2\times2$ cube, so that the sum of the points on each side is the same. $\hskip2.7in$ Here is one of 20 736 ...
2
votes
1answer
346 views

Simple Dice Rolling Problem

If you play poker dice by simultaneously rolling 5 dice, why is $P\text{{five alike}} =.0008$? I guess I understand the fact that each dice has the probability to land on the same number $1/6$ of the ...
5
votes
2answers
192 views

Probability of throwing the same multiset twice in a row with six dice

Six dice are thrown. The six dice are thrown a second time. What is the probability of getting the same numbers as in the first throw? If the order of the six numbers matters, the problem is easy, but ...
4
votes
2answers
2k views

Probability of either dice showing a specific number

If I throw 4 dice together, what is the probability that either one of them will show the number 3 ? I tried to calculate it and got to $\frac{(4)}{6}$ (which is highly unlikely to be correct).. any ...
6
votes
3answers
419 views

Probability of rolling a die

I roll a die until it comes up $6$ and add up the numbers of spots I see. For example, I roll $4,1,3,5,6$ and record the number $4+1+3+5+6=19$. Call this sum $S$. Find the standard deviation of ...
2
votes
2answers
211 views

Two combinatorics problems. I'm not 100% confident in my answers

These are two problems from my combinatorics assignment that I'm not quite confident in my answer. Am I thinking of these the right way? Problem 1: On rolling 16 dice. How many of the $6^{16}$ ...
6
votes
4answers
1k views

Confusion over probability problems

I am stuck with these probability problems, A pair of unbiased dice is rolled together till a sum of either $5$ or $7$ is obtained. Find the probability that $5$ comes before $7$? A letter is ...
18
votes
2answers
1k views

Expected number of rolling a pair of dice to generate all possible sums

A pair of dice is rolled repeatedly until each outcome (2 through 12) has occurred at least once. What is the expected number of rolls necessary for this to occur? Notes: This is not very deep ...
7
votes
2answers
1k views

Probability of 3 of a kind with 7 dice

Similar questions: Chance of 7 of a kind with 10 dice Probability of getting exactly $k$ of a kind in $n$ rolls of $m$-sided dice, where $k\leq n/2$. Probability was never my thing, so please bear ...
2
votes
3answers
450 views

Probability of Sum of Different Sized Dice

I am working on a project that needs to be able to calculate the probability of rolling a given value $k$ given a set of dice, not necessarily all the same size. So for instance, what is the ...
12
votes
3answers
580 views

Best Strategy for a die game

You are allowed to roll a die up to six times. Anytime you stop, you get the dollar amount of the face value of your last roll. Question: What is the best strategy? According to my calculation, for ...
4
votes
2answers
2k views

How can I (algorithmically) count the number of ways n m-sided dice can add up to a given number?

I am trying to identify the general case algorithm for counting the different ways dice can add to a given number. For instance, there are six ways to roll a seven with two 6-dice. I've spent quite ...