Questions tagged [dice]
Dice (singular: die) are typically small cubical objects marked with spots, numbers (1-6 usually) or symbols to generate random outcomes, particularly in games. Other polyhedral dice are also used in games.
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Lower threshold for Sequential Probability Ratio Test on Contingency Table testing
For testing whether a die is fair, we have the log likelihood ratio:
$$
\Lambda = \frac{1}{2} \sum_{i} \mathrm{observed}_i \log\left(\frac{\mathrm{observed}_i}{\mathrm{expected}_i}\right).
$$
Suppose ...
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Probability to get a 1 in 5 rolls 3 or more times
If I roll a dice 5 times, what is the probability to get 3 or more ones?
That is, to roll a one three or more times?
Because I think it's near 0.05:
$ \binom{5}{3} \left(\frac{1}{6}\right)^3 = 0.046 $
...
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Infinite dice roll probability
The following is an interview question:
Two players A and B play a game rolling a fair die. If A rolls a 1, they immediately reroll, and if the reroll is less than 4 then A wins. Otherwise, B rolls. ...
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Formula to find percentage of winning between two different numbered dice
Lets say I have a dice with the numbers from 1 to 10 and another one numbered from 1 to 7. I roll both dices once. Whats the chances in percentage that the 10 numbbered dice will win in terms of ...
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What is the probability a difference of two appears before 3?
Given a sequence of trials, where each trial is rolling two dice, each trial's outcome is the absolute difference between the values on the die. What is the probability that the outcome of 2 occurs ...
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How to graphically show how "normal" a collection of dice rolls are in a game
I was trying to think of a way to show how "normal" a set of dice rolls are in a game like catan. In Catan, each turn you roll 2d6 and the sum of those 2d6 dictate game outcomes. A game can ...
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Expected value for a fair die game
You roll a fair die until the cumulative sum rolled so far is a multiple of 3. You get $1 for each roll. What is the expected amount you will get?
I started by finding the probability of the game ...
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Dice rolling problem
A game is played with $n$ dice, and an additional parameter $r<=6$. The game has one player who must throw all $n$ dice on each round and add the score to the total. The game works as follows:
The ...
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Comparison of Squared Dice Loss vs. Standard Dice Loss
I've been diving into segmentation tasks and came across two variations of the Dice Loss that I'm considering for my neural network: the standard Dice Loss and the Squared Dice Loss.
The Standard Dice ...
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Interview Question: Expected value of dice game where each subsequent roll determines number of dice sides
Consider the following game:
You are playing a game where you roll a die and earn $1 each time you roll higher than 1. For the first roll you get a 4 sided die, and for each subsequent roll you get a ...
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Why is the distribution of the sum of the values on two dice bell-shaped and symmetric if two uniform dist is triangular distribution?
Why is the distribution of the sum of the values on two dice bell-shaped and symmetric if two uniform dist. sum is triangular distribution via Irwin-hall distribution?
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Number of configurations in which you can roll 2 6's in a row
A colleague at work gave me a problem to think about.
If you throw $n$ dice, how many configurations are there where you get at least 2 6's in a row?
I worked a lot with Pascal's triangle and in the ...
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Hausdorff and IoU are stopped changing while dice metric is decreasing
I am facing a problem in Hausdorff and IoU, where they stop learning when reaching a specific value! While the loss and dice metric keeps changing. surface_distance also has a problem since it is ...
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Probability of a given result with multiples of mixed dice with different number of faces
What is the formula to calculate the probability of getting 41 when I throw two 10-sided dice and four 8-sided dice? I’m looking for an algorithm for the general case of throwing multiples of two sets ...
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Quantifying the confidence that the most sampled outcome is the most probable outcome
Let us say we have a cheater's six-sided die, which we can assume to be unfair with an unknown probability distribution. We want to know the most likely roll with this die, and so we roll it $N \gg 6$ ...
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