3
votes
1answer
43 views

Statistical test for “too perfect” random number generator?

I am attempting to characterize some random number generator programs in a very simple way. Specifically, I'm rolling a simulated 6-sided die $3 \times 10^8$ times and keeping a count of how many ...
2
votes
2answers
53 views

Expectations and variance with rolling a dice 10 times

Let's say you roll a fair dice 10 times and X is the number of sides that never show up. (i.e. Roll 1 - 10 = 1424145221, X = 2 because 3 and 6 never show up) Values of $N=0,1,2,3,4,5.\\ P(N=6) = 0$ ...
0
votes
2answers
27 views

clarify basic probability question

You have a loaded die. $A =$ even numbers $B =$ odd numbers $P(A)=3/4$ $P(B)=1/4$ $P(\{1\})=1/12$ $P(\{2\})=1/4$ How was $P(\{1\})$ and $P(\{2\})$ calculated? Is it beacuse there are 3 odds ...
0
votes
2answers
66 views

Sum of 3 dice rolls

If we roll a fair dice 3 times, what is the probability that the sum of values of the three rolls is greater than 9? I approached it like this: Let X be the result of a single dice roll. Let Sn = X1 ...
-3
votes
1answer
44 views

Roll Dice- Expected Winnings [closed]

I have a problem like this: At a charity game you pay \$1 to roll a die. If you roll a 6, you get \$5. Otherwise, you get nothing. How do I set up a probability distribution and what is the ...
0
votes
1answer
41 views

How many times to roll a die before getting $n$ consecutive sixes given $m$ occurences?

Given a unbiased dice how to find the average number of rolls required to get $n$ consecutive sixes given already $m$ number of sixes occurred where $m\leq n$. I know how to solve using n consecutive ...
1
vote
1answer
48 views

Probablility of a Dice Game

Player A rolls $m$ dice, while Player B rolls $m + 1$ dice. If Player A rolls $a$ $n$'s and Player B rolls $b$ $n$'s, then Player A wins if $a > b$ . Otherwise, Player A rolls up to $k$ of the $m$ ...
1
vote
1answer
49 views

Probability Dice Game Question

I have the following problem to solve that deals with probability (something I haven't done since Grade 8 (6 years ago)) This is a one player game and it is described for $q$ sided dice. You start by ...
-1
votes
1answer
22 views

Calculating probability of a dice with different numbers [duplicate]

I was given a problem in class: ...
2
votes
2answers
92 views

Probability of always rolling 6 on a dice

Suppose I roll a six-sided die $10$ times and each time it shows a $6$. What is the probability of the next roll coming up $6$? You might say $1/6$. But it was never declared to be a fair die. In ...
3
votes
1answer
92 views

What is the expected number of k-length streaks in n rolls?

Given $n$ flips of a coin with success probability $p$, what is the expected number of $k$-length win streaks in $n$? (I've looked for this question online, but the answers always restrict $n$ to be ...
0
votes
3answers
112 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) ...
1
vote
4answers
5k 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). ...
-1
votes
2answers
414 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.
0
votes
2answers
94 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: ...
0
votes
1answer
27 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 ...
3
votes
2answers
104 views

Roll dice and ignore worst results

I am at my wits' end with my very basic statistics knowledge. I roll $n$ dice with $k$ sides each (numbered $1$ thru $k$, laplace). I then add the numbers of the $m$ best dice (the higher the roll ...
0
votes
1answer
85 views

Probability of rolling three dice without getting a 6 in 8 rolls

I know the propability of rolling three dice without getting a $6$ in $1$ roll is $91/216$, but what about rolling it in $8$ rolls consecutively with three dices?
1
vote
2answers
94 views

Coinflip statistics

There is a betting strategy for coinflips, called Martingale, in which the player should pick heads or tails and keep betting on it (doubling their bet on every loss) to eventually make a win when it ...
3
votes
1answer
173 views

How do you calculate the probability of army loss in Risk, but with modifiers to dice?

I was wondering how you can calculate the outcome of dice rolls in the board game Risk, but with modifiers, assuming 3 attackers and 2 defenders. In Risk the attacker rolls 3 dice, and the defender ...
0
votes
1answer
356 views

Statistics question on probability

Suppose that one hundred fair dice are tossed. Estimate the probability that the sum of the faces showing exceeds 370. Include a continuity correction in your analysis.
1
vote
1answer
117 views

Probability of A given B & C?

I would like to sum the probability that given 3 (potentially biased) die rolls, all 3 rolls will be different-- what is the correct way to do this? So far, I have: $$ 1 - ...
0
votes
1answer
2k views

Variance of a random variable representing the sum of two dice

$\newcommand{\Var}{\operatorname{Var}}$ The formula for the variance of the sum of two independent random variables is given $$ \Var (X +X) = \Var(2X) = 2^2\Var(X)$$ How then, does this happen: ...
0
votes
1answer
2k views

Variance and Standard Deviation of multiple dice rolls

I'm trying to determine what the variance of rolling $5$ pairs of two dice are when the sums of all $5$ pairs are added up (i.e. ranging from $10$ to $60$). My first question is, when I calculate the ...
2
votes
2answers
578 views

Probability that the sum of all values of 5 pairs of dice will be between 30 and 40

I'm trying to solve a question that asks: If 5 pairs of fair dice are rolled, approximate the probability that the sum of the values obtained is between 30 and 40 inclusive. My approach so ...
2
votes
1answer
86 views

Help with probabilities on a game I am making

I asked over at the RPG stack exchange and they sent me here. I am working on making a RPG and am trying to understand the statistics of the core mechanic so I can determine how effective leveling ...
5
votes
4answers
6k views

How many times to roll a die before getting two consecutive sixes?

Basically, on average, how many times do you have to roll a fair six-sided die before getting two consecutive sixes?
4
votes
3answers
489 views

Statistical Significance Dice Probability

I think I just need to be pushed to the right formula or algorithm... Imagine you've got a "real" dice which is not an optimal one. And you want to know the confidence intervals for each result. So ...
1
vote
1answer
2k views

How do you calculate probability of rolling all faces of a die after n number of rolls? [duplicate]

Possible Duplicate: Expected time to roll all 1 through 6 on a die Probability of picking all elements in a set Im pretty new to the stackexchange, and posted this is statistics, and then ...
7
votes
3answers
948 views

What is the expected number of dice one needs to roll to get any monotonically increasing series of 1 to 6?

Similar to: "What is the expected number of dice one needs to roll to get 1,2,3,4,5,6 in order?" but we allow repeats so 1,1,2,2,3,4,4,4,4,5,5,6 would count. My answer (or simulation) is flawed as I ...
6
votes
2answers
944 views

What is the expected number of dice one needs to roll to get 1,2,3,4,5,6 in order?

If I have a fair die and throw it until I get a run of 1,2,3,4,5,6 in order, how many times on average must I throw the dice?
1
vote
1answer
2k views

Poker dice probability

I am working on a maths excersice and got stuck on this question where I need to calculate the probability of poker dice. The game poker dice is played with 5 dice. It's possible to get one of the ...
5
votes
3answers
5k views

How many rolls do I need to determine if my dice are fair?

Roughly how many times do I need to roll a 6-sided die to feel confident that it's giving "fair" results? What about a 10-sided or 20-sided die? Note that I will be actually manually rolling physical ...
4
votes
1answer
539 views

Magical Loaded Dice and expected values

Let's say we have a magical biased die that allows us to set the probability of every side to whatever we want (nonzero and add up to 1, of course). And let's say this die enforces the condition that ...