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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111 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
113 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
278 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
104 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
82 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
477 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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1answer
657 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
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 ...
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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 ...
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2answers
256 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
86 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
256 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
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 ...
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1answer
99 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
94 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
223 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
94 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 ...
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4answers
75 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 ...
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2answers
212 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 $4$ ...
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1answer
40 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 ...
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1answer
174 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 ...
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1answer
163 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 ...
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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 ...
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2answers
170 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 ...
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2answers
298 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: ...
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2answers
600 views

Rolling a fair die 4 times, what is the probability of getting an increasing sequence of numbers?

Game: I roll a die 4 times. What is the probability that I get a strictly increasing sequence of numbers. My initial thought is as follows: we condition on R1 (the first roll) being a 1, 2, or 3 ...
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1answer
56 views

Player 1 and Player 2 toss n and m fair dice respectively. What is the probability that there's no single coincidence between their results.

Coincidences within results of each player are possible. Example of "successful" event (n=m=3): {1,1,6} and {3,4,5} (no coincidences) Example of "unsuccessful" event (n=m=3): {1,2,6} and {2,4,5} (1 ...
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1answer
117 views

Expected number of different faces in multiple die roles

I roll 6 6-sided regular dice. What is the expected number of unique up-facing sides I will find among those dice?
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2answers
313 views

Rolling dice Probability that Sum

If 10 pairs of fair dice are rolled, approximate the probability that the sum of the values obtained (which ranges from 20 to 120) is between 30 and 40 inclusive. I dont know where to start with this ...
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1answer
301 views

What are fair point values for Zombie dice?

Described below is a modified version of Zombie dice ( http://www.sjgames.com/dice/zombiedice/ ) which the kids and I play. As in the original game, the idea is to sequentially roll sets of 3 ...
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1answer
356 views

Statistics question on probability

Suppose that one hundred fair dice are tossed. Estimate the probability that the sum of the faces showing exceeds 370. Include a continuity correction in your analysis.
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3answers
120 views

Probability of a dice game

Here is my question... n players playing a dice game which any of them who trows a 6 the game is over and he wins. They do it 1 by 1 .So what is the probabilty of winning for any 1 of them ? My ...
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2answers
79 views

Three equal die rolls in a row in a $3\times 3$ array

If 9 six-sided dice were rolled consecutively and displayed in a $3\times3$ format, what is the probability of a line of 3 of the same number occurring? Considering the 8 ways that are possible; 3 ...
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2answers
191 views

Probability of winning blackjack dice game?

I know a little bit about probability but I am not sure how to calculate this: In a dice game of blackjack, there are two parties. The player and the dealer. The aim of this game is to get as ...
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2answers
1k views

Solve for numbers to appear on two six-sided dice

I have a small wooden calendar that uses two six-sided dice to display day of month. One die carries numbers 0, 1, 2, 6, 7, 8 and the other carries 0, 1, 2, 3, 4, 5. The six of course doubles as the ...
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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' ...
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1answer
96 views

Dice game modelling: Lose everything on “3”, double everything on “1” or “6”

I was recently playing a quite easy dice game: You trow a fair dice: if you get a "3" the next player continues, if you get something else it is up to you to continue. If you continue and you throw ...
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1answer
53 views

Finding range, partiton and finding the dependency of a random variable

How to do this question part (a) range(X) =(2,3,4,5,....12) right the range is usually from 2 to 12 range(y) =(2,3,4,5,6) the range is usually from two to 6 right? range(z) = (0,1,2,3,4,5) ...
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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?
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1answer
165 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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2answers
149 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 ...
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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. ...
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1answer
2k views

Rolling 2 fair, 6 sided dice find P(sum=12, 2times in 36 rolls)

I have a dice problem. If we roll 2 fair dice, and the sum is 12 then our test is a pass, otherwise its a fail. What is the probability that the number of passes in 36 tests is greater then 1. ...
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2answers
74 views

Probability of a unplayable layout in a boardgame

I was at the store the other day and saw a game called Rubik's Race. The game consist of: two 5x5 sliding puzzle boards each populated with 4 tiles of each of the 6 colors of a Rubik's cube, 9 six ...
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1answer
94 views

Rolling 5, 6 sided dice where top 3 equal 15. How many rolls? How in Recursion?

Let's say that I have 5 (n), 6-sided (d) normal dice. How would I figure out how many possible rolls there are, where the top 3 (k) numbers rolled, equal 15 (t)? How would I do this using recursion ...
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2answers
135 views

Choosing between $n$ things using dice?

For which $n$ is there a finite algorithm to choose between $n$ things with the same probability using a die? For example, we can choose between 2 things, 3 things, 4 things, 6 things, and 8 things, ...
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1answer
262 views

What's the optimal strategy of this dice game?

I'm working on dynamic programming problems this week. The following is a dice game. I'm trying to find the optimal strategy using dynamic programming. The game's description : The player rolls ...
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2answers
342 views

What's the optimal strategy of this dice game?

I'm working on a dynamic programming problem. I want to find the optimal strategy and simulate it. The game's description: The player rolls two dice. If the numbers shown by the two dice are ...
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1answer
117 views

Probability of A given B & C?

I would like to sum the probability that given 3 (potentially biased) die rolls, all 3 rolls will be different-- what is the correct way to do this? So far, I have: $$ 1 - ...