# 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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### Calculate card percentage return [closed]

No sorry this isn’t how things work around here
1 vote
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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 ...
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 ...
1 vote
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### 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 ...
51 views

### 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 ...
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-...
65 views

### 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 ...
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 ...
1 vote
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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 ...
1 vote
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### 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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### 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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### 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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### 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 ...
1 vote
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### 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 ...
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 $\frac2{25}$ ...
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,...
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, ...
1 vote
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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 ...
1 vote
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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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### 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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### 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 - ...
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 ...
1 vote
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### 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 - ...