# 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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### 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 ...
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### 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 ...
38 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 ...
60 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 dice 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 dice but it does not ...
46 views

### 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 ...
246 views

### 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 ...
52 views

### 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 ... 126 views

### What is the probability of getting exactly doubles when rolling N number of dice

For example if i roll 2 dice the probability of getting exactly doubles is 6/36. similarly if i roll 3 dice the probability of getting exactly doubles not considering triples is 90/216. How can i ...
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### Interpreting frequency statistics to find fair dice

I was just in a lecture where my (bayesian evangelist) professor claimed that for questions like 'Is this a fair die?', frequency statistics gives an answer of {0, 1}, meaning that the probability is ...
1 vote
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### Probability of getting a 6 on at least one die from a pair of dependent dice

I am stuck on this particular question: Suppose you have two dice. These dice however are not independent: the probability that both dice will roll a 6 is 0.29. What is the probability that at least ...