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131 views

Chi-squared distribution for dice not returning expected values?

I'm trying to verify that my dice are reasonably fair and balanced. I'm not sure I'm doing it right, though, since I'm basically teaching myself stats without references. To achieve this, I've settled ...
157 views

Using R for dice probabilities

Using R, what function(s) would I use to obtain the following probabilities? Roll at least one 1 when rolling 2 six-sided dice (2d6) = 11/36 Roll at least one 1 when rolling 3 six-sided dice (3d6) ...
627 views

How often do you have to roll a 6-sided dice to obtain every number at least once?

I've just played a game with my kids that basically boils down to: whoever rolls every number at least once on a 6-sided dice wins. I won, eventually, and the others finished 1-2 turns later. Now I'm ...
220 views

How to compute the distribution of sums when rolling 'N' dice with 'M' faces?

I stumbled upon the following problem: Given 'n' dice with 'm' faces with values 1 to m and a number 'x' what is the probability that the sum of the numbers on the 'm' dice is greater than or equal ...
171 views

Non-fair die - College Probability

How many times must you roll a non-fair die to be at least 84% sure that the sample probability will be within 3% from the actual probability. Since the die is not-fair, we do not know p. My question ...
148 views

Maximum entropy of dice

How can be proven that the entropy of a dice with equal probability for all its faces is at its maximum? It's clear that the entropy will be smaller if there are more chances for a particular face, ...
425 views

Does the probability of multiple independent events follow a normal distribution?

I'm heavily into role-playing systems, scripted a set of utilities in ruby for pen-and-paper games and I sort of understood statistics when I took it, but I could never for the life of me figure out ...
153 views

Relevancy of order statistics to the roll-and-keep dice mechanic?

Throw $x$ dice, each of which has $z$ sides, keep the $y$ highest values rolled, and find their sum $s$. In roleplaying games, this is called a "roll and keep dice mechanic" and notated "$x$d$z$k$y$" ...
238 views

Is there such a thing as a fair die?

Is there such a thing as a fair die? On dice where the number is represented by a scooped out dot, surely that makes a difference? Has anyone done any research? In fact thinking about it, why would a ...
319 views

What is the probability of rolling all faces of a die after n number of rolls

It is fairly easy to figure out what is the average number of rolls it would take to roll all faces of a die [$1 + 6/4 + 6/4 + 6/3 + 6/2 + 6/1 = 14.7$], but that got me thinking of a seemingly more ...
130 views

Distribution of complex results for pool of ten-sided dice, specific to custom tabletop RPG system

I'm no statistician, but I do find the area of mathematics fun and fascinating. I have a friend who has designed a "roll-mid" dice system for his custom tabletop RPG and as part of the game balancing, ...
2k views

Dice probability for Yahtzee large straight

I had a discussion with a friend of mine about what is the best course of action in the following Yahtzee scenario: The first throw with 5 dice results in the following values: ...
477 views

Designing a test for a psychic who says he can influence dice rolls

Let's say that I have a friend (let's call him "George") who says that he can control the roll of dice using his mind (ie, make the dice more likely to fall on a specific number he is thinking of). ...
175 views

Does the average increase of a “re-roll” increase with the size of the dice?

I'm having trouble modeling the following scenario: Roll two dice and take the best result. What is the proper way to model the average result from this? I understand intuitively that the ...
826 views

Probability of a certain sum of values from a set of dice rolls

A six-sided die is rolled 100 times. Using the normal approximation, find the probability that the face showing six turns up between 15 and 20 times. Find the probability that the sum of the face ...
486 views

Multinomial distribution for 4 side dice roll

Suppose I roll a 4-side dice 25 time to get a final sum between 25 and 100. How I calculated the distribution of probability for each sum between 25 and 100? Thank you
2k views

Odds of rolling doubles or triples given N 6-sided dice

Over the holidays I played a dice game where each player had 3 to 7 d6 to roll each turn. The game gave certain advantages to doubles and triples. I wanted to know the odds of rolling doubles or ...
590 views

Maximizing probability of winning on loaded coin

If we have a loaded coin that plays out 75% heads, 25% tails, what would be the best way to bet on the outcome of each of $n$ trials? How could we maximize our probability of winning? Is it possible ...