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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What is the probability there are a higher total of red “5’s and 6’s” than white “5’s and 6’s”?

You have 3 red 6-sided dice and 3 white 6-sided dice. When you throw the dice, what is the probability there are a higher total of red “5’s and 6’s” than white “5’s and 6’s”? Note: When any 6-sided ...
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1answer
61 views

rolling a seven when at least one die is a four?

I have been working on some stuff like this and I am fairly confused, I wrote some code to see how it works when simulated and I am further from an answer. ...
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1answer
438 views

Expected sum of all the n-sided dice rolls until we get n

So the problem is the following. We have an $n$-sided die. We throw it until we get $n$. What's n, if the expected sum of all the throws including the $n$ one is $21$. Now, I did manage to solve it ...
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2answers
72 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
182 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: ...
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2answers
539 views

How to calculate probability of dice rolls [closed]

I'm playing board game of Zombicide. One of the actions in there is attack, where you roll a number of 6 sided dice, and you get a hit for every dice that showed more than "m". For example - roll 4 ...
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1answer
92 views

Four sided dice rolled to match number

I've been cracking my brain about this one for some time now. I've just started this statistics course. The problem is: A four sided dice is rolled once and then rolled as many times to not get the ...
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3answers
125 views

How can I linearly decrease chance?

Suppose there are 10 different people, each holding 1 lottery ticket, and I give each of them 10% chance of becoming the 'winner'. Now let's say one of those 10 people (I dont know which one) ...
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3answers
135 views

I flip M coins, my opponent flips N coins. Who has more heads wins. Is there a closed form for probability?

In this game, I flip M fair coins and my opponent flips N coins. If I get more heads from my coins than my opponent, I win, otherwise I lose. I wish to know the probability that I win the game. I ...
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0answers
223 views

Probability In Multi-Throw Dice Game

I am having some trouble coming up with a probability table for a game that I wrote. The game uses 6 dice. The player can throw the dice multiple times, but must retain at least 1 on each throw. In ...
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2answers
226 views

dice roll of 20

what formula would be correct to find the odds of rolling 2 dice "X" number of times without a seven showing. There are 36 combinations when rolling 2 dice with six sides. Im wondering how often one ...
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3answers
188 views

If we roll a dice 10000 times and we gain 1€ if the result is odd, 2€ if it's 2 or 4 and 5€ if it's 6, what is the prob of gain 22000€ or more?

In the end I modeled a random variable as { 1 = 3/6; 2 = 2/6; 5 = 1/6 } And the situation is that we roll a dice 10,000 times and we want to know ...
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4answers
192 views

Probability that $ax^2+bx+c$ has no real roots after rolling 3 dice.

Suppose that I roll $3$ dice and write down the outcome as the coefficients $a,b,c$ in the polynomial $ax^2+bx+c$ respectively. What is the probability that this polynomial has no real roots? So, I ...
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2answers
44 views

Probability problem and number theory

A standard fair 6-sided dice is rolled $n$ times. Let $X_k$ be the spot which faced up inthe k-th round. What is the probability that $X_1+X_2+...+X_n$ is divisible by 7? I tried to solve it by ...
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2answers
104 views

Asymptotics of probability of Newton-Pepys problem

In Newton-Pepys problem one is interested in probability $p_n$ of getting at least $n$ sixes in $6 n$ independent throws of regular 6-sided die. The number of sixes $S_m$ obtained in $m$ throws ...
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2answers
190 views

Probability of two rolling dice

As I am taking some distance course on probability theory, I have no other option to ask my question than here. If they sound too basic, please bear me. Q: I roll two dice. What's the probability I ...
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1answer
200 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 ...
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2answers
566 views

Optimal Strategy for Bar Dice

This game is played in bars in Wisconsin, USA, but I'm sure variations are played many places around the world. The game has practical value, since once mathematicians figure out the best strategy, ...
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2answers
55 views

Dice problem, with image explanation.

Four dice are rolled SIMULTANEOUSLY. $X_1$ is a random variable that represents how many 1's you get in a single roll. $X_2, ... , X_4$ are defined in the same fashion, like in the picture below. ...
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1answer
44 views

Question from a test concerning dice probability

There are 4 dice in the following colors: blue, yellow, black and red. They're rolled at the same time. Consider $X_1$ to be the quantity of dice in which the face value scored was one. Let $X_2, ... ...
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1answer
31 views

Question refering to dice probability from a test.

There are 4 dice in the following colors: blue, yellow, black and red. They're rolled at the same time. Consider $X_1$ to be the quantity of dice in which the face value scored was one. Let $X_2, ... ...
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4answers
19k views

If I roll two fair dice, the probability that I would get at least one 6 would be…

11 out of 36? I got this by writing down the number of possible outcomes (36) and then counting how many of the pairs had a 6 in them (1,6) (2,6) (3,6) (4,6) (5,6) (6,6) (6,5) (6,4) (6,3) (6,2) (6,1). ...
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2answers
676 views

If you roll four fair dice, what is the probability that you will end up with two 1's and two 3's?

Can someone help me with this? I'm completely stumped on how to go about it and no one I know can help. I just need to be shown how to do it.
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1answer
75 views

Probability that one die will match another

I am working on a Dice game involving players rolling dice to match a shared die. Example: 6 6-sided dice are thrown, one Black and the rest white. Players score more points for each white die that ...
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1answer
145 views

Expected length of generating a pattern (throwing dice)

A fair die is tossed repeatedly. The experiment ends as soon as the last six outcomes form the pattern 131131 What is the expected length (i.e. the number of rolls of the die) of this experiment?
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1answer
80 views

Using Generating Series to Find Sum of Sides of Dice

Question: " Let k be a non-negative integer. Use the theory of generating series to find the expected value of the sum of the dots when k (6-sided) dice are rolled. " I know that the generating ...
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2answers
482 views

dice biased such that a 3 comes up twice as often as each other number?

I just attempted to solve a problem that involved the title. So, it turns out I was getting an incorrect answer b/c I computed the probability of getting a 3 as 2/6 as opposed to 2/7. I don't fully ...
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3answers
339 views

Probability of rolling a cuboid dice

It's easy to count the probability of events on a regular dice because we know the probabilities ($P(1)$, $P(2)$, $P(3)$, $P(4)$, $P(5)$, $P(6)$) of all the basic outcomes ($P(i)=\frac{1}{6}$). ...
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1answer
665 views

The Probability of Rolling a Large Straight with 5 Six-Sided Dice [duplicate]

I don't know the probability of rolling a large straight with 5 six-sided dice, so I need to know what the probability is. What is it?
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2answers
324 views

The Probability of Rolling the Same Number with 10 Dice That Have 19 Sides

I like dice and I want to know what the probability is for rolling the same number with 10 dice that have 19 sides. Also, do these dice exist or not?
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0answers
41 views

If you roll a dice twice, and substract result of

If you roll a dice twice, and subtract $ Result_1 $ from $ Result_2 $, in what interval with 97% probability will lie number of all zeros, if we will do this experiment 1200 times. I assume, I ...
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2answers
151 views

Calculating dice probability and risk-reward value

Having trouble how to model this cost-risk question with Probability. Assume that you are given 5 standard six-sided dice, what's the probability you get at least three 2s? I have calculated this: ...
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1answer
38 views

Let's throw with a regular dice (probability)

Let's throw with a regular dice twice (independently). Let $X_{1}$ be the number of dots thrown on the first try and let $X_{2}$ be on the second. We know, that $X=X_{1} + X_{2}$. Calculate the ...
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1answer
92 views

Occurrences of 1,2, and 3 out of 4d6

I have 4d6 and I'm concerned with the odds of the numbers of ones, twos, and threes that show up in a roll of 4d6. Would I be correct in calculating the odds of one of these combinations, Say 1 one, 0 ...
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1answer
119 views

Dice probability of a winning more than $X\%$ of the time over $Y$ Throws

I have a die with three possible outcomes. The three outcomes are win (+1), draw (0) and lose (-1). $P(w) + P(d) + P(l) = 1$. (1) If I throw the die Y times, what is the probability I will win $X$ ...
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2answers
211 views

Dice sum probability range

If you roll one 6 sided die 1000 times, what is probability that sum of fallen numbers will be between 3400 and 3550 ?
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2answers
161 views

Probability of an event happening more times than at least one other event

I'm having trouble formulating this problem: How to find out the probability of an event A happening more times than at least one of events B, C or D? Assuming the events may have different chances of ...
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1answer
378 views

Probability in Rolling dice 6 times

If I have one die and I'm rolling the dice $6$ times. What is the probability that in the all $6$ times the result will be the same? I know that the probability for each number in $6$ sides dice is ...
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2answers
484 views

Expected number of rolls required to get sum greater than n for n faced die?

Suppose a guy has a die with $n$ faces. He can go on rolling it as many times as possible and add the sum of each outcome. What is the expected number of rolls after which the sum is at least $n$?
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4answers
686 views

Throwing dice: Probability Total is Divisible by 3

Suppose I throw a fair die $1995$ times. What is the probability that the total is divisible by 3? I tried to attack this problem inductively, storing the total in a variable $t \mod 6$, and ...
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2answers
129 views

permutations rolling die 6 times [closed]

How would you calculate the probability that if you roll a six sided die six times you will roll 1,2,3,4,5,6 consecutively. I am totally lost on how to even calculate this.
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1answer
145 views

The number of rolls of $6$ dice with exactly $4$ distinct values.

I know the answer is $${6 \choose 4}{5 \choose 3}$$ However, I don't understand why this is true?
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4answers
83 views

Roll summing over a long stretch

Say I roll a 6-sided die until its sum exceeds $X$. What is E(rolls)?
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1answer
49 views

Probability of a dice game with an emphasis on the number $4$

If I were to roll a set of $4\,$ four-sided dice $4\,$ times, what is the probability that on each of the $4\,$ dice rolls, the sum of the dice will be divisible by $4\,$?
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1answer
33 views

3 dices probability that number 5 comes up on exactly two of the three dice?

I roll three different loaded dice. For the first die the probability of getting a 5 is 0.7, for the second die the probability of getting a 5 is 0.48, and for the third die the probability of getting ...
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3answers
795 views

Throw 10 dice, probability of getting 6 identical numbers?

I got this result when I threw a set of 10 dice (btw. for the first with this set): What is a probability of getting 6 identical numbers (any) with 10 dice, with no particular order?
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1answer
148 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 ...
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4answers
233 views

Expected number of tosses before you see a repeat.

Suppose we roll a fair die until some face has appeared twice. For instance, we might have a run of rolls 12545 or 636. How many rolls on average would we make? What if we roll until a face has ...
2
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2answers
118 views

Probability of getting Required Sum

What is the probability of when four dice rolled together once,and getting a sum of Thirteen If we do by just calculating all possible values of sum, then it will take more time; so we can solve ...
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2answers
79 views

Probability theory - Dice

Two guys are playing dice with each wagering $50. Player 1 chooses 2 as his lucky number, and Player 2 chooses 6. Every time their lucky number appears as a result, the player gets one point. The ...