The dice tag has no wiki summary.
5
votes
1answer
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 ...
1
vote
2answers
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) ...
16
votes
4answers
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 ...
3
votes
3answers
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 ...
1
vote
2answers
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 ...
2
votes
1answer
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, ...
3
votes
2answers
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 ...
3
votes
1answer
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$y$" ...
10
votes
2answers
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 ...
5
votes
1answer
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 ...
2
votes
1answer
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, ...
1
vote
3answers
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:
...
8
votes
2answers
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).
...
4
votes
3answers
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 ...
3
votes
2answers
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 ...
1
vote
1answer
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
0
votes
3answers
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 ...
3
votes
4answers
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 ...
9
votes
6answers
6k views
How to easily determine the results distribution for multiple dice?
I want to calculate the probability distribution for the total of a combination of dice.
I remember that the probability of is the number of combinations that total that number over the total number ...
16
votes
6answers
1k views
How can I test the fairness of a d20?
How can I test the fairness of a twenty sided die (d20)? Obviously I would be comparing the distribution of values against a uniform distribution. I vaguely remember using a Chi-square test in ...
