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 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
5k 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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434 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
112 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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350 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
75 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
137 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
147 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
357 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
154 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
86 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
226 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
57 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
252 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
331 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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2k 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
186 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
497 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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1k 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
64 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
198 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
773 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
491 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
604 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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131 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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95 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
291 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
2k 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
102 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
54 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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10k 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
314 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
349 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
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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
3k 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
84 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
119 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
149 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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437 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
476 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
122 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 - ...
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2answers
3k views

Probability of dice double - why not count duplicates?

What is the probability of getting double dice? (one throw) All possible dice rolls are 36 (counting even rolls like 1-4 and 4-1). But when counting the doubles, why not count 1-1 twice, for ...
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2answers
3k views

Probability, Expected Value and Variance of a Dice Roll

Roll 5 fair six sided dice. Let X be the number of sixes. 1) Find $\ P(X=2)$ 2) Find $\ P(X <= 1)$ 3) Find $\ E[X]$ 4) Find $\ Var(X)$ I've been able to find the first two answers on ...
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1answer
130 views

Find E[N]. (Absorbing States MC)

Assume we toss a dice until odd number appears four consecutive times, and in such a case we stop the game. Let $N$ be the total number of times we will toss the dice. Find $E[N]$. Lets say for ...
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1answer
351 views

Probability problem of dice game

I heard a problem from a riddle book: $A$ and $B$ roll two standard dice and record the sum of two numbers. $A$ wins when two consecutive outcomes are $7$ and $B$ wins when three consecutive outcomes ...
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1answer
227 views

probability of rolling at least $n$ on $k$ 6-sided dice

Is there a simple form for the probability of rolling at least $n$ on $k$ 6-sided dice? Of course you can do it by recursion (see here). But is there a way to do it with just a few binomial ...
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2answers
418 views

Multiple dice rolls (D&D Skill challenge)

In Dungeons and Dragons there is something called a skill challenge, which involves rolling some dice (no surprise there). An example of a skill challenge: Skill challenge DC 25 thievery. Roll a d20* ...
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2answers
86 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 ...
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2answers
6k views

Probability of rolling the same number twice

Math novice here. With a 10-sided die, the probably of rolling '1' is 10%. I'm tempted to think the probability of rolling '1' with two consecutive rolls is 20%. Would I be correct? Not sure if I ...