# Tagged Questions

For questions on dice, a small throwable object with multiple resting positions, used for generating random numbers. This makes dice suitable as gambling devices for games like craps, or for use in non-gambling tabletop games.

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### Get dice from matrix of win chances. Is it always possible?

As an example, consider a set of nontransitive dice $D_1: 2, 2, 4, 4, 9, 9$ $D_2: 1, 1, 6, 6, 8, 8$ $D_3: 3, 3, 5, 5, 7, 7$ On the long run D1 wins vs D2, D2 wins vs D3 and D3 wins vs D1. ...
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### Dice rolls - Combinatorics with limitations

Given 2 players, one rolling $x$ d6 dice and the other rolling $y$ d6 dice, what is the probability of a match between the two players? I'm getting stuck on the sub-set comparisons - I can calculate ...
1answer
86 views

### The probability that the product of 100 die rolls $\le$ $a^{100}$ for $1 < a < 6$

Suppose that a fair $6$ sided die is rolled 100 times. Let $X_i$ be the value obtained on the $i$th roll. Compute an approximation for $P\left(\prod X_i \le a^{100}\right)$ for $1 < a < 6$. I'...
1answer
58 views

### Dice probability

I had a rather interesting yatzee experience. This is Maxiyatzee, 6 dice game. He had 13 throws. All together 78 dices. He only managed to throw one 2 on all those throws. And I am trying to find out ...
0answers
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### Trickster and dice

Suppose a trickster has three six-sided dice all of which evenly weighted (so each face is equally likely). One has all 6s, one has half 6s and half 1s, and one is a normal die. The trickster randomly ...
1answer
30 views

### Choosing dices out of a box

In a box we have 5 dices, 3 of them are proper, one has two sixes, second has six sixes. Given the events A - after first throw we have a six, B- after next two throws we have six and something else. ...
1answer
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### “Exploding Dice” vs. “Non-Exploding Dice”

For a roleplaying game I'm designing, I'm using a core resolution mechanic that comes down to counting "successes" on rolled dice. Characters roll a handful of dice (six-sided) and count each die that ...
1answer
139 views

### Given a biased die, what some of the probabilities

I recently asked this question: Roll a fair 6 sided die twice, What is the probability that one or both rolls are 6? And that makes sense, however, the reason I was confused in the first place is ...
3answers
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### Roll a fair 6 sided die twice, What is the probability that one or both rolls are 6?

Roll a fair 6 sided die twice, What is the probability that one or both rolls are 6? This question is confusing me on a conceptual level, specifically the "or both rolls." With out that, the ...
0answers
63 views

### Probabilities in a dice game (Ashens' game)

This question relates to a card/dice game by Stuart Ashen which unfortunately I cannot name here because its name is Norfolk slang for male genitalia. This game is played in several phases, but the ...
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### Probability n Dice Results are subset of m Dice Results

Let D(n,m) be the probability that a multiset of n dice results will be a submultiset of m dice results. Multiset indicates repeats are counted: If n=3, {3,3,4} is a submultiset of {3,3,4,5,6} but ...
2answers
118 views

### What is the pmf of rolling a die until obtaining three consecutive $6$s?

I am trying to find the pmf of rolling a die until 3 consecutive 6s turn up. I am able to find the expected value using a tree diagram, but the pmf is not obvious to me. Let A be the event of not ...
2answers
87 views

### Game probability

I hope you could help me with this problem... The game goes this way: There are 6 players, numbered 1 to 6. Player 1 starts the game, he rolls a die with six faces. If the result (x) of rolling ...
1answer
42 views

### Probability game problem

I hope you could help me with this problem... The game goes this way: There are 6 players, numbered 1 to 6. Player 1 starts the game, he rolls a die with six faces. If the result (x) of rolling ...
3answers
136 views

### Probability six game player [duplicate]

The game goes this way: There are 6 players, numbered 1 to 6. Player 1 starts the game, he rolls a die with six faces. If the result ($x$) of rolling the die is 1 then Player 1 wins. Else the player ...
2answers
336 views

### Is rolling a dice a Gauss distribution?

I'm in an argument with a friend over rolling a dice several times, for example rolling 5 times. His argument is, that is far more difficult to roll out 1-1-1-1-1 than any other combination (for ...
1answer
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### Probability of getting at least 4 numbers by rolling dice n times

I want to compute probability of getting at least 4 numbers by rolling dice n times. Now my formula is $$P = \frac{6^n - 2^n * {6 \choose 2} + 4 * 1^n * {6 \choose 1}}{6^n}$$ But by principle of ...
2answers
534 views

### Probability of rolling a 6 before an odd number [closed]

A dice is rolled many times. What's the probability of rolling a 6 before an odd number? I'm unsure of where to start with this, please help.
2answers
69 views

### Loaded die probability

The loaded die has the following probabilities: $0.3,0.2,0.1,0.1,0.2,0.1$ for $1,2,3,4,5,6$ respectively. The question asks What is the probability of rolling at least one $1$ and no $2's$ in $4$ ...
1answer
55 views

### Probability's Game

The game goes this way: There are 6 players, numered 1 to 6 (Player 1, Player 2,...,Player 6). Player 1 starts the game, he rolls a dice with six faces. If the result (x) of rolling the dice is 1 ...
1answer
132 views

### Puzzle on rolling dice game

A gambler goes to bet. The dealer has 3 dice, which are fair, meaning that the chance that each face shows up is exactly 1/6. The dealer says: "You can choose your bet on a number, any number from 1 ...
1answer
136 views

### Roll dice, high number wins.

Me and my brothers (3 of us) decided to roll a single dice to see who would get to have my fathers old pocket knife. The guy who rolled the highest number would win. So I rolled first and got a 6, ...
2answers
232 views

### Proving pairwise independence and mutually independent

I have this problem that states: A = {red die is 3, 4, or 5} B = {blue die is 1 or 2} C = {sum is 7} Both the red and blue die are under equally likely probability. I need help ...
2answers
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### If I do not know how much sides a dice has, how often should I throw it to know the number of sides?

Lets say we have a dice with an unknown number of sides, and we are only allowed to see the results of the rolls. How often do I have to throw the dice to know the number of sides?
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2k views

### Probability that the sum of 6 dice rolls is even

Question: 6 unbiased dice are tossed together. What is the probability that the sum of all the dice is an even number? I think the answer would be 50%, purely by intuition. However, not sure if ...
1answer
106 views

### Use any dice to calculate the outcome of any probability

While looking at this question, I had a gut feeling that you can use any fair, single die with any number of sides to calculate the outcome of any probability. Assuming we express the probability as ...
3answers
738 views

### One die probability questions [closed]

I was given this exercise: If a standard die has twice the probability of rolling an odd number than an even number. Find the probability of rolling a non-prime number with this die. My attempt: P(...
3answers
81 views

### Statistics dice question

$6$ people, $A, B, C, D, E, F$ sit in a circle to play a dice game. Rule of game: as you roll a die and get a number which is a multiple of $3$, give the die to the person on the right(...
1answer
50 views

### two rolls of a die. independent.

for two rolls of a die, the dice fall independently. an even number shows on the first die and the event that an even number shows on the second die? this is what i got= the probability that the ...
3answers
47 views

### Probability. Fair dice with $n>6$ sides. Who wins?

I am fairly new to statistics so bear with me. Two players are playing a game with a fair dice that has $n>6$ sides. The sides are labeled $1,2,3,..,n$. The one who throws a larger number wins but ...