Questions tagged [dice]

For questions on dice, small throwable objects 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 NOT getting the same number when rolling 6 dice.

Problem Suppose we roll 6 dice. We want them to not be all the same number, we don't care what number or how many dice are different. What is the probability of this event? Solution We are simply ...
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-4 votes
1 answer
72 views

Calculate card percentage return [closed]

No sorry this isn’t how things work around here
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1 vote
1 answer
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Approximate chances of rolling primes on unknown-sided dice

There is a function for approximating the number of primes below a certain integer What would be the function for determining the chances of rolling a prime number when rolling n number of d-sided ...
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Alternative general formula for the probability of rolling two dice and getting one number on at least one of them.

Let's say I want to know what's the probability of rolling two 6-sided dice and getting a 6 in at least one of them. The probability of not getting a 6 in one die is 3/6. I know I can use the ...
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5 votes
2 answers
84 views

The probability of throwing $n$ dice with each result being contained in a set

I recently asked this question on MSE: The probability of throwing two dice with each result being contained in a set and although I am happy with the answer, I cannot figure out how this generalizes ...
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1 vote
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Probability that the numbers of a die appear with the same frequency

Let's assume we throw a die $n$-times. What is the probability that all numbers appear with the same frequency if $n\to\infty$? My approach: Let be $P(A_n)$ the probability that each number appears $...
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Probability of rolling at least one 5 before the first 6

The question has two parts and is: Suppose you repeatedly roll a fair six-sided die with numbered faces 1 to 6. Determine the following The probablity the $n^\text{th}$ roll produces the first 6 You ...
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1 answer
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dice probability with multiplikator mechanism [closed]

I am thinking about a game that includes (or should include) the following dice mechanic. You have a normal dice and before you begin your turn you can decide if you want to throw the dice 3 times and ...
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probability of rolling repeated numbers

if you roll an x-sided die, n-number of times, what are the chances of getting r-number of repeated values? if I roll a twenty-sided die, eighty times, what are the chances that I'll roll a six twice ...
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Expected payoff rolling 3 dice once, and winning the value of the highest rolled number [duplicate]

Hi I have a question I was wondering Roll 3 dice. Win the value of the highest number rolled, in dollars. What is the expected value of 1 roll of the three dice? I was thinking about adding all cases ...
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Probability of failure in a multinomial experiment

Generalised version of Probability of failing to decode a biased die Say we are given a biased die having a total of $N$ sides that shows up $M$ of its sides with a probability of $p$ and the rest of ...
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probability of rolling a consecutive 1, 2, 3, 4, 5, 6 on a die

Questions I was wondering what the probability of rolling a consecutive $1 ,2, 3, 4, 5, 6$ on a dice is? For realism, is there any way to calculate an 'extra' factor, such as someone kicking the table ...
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Identify the number of Repetitions to decode a biased die

Related to Probability of failing to decode a biased die Say we are given a biased die that shows up M of its sides with a probability of $p = 0.8$ and the rest of the sides (6 - M) with a probability ...
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73 views

Probability of failing to decode a biased die

Say we are given a biased die that shows up two of its sides (maybe $1$ and $2$) with a probability of $0.8$ and the rest of the sides (maybe $3,4,5,$ and $6$) with a probability of $0.2$.In order to ...
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4 votes
2 answers
284 views

How do I design the most unfair dice for this game?

I was thinking about a simple dice game where the goal is to roll all the face values of a six-sided die consecutively in order (1,2,3,4,5,6). If I'm not mistaken, the probability of doing this with a ...
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How many times must a pair of 6-sided dice be rolled until all sides appear at least once

This is problem 11 in "A Collection of Dice Problems" by Matthew Conroy. Let state i be the state that i different sides have appeared, then 6 is the state that all sides have appeared, make ...
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Expected return of dice game

Assume our bet is always X. To win the bet, I roll two dice and aim to make the total greater than my opponent's. The rules apply to both players Rule 1. Win twice as much if toss a double. Rule 2. If ...
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Origin of the problem of waiting until each of several dice have shown a six at least once

I am looking for the origin of the following problem. Let there be three independent fair dice. What is the expectation of the number of tosses until each die has shown six at least once? One can ...
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1 vote
1 answer
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We have three players A, B and C. They roll an honest die, first A, then B, and lastly C until someone is the first to get an even number...

We have three players A, B and C. They roll an honest die, first A, then B, and lastly C until someone is the first to get an even number. This player will be the winner of the game. If after all 3 ...
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1 answer
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Probability that the histogram for the sum of two dice has an expected shape

Suppose that two 6-sided dice are thrown $n$ times and that the sum after each throw is plotted on a histogram. Let $s_i$ be the frequency of the sum $i \in \{2, 3, \dots, 12 \}$. As $n \rightarrow \...
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Expectation of fair die game when all but one branch cut off

Any roll of a 1, 2, or 3 results in the player winning the amount of the die roll, in dollars, and the termination of the game. Any roll of a 4 results in the player winning $2 and continuation of ...
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Is there a name for right a prism with convex bases?

Is there a name for a prism where the bases are convex, as in, they curve or jut outward? Context and application: These shapes can be used to create fair dice of "wacky" sides like a d3 (...
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2 votes
1 answer
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What are the chances of rolling 2 dice 43 times without rolling a 7?

Forgive my very long explanation. I play craps and I attempt to make my throws less random. I track my throws and collect data from sets of 900 throws. Obviously, a random thrower is likely to throw ...
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2 votes
3 answers
115 views

A gambler with 3 alike dice.

Here's the problem:- We are given 3 alike dice and (this problem had multiple parts when I tried it, Here I am taking only one scenario) it is said that we will win the game if the sum of numbers ...
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3 votes
1 answer
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We roll a die 12 times. a) What is the probability that we get exactly 3 times the result greater than or equal to 4? .....

We roll a die 12 times. a) What is the probability that we get exactly 3 times the result greater than or equal to 4? b) What is the probability of getting at most 3 times the result greater than or ...
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2 answers
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Algebraic solution for combinatorics

Let $P(x)$ be the probability that the sum of the faces of 5 fair and independent dice is x We are all aware that we can find $P(x)$ manually. However, is there an algebraic proof for $P(5) < P(6) &...
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1 answer
105 views

50 player roll-off with favored players

I'm trying to pick $x$ options out of a large number $N$, options by assigning each option a random integer weight in $[1,A]$, and then choosing the options with the $x$ highest values. Some of the ...
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roll some dice, each with different number of sides, what are the odds of that roll to happen?

Suppose you have dice each with 4, 6, 8, and again 8 sides, and you roll them. What are the odds of the result being 2 4 5 7? The number 7 must come from an 8-sided ...
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1 answer
37 views

Probability of more "hits" comparing the result of two uneven dice pools

I'm designing a board game and trying to evaluate roll probabilities, but I'm in over my head. What I'm looking to determine is: I roll two different sized pools of six-sided dice, sort them high-to-...
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1 answer
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Number of rolls of a single die until both a 6 and an odd number appear

I have a probability question. The problem goes: John (J) and Max (M) are rolling a die (one die together). John wants to see an odd number on the die and Max wants to see a 6. X ... number of rolls ...
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9 votes
3 answers
1k views

Probability of winning a game by rolling the die first

Two persons are playing a game where they take turns rolling a die (so A rolls first, then B, then A again and so on). The first person to roll a $6$ wins the game. What is the probability that the ...
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1 vote
1 answer
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Calculating probability of values for multiple dice rolls where sum is equal or greater than 4

Assuming we have 6 sided dice and play game of rolling dice each turn until we get sum value of at least 4. For example we know that game will always finish with value less or equal than 9 because on ...
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1 vote
1 answer
117 views

Probability that one set of dice rolls is greater than or equal to a given set

Context In tabletop roleplaying games (TTRPGs), the characters in the game usually have numeric scores tied to certain statistics. In general, these scores can be determined according to a bounded-...
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2 votes
1 answer
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Optimal strategy for dice roll game

I came across an interesting dice roll game that involved expected values and wanted to know if my approach and answer were correct, and if there are other ways to solve this. Problem statement: You'...
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0 votes
0 answers
26 views

Two dice thrown, one of them is a 4. Then.. [duplicate]

Suppose you have two fair dice. You throw the dice in a box. You ask a friend to look in the box. Your friend then tells you that one of the dice is a 4. Given this information, what is the ...
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2 votes
1 answer
102 views

Probability question about tetrahedral dice

Question: “Jeffrey has a set of tetrahedral dice. Each has a distinct arrangement of exactly six dots painted on the four faces, and no two dice can be rotated to appear the same. Faces can have any ...
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1 vote
2 answers
71 views

What is the idea of ‘probability p’?

Hello mathstackexchange I’m working my way through a book on mathematics and have come to a section on probability. I’ve not done probability before and whilst the resource has been excellent, in the ...
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9 votes
2 answers
142 views

A wavy histogram from a maximum likelihood algorithm

This question is based on a Puzzling Stack question I answered. Suppose you have a loaded $10$-sided die that gives one value with probability $\frac7{25}$ and the rest with probability $\frac2{25}$ ...
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3 votes
2 answers
81 views

Rolling dice game - who first will roll number 3

Let's consider very easy game with players A and B - they roll a dice starting with player A. If any of players roll a three, then he wins. I want to calculate probability that player B wins. ...
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Yet another dice game

I'm doing a little self study in probability theory and read about the coupon collector's problem, which lead me to think about the following dice game: Suppose you have seven regular fair 6-sided ...
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Probability of Choosing Higher Number From 2 sets of N Numbers?

Given two sets of N numbers with equal length, how would I calculate the probability of picking a higher number from the first set than the second set? For example, given the sets {4, 5, 6, 7} and {2,...
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2 votes
2 answers
132 views

A fair six-sided die is rolled 6 times. What is the probability of 5 and 6 appearing at least once?

My approach was to calculate the probability of not throwing a 5 or a 6, and to time that by the number of throws. 4/6^6 = 0.09 and thus the opposing probability would be 91%. That, unfortunately, ...
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1 vote
0 answers
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Computing house edge of Lunar New Year dice game

Here is an apt description of the game: https://medium.com/@Rob_TactVP/how-to-play-hoo-hey-how-812532d405a1 I’ll repeat the rules of the game here. Traditionally, Hoo Hey How uses the following pay ...
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1 vote
1 answer
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Optimal strategy for dice game

Slightly modified repost of an older question that I don't think was answered fully. The Game: You are competing in a game with 2 other players with a 21-faced dice (faces labelled 1-21). All three of ...
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0 votes
2 answers
82 views

Probability Question (fair dice)

Roll a fair (six-sided) die, and let $N$ be the result. Now toss $2N$ fair coins and let $M$ be the number of heads. i) Find $\mathbb{E}[M]$. ii)Find $\mathbb{P}(M = 7)$. I have given a shot at this ...
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-1 votes
1 answer
31 views

Average probablity to get a specific outcome on a ten sided dice

A man is playing a game with a ten-sided die, he will roll it every minute and will win if it gives the number $10$. On average, how many minutes would it take him to win the game? My working - ...
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0 votes
1 answer
139 views

Roll 4 dice. What is the probability that any 2 of them will have a sum of 7? [duplicate]

Given a set of 4 dice, what is the probability on a given roll that any 2 of them will have a sum of 7? (Assume that the two dice are selected in favor of getting a $7$, such that if it's possible to ...
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1 vote
1 answer
67 views

Binomial probability doesn't give the correct number?

If you roll five dice your chances of getting all five matching is $\frac{1}{6^5} = \frac{1}{7776} \approx 0.08\%$. I recently learned the binomial probability formula: $P = nCr \times p^r \times (1 - ...
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4 votes
2 answers
177 views

What is the probability of throwing all the even numbers with a dice, before you throw any odd number? [closed]

I came across this question via a friend, and I am still thinking about it. So we need to throw all even numbers before we throw any odd number. The first throw can be even or odd, that is simple. ...
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4 votes
2 answers
169 views

If you throw a dice 5 times, what is the expected value of the square of the median?

My question: If you throw a dice 5 times, what is the expected value of the square of the median of the 5 results? A slightly modified question would be: If you throw a dice 5 times, what is the ...
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