# 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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### Comparison of Squared Dice Loss vs. Standard Dice Loss

I've been diving into segmentation tasks and came across two variations of the Dice Loss that I'm considering for my neural network: the standard Dice Loss and the Squared Dice Loss. The Standard Dice ...
1 vote
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### Pseudo-dice probability distribution

Given the following data, is there an algorithmic way to generate a probability distribution? Data: min, max, and average results of "die". Known Trend: results will always be weighted ...
1 vote
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### Probability of same outcome for a pair of dice/urn draws with correlation $\rho$

This is surely a simple problem, but there are so many probability questions with dice, urns, etc. that I have not been able to find an answer to this specific problem. Say you have a pair of $n$-...
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### Is there a formula for finding the number of ways 3 dice throws can add to 6?

Consider 3 dice throws: t1,t2,t3 Let E be the event that t1+t2+t3 add up to 6 What is the probability of event E? I know the denominator is an example of ordered repetition. So with n=6 and k=3 there ...
1 vote
205 views

### what is the probability of this event?

given this outcome of the dice {2, 3, 4, 6, 6}. You decide to re-roll both sixes. What is the probability that you roll either a small straight (four dice are in a row) or a large straight (all five ...
113 views

### Difference between geometric distribution expectation and 1 - failure with Binomial

I'm trying to understand a simple problem: How many times you'd need to roll two dice to get two ones in a single roll. One way I see this is as a problem the geometric distribution describes. You ...
1 vote
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### Super noob requesting help testing dice balance [duplicate]

So, I have a few sets of polyhedral dice (77 individual dice) that I'd like to try to test for balance. I'm thinking a decent sample size is to roll each of them 100 times, then plot the proportional ...
47 views

### How much compensation is needed to take on risk?

We roll three, 8 sided dice. If same face appears 3 times we win 80 dollars. We have a bank of 10,000 dollars. How much are we willing to pay to play? What if we increase the prize to 80,000 dollars? ...
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1 vote
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### What is the probability that in 3 rolls of a pair of six-sided dice, exactly one total of 7 is rolled?

I tried to solve the exercise and it seems meaningful, but the problem is that in the book the result is $25/72$, while mine is $1/7776$. I don't know if maybe I didn't understand the problem, but by ...
74 views

### Halving time for a population of dice

The following question arose today on a Norwegian facebook forum for math teachers, with some unclear definitions and a lot of simulation. We have a population of $K$ (regular, 6-sided, equal-...
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### How many unique values can you expect after throwing a die with k sides?

I ended up asking here. My problem might be familiar with the coupon collector's problem and related to this post Probability of throwing n different numbers in m throws of a die but it does not solve ...
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### How far from "even" is (or is not) significant?

If a six-sided die is rolled 600 times, an even distribution would be 100 rolls for each number. If I actually rolled 600 times and tallied the results... How far away from 100 would a count need to ...
1 vote
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### Generalization of a boy or girl paradox with die!

Here is the link to the boy or girl paradox Wikipedia page. The question I have is: Let's say you have two fair 6-sided dice and you roll them simultaneously. If at least one is 6, what's the ...
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### How many rolls required for 90% chance to reach expected values of consecutive dice rolls in tabletop game?

I'm trying to work out if random variance in dice rolls is more likely to influence a given situation in a game rather than the overall expected values of those dice rolls being significant. The game ...
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### Variance of one die with binary result

I have a task that is worded: "You have a deciding die-throw ahead of you in a game (using a fair 6-sided die) and you realize that you will win if you get a 4 and lose in every other case. You ...
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### A fair die is rolled 1,000 times. What is the probability of rolling the same number 5 times in a row?

A fair die is rolled 1,000 times. What is the probability of rolling the same number 5 times in a row? How do you solve this type of question for variable number of throws and number of repeats?
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### 10-faces dice "emulation" from N 6-faces dices [duplicate]

I want to play a game which uses one 10-faces dice, but I only have 6-faces "classic" dices at my disposal. Is it possible to approximately recover, to an arbitrary precision, a 10-faces ...
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### Probability that number of heads exceeds sum of die rolls

Let $X$ denote the sum of dots we see in $100$ die rolls, and let $Y$ denote the number of heads in $600$ coin flips. How can I compute $P(X > Y)?$ Intuitively, I don't think there's a nice way to ... 