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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How to calculate the probability of a die with a wild side?

So I have a 6-sided die with 5 different values in 5 of their sides. Its sixth side can be treated as any of the other 5 values. So my question revolves around which is the probability of getting any ...
5
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3answers
493 views
+100

Probability of some die face being missed N or more times in a row in M rolls? [Clarified]

2015/01/28 Clarification: Question rewritten to remove ambiguity that elicited (interesting) responses to a different problem (use edit should you wish to view). From Markus' feedback on the earlier ...
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2answers
48 views

Expected value problem on dice reroll

The question is here: Roll N* 3-sided dice(0,0,1), roll them twice and choose a better result, what is the expected value? If possible I would also like an answer for dice {0,1,2} or {1,2,3} if ...
0
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3answers
36 views

Chance of winning simple dice game

Tossing two fair dice, if the sum is 7 or 11, then I win; if the sum is 2, 3 or 12, then I lose; if the sum is one of rest of numbers then I toss the two dices again. What is probability of winning? ...
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3answers
2k views

On average, how many times must I roll a dice until I get a 6?

On average, how many times must I roll a dice until I get a 6? I got this question from a book called Fifty Challenging Problems in Probability. The answer is 6, and I understand the solution the ...
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3answers
33 views

Determining number of combinations on odd dice

Suppose we had four dice with four sides. Two sides have a $\frac{1}{10}$ chance of being rolled, two sides have a $\frac{4}{10}$ chance of being rolled. The dice score points equal to 1, 3, 4, and 6, ...
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0answers
49 views

Expected outcome for repeated dice rolls with dice fixing

Here is another dice roll question. The rules You start with n dice, and roll all of them. You select one or more dice and fix them, i.e. their value will not ...
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1answer
35 views

Formula for X “successes” with X 10 sided die.

I am trying to create a formula for the % chance of having Y number of dice hit a number 8, 9 or 10 out of X possible. For example the chance of having 7 dice out of 10 dice be one of the 3 numbers. ...
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2answers
53 views

combinatorics dice question

There are $10$ identical dice ($1$ - $6$). How many different results can we get so that the set of results will be exactly $3$. for example: $7$ dice will be the number $2$, $2$ dice will be $3$ and ...
0
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2answers
30 views

An $m$ sided dice is rolled $n$ times what is the chance of getting an average of $\frac{m+1}{2}$?

If I roll a six sided dice twice there is a $1$ in $6$ chance that the results will sum up to $7$ (giving an average of $3.5$ per dice). And if I only roll it once it is not possible to get a $3.5$. ...
2
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1answer
39 views

Tetra Master Dice Rolls

In the game Tetra Master, two players play a card with a number n between 0 and 15, inclusive. Then, both players roll a 16-sided die numbered from 0 to 15. Both players than add up their dice rolls ...
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2answers
65 views

Probabilities of Dice Pools

Given 5 fair, 6-sided dice, calculate the probability of an equal or greater number of dice showing 1 appearing than the number of dice showing 4,5, and 6 combined. For example: if 5 dice are rolled ...
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2answers
41 views

Question about combinatoris of four dice

We have $4$ dice with $4$ different dyes : Green, Yellow, Red and Blue. I need to know how many options do i get so that I'll get the number $3$ at least once. These are 6 sided dice, color does ...
0
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1answer
129 views

Probability of a result from 3d6, lowest to highest

I have a fascination with tabletop sports games, and through that, I've developed an interest in probability. That said, it's not my strong suit, so I wanted to pose this question because I think ...
2
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1answer
61 views

Derivation of dice-sides polynomial

This question on PPCG.SE fascinated me. In particular @xnor's brilliant answer providing an elegant polynomial to provide the solution. In summary, the question asks for a program that, for an ...
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1answer
44 views

Four dice showing 3 values

I have 4 different color dice: blue, red, yellow and green. I need to check how many possibilities we get if the set of the numbers that are on the dices consists of 3 distinct numbers. In other ...
7
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2answers
168 views

A fair die is rolled $N > 6$ times. What is the probability the last 6 rolls were exactly $1,2,3,4,5,6$?

You rolls a fair die $N > 6$ times and you want to rolls the sequence $1,2,3,4,5,6$ in this order. What is the probability that the last 6 rolls were (in consecutive order) $1,2,3,4,5,6$, (So, on ...
2
votes
1answer
66 views

Probability Sum of One, Two, or Three out of Three Dice

I was given a problem in my stats homework that I had some trouble with. The question is as follows: If three six-sided dice are thrown, what is the probability of obtaining a four when obtaining a ...
2
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1answer
62 views

Expected number of moves of a random walk inside a simplex

Few days ago, Roger Blazey, retired head maths teacher, at LinkedIn group told about the following problem: “This problem was raised as part of a lecture at The Biennial AAMT (Australian ...
9
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3answers
220 views

The rotation of dice on a grid

Imagine you have a plane, flat surface with a square grid drawn on it. You have a standard cubic die which is placed flat on the surface. Its length is the same as the length of side of each grid ...
2
votes
2answers
239 views

Why does it seem to decrease probability to roll more times?

I am looking how to find the probability of rolling 10 sixes in 60 rolls. After reading Calculate probabilities. 40 sixes out of a 100 fair die rolls & 20 sixes out of a 100 fair die roll, it ...
3
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2answers
68 views

Probability of rolling a sum of N with up to infinite rolls of a die

I'm trying to figure out if there is some (relatively simple) formula for calculating the probability of rolling a sum of N with as many rolls as needed with a single regular six-sided die. For ...
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3answers
75 views

Probability of rolling $111, 222, 333, 444, 555, 666$ in that order

What are the odds of rolling triples with $3d6$ like this: $111, 222, 333, 444, 555$, and $666$ perfectly in a row? I know that the odds of rolling triples in a row without any specific order is $36^3 ...
4
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1answer
186 views

Probability that one player rolls more more 5s or 6s than the other player when one player rolls $X$ dice and the other player rolls $Y$ dice

There is a game I play that utilizes a particular mechanic that I am trying to assess mathematically. Me being a layman, I am having some problems figuring out one of the aspects for myself. The ...
8
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3answers
405 views

What is the probability on rolling $2n$ dice that the sum of the first $n$ equals the sum of the last $n$?

The Question What is the probability, rolling $n$ six-sided dice twice, that their sum each time totals to the same amount? For example, if $n = 4$, and we roll $1,3,4,6$ and $2,2,5,5$, adding them ...
2
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1answer
49 views

Dice 10000 probability of not scoring

There is a dice game I played recently, called "Dice 10,000", that is very similar to Farkle but a little simpler. In the version I played (house rules) a person scores on any given turn if they get ...
2
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0answers
72 views

Simulating dice by coins

Suppose you have a fair n-sided die $D_n$ - or rather suppose you don't have a $D_n$ but want to simulate one by repeatedly (but finitely many times) throwing a single (possibly biased) coin $C_p$ ...
3
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1answer
62 views

Probability that rolling X dice with Y sides and summing the highest Z values is above some value k

Some background: There is an RPG called Legend of the Five Rings, with an interesting dice system. You roll X dice, and keep the highest Z of them. You add those Z dice together. This is phrased as ...
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2answers
34 views

Permutation/Combination question on dice

Question: Three dice (six faces: each face -> number 1 to 6) are rolled. What is the number of possible outcomes such that at least one die shows number 2? My attempt: One die has to show two. ...
2
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5answers
94 views

Jamie rolls a die multiple times. find the probability that she rolls her first 5 before she rolls her second even number

Jamie rolls her fair 6-sided die multiple times. Find the probability that she rolls her first 5 before she rolls her second (not necessarily distinct) even number? This is what I have so far... ...
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2answers
44 views

Expected value of a die when decision to role again depends on previous outcome

(Introduction to Probability, Blitzstein and Nwang) A fair die is rolled some number of times. You can choose whether to stop after 1, 2, or 3 rolls, and your decision can be based on the ...
29
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2answers
17k views

Expected time to roll all 1 through 6 on a die

What is the average number of times it would it take to roll a fair 6-sided die and get all numbers on the die? The order in which the numbers appear does not matter. I had this questions explained ...
1
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1answer
49 views

Getting a simultaneous first $6$ with two dice

What's the probability that two players that each throw a normal dice get their first six at the same time ? Let $X_k,Y_k$ denote the numbers obtained with the first ($X$) and second ($Y$) dice at ...
1
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1answer
65 views

Uniform distribution of the sum of two dice

Is it possible to build two dice such that the sum of the two dice follows an uniform distribution on $\{2,\dots,12\}$ ? EDIT : Both dice must have sides 1-6, but the probability that the dice falls ...
2
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2answers
2k views

Solve for numbers to appear on two six-sided dice

I have a small wooden calendar that uses two six-sided dice to display day of month. One die carries numbers 0, 1, 2, 6, 7, 8 and the other carries 0, 1, 2, 3, 4, 5. The six of course doubles as the ...
3
votes
1answer
54 views

What's the probability of rolling 10 dice each with 10 sides and each will have to same number?

I think the probability is $1\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}\cdot{1\over 10}={1\over 10^9}={1\over ...
7
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3answers
177 views

Roll a fair die until a 6 appears for the third time. What is the chance that all six values have occurred?

The question in the title is a homework question that I have been stumped on for some time. My approach thus far was to treat it as an occupancy problem. From class we derived the following formula ...
65
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9answers
18k views

Given a die, what is the probability that the second roll of a die will be less than the first roll?

If you are given a die and asked to roll it twice. What is the probability that the value of the second roll will be less than the value of the first roll?
0
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1answer
147 views

Dice roll game fair price

You and I each roll 1 die each at the same time. I win if I roll a six on one roll, and then a five on the next. You win if you roll two sixes in a row. Who would you bet your money on? Note that You: ...
2
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1answer
45 views

What is the probability of not rolling any given number on 10 rolls of a die?

In other words, ALL combinations which don't contain at least one of the number from 1-6 would count. So for example... 5, 2, 3, 3, 4, 1, 5, 5, 3, 1 would be counted because there is no 6 Also 5, ...
3
votes
3answers
81 views

Calculating the probability that throwing two dice will yield a higher number than throwing one die

How do I work out the probability that Andy, rolling two dice, will roll a number higher than Candy, rolling one die? The highest number you can roll with one die is six. The probability of rolling ...
2
votes
1answer
57 views

what is a formula for working out dice chance percentages?

I am not a student or a maths type person. Instead I play a lot of board games and one in particular. Arkham Horror / Eldritch Horror. It uses a dice system to calculate successful rolls and I would ...
0
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1answer
56 views

What is the chance of this dice appearing twice in a row? [closed]

3 friends roll a 6-sided dice. What is the probability that at least two of them roll the same number?
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2answers
62 views

Probability number comes up before another

In craps, say I roll a 5 for the place bet. What is the probability that I roll another 5 before rolling a 7? Is this correct?: $P(5 \text{ before 7}) = P(5) + P(\neg 7 \neg 5, 5) + P(\neg 7 \neg 5, ...
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1answer
79 views

Probability of rolling two dice

Consider two dice, each one having one face showing the letter a, two faces showing the letter b, and the remaining three faces showing the letter c. You roll each >die once, independently of the ...
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1answer
31 views

Probability that at least two $9$'s appear as sum in four tosses of a Pair of fair Dice.

I can calculate in the following way : $P(9 \text{ in one toss}) = 1/9$ sum the following : $P(9 \text{ in two toss})$, $P(9 \text{ in three toss})$, $P(9 \text{ in 4 toss})$ And the answer I get ...
0
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2answers
85 views

Trick dice Probability

I was given this exercise: We have 2 dice, the first is normal $\Omega = \left\{1,2,...,6 \right\}$ and the other is a trick dice, with sample space $\Omega = \left\{2,3,4,5,6,6 \right\}$. If there ...
1
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2answers
30 views

Probability of dice rolls

Two regular cubic dice are rolled. One is red and the other blue. What s the probability that the red die roll is greater that or equal to the blue die?