# Questions tagged [dice]

Dice (singular: die) are typically small cubical objects marked with spots, numbers (1-6 usually) or symbols to generate random outcomes, particularly in games. Other polyhedral dice are also used in games.

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### Cracking a safe: matching $n$ unique numbers with $d$ dice. What is the expected number of rolls?

This problem is inspired by the board game Burgle Bros. In the game there are safes to crack. You have to match $n$ unique numbers with $d$ dice, where $n = 1,...,6$ and $d=1,2,...$. For example, ...
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### Which game is more advantageous?

I got a pretty simple problem but I'm not sure about my solution. Game $A$: We roll a fair die 4 times. If we get the "6" at least one time, we win. Game $B$: We roll a fair die 8 times. If we get ...
90 views

### What is the probability of getting three pairs that makes up seven when six dice are rolled?

Stumbled upon this question in a game of dice where a point is dealt for each pair that makes seven. In the game there were a total of six dice that were to be thrown up to three times. Each time a ...
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### Using R to calculate probability of rolling 2 numbers in 20 throws [closed]

We have an 8-sided die. Throwing it 20 times, what is the probability of rolling a number larger than 6 at least 12 times and at most 16 times? If you know of an efficient program to write so that I ...
201 views

### Does Sørensen–Dice Coefficient (Dice Score) only account for true positives?

I'm working in a project on medical image segmentation which uses the Dice Score as part of the loss function, but I got some doubts with the commonly adopted implementation. The definition of Dice ...
328 views

### Draw integers independently & uniformly at random from 1 to $N$ using fair d6?

I wish to draw integers from 1 to some specific $N$ by rolling some number of fair six-sided dice (d6). A good answer will explain why its method produces uniform and independent integers. As an ...
36 views

### Rolling a fair dice [closed]

If I roll a dice three times, how do you calculate the probability that at least 2 dice are less than four?
98 views

### comparing probability of two polyhedron dice

I'm trying to figure out the probabilities associated with rolling two different types of dice and one coming out higher than the other. Example: Rolling a 4 sided die vs a 6 sided die, what's the ...
211 views

### Bayesian posterior pmf for weighted dice with uniform prior

We want to find posterior probability mass function for dice tossing with uniform prior. We are interested in rolling of weighted dice. The outcome is 1,2,...,6. We assume that prior probability ...
73 views

### Two dice roll with {1,2,3,4,5,6} and {10,20,30,40,50,60} and importance of RV mapping

We're all too familiar with a two-dice-roll experiment where we start with a uniform sample space of $S_{die}=\{1,2,3,4,5,6\}$ and end up in a non-uniform pmf for the sum of the numbers on the two ...
2k views

### If I roll a die 25 times what is the probability that the mean outcome is greater than 4?

Consider a problem: You take a fair die to a party and announce that you will roll it 25 times. You will record each outcome and at the end average the 25 outcomes together to get their ...
42 views

### Probability of 3 dice with rethrown [closed]

In a game, three ordinary dice are thrown. If the first throw results in just two dice showing the same number, the die with different number if thrown again. If all numbers are different in the first ...
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### How many times must I roll a die to confidently assess its fairness?

(Apologies in advance for use of lay language rather than statistical language.) If I want to measure the odds of rolling each side of a specific physical six-sided die to within about +/- 2% with a ...
166 views

### Generating Function for sum of N dice [or other multinomial distribution] where lowest N values are “dropped” or removed

Background I found this interesting question Formula for dropping dice (non-brute force) and excellent answer https://stats.stackexchange.com/a/242857/221422, but couldn't figure out how to ...
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### Distribution of a dice pool [duplicate]

The article Three Basic Distributions from AnyDice shows the distributions (and cumulative distributions) of 1d10, 2d10 and 3d10. Looking at the graphs, it seems there is a pattern here: 1d10: the ...
135 views

### R dice support problem [closed]

Could someone please help me with the code for the following problem (I am brand new to R so it is being a bit complicated for me): Consider the variable X, the sum of three, fair, 8-sided dice ...