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Related Concept Videos

Random Variables01:09

Random Variables

A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
Bias01:22

Bias

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Randomized Experiments01:13

Randomized Experiments

The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
Simple randomization
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Unusual Results01:16

Unusual Results

Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In problems involving probability, unusual results can be observed in 2 instances – an unusually high number of successes or an unusually low number of successes.
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Random Sampling Method01:09

Random Sampling Method

Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest. Among the various sampling methods used by...
Wald-Wolfowitz Runs Test I01:17

Wald-Wolfowitz Runs Test I

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Related Experiment Video

Updated: Jun 29, 2026

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
13:04

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

How random is dice tossing?

Jan Nagler1, Peter Richter

  • 1Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
PubMed
Summary
This summary is machine-generated.

Dice are not truly random. Their outcomes are pseudorandom, meaning they appear random but are determined by deterministic classical mechanics and initial conditions, making them unpredictable but not truly random.

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Area of Science:

  • Physics
  • Chaos Theory
  • Classical Mechanics

Background:

  • Dice are widely accepted as random number generators.
  • The underlying mechanics of dice tossing are governed by deterministic classical laws.
  • The apparent randomness of dice necessitates a deeper analysis.

Purpose of the Study:

  • To investigate the source of randomness in dice tossing.
  • To analyze whether dice outcomes are truly random or pseudorandom.
  • To understand the influence of initial conditions and dissipation on dice outcomes.

Main Methods:

  • A simplified model of a die (a barbell with two masses) was analyzed.
  • The model considered only two possible final positions.
  • The study examined the effects of varying initial conditions and dissipation during bounces.

Main Results:

  • Dice outcomes are not truly random but pseudorandom.
  • The unpredictability of dice outcomes depends on initial conditions and the degree of dissipation.
  • Even under seemingly random conditions, the system remains deterministic.

Conclusions:

  • Dice function as pseudorandom number generators, not true random number generators.
  • The deterministic nature of classical mechanics underlies dice outcomes.
  • Understanding the factors influencing predictability is key to analyzing dice behavior.