# How random is dice tossing?

@article{Nagler2008HowRI, title={How random is dice tossing?}, author={Jan Nagler and Peter H. Richter}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2008}, volume={78 3 Pt 2}, pages={ 036207 } }

Tossing the dice is commonly considered a paradigm for chance. But where in the process of throwing a cube does the randomness reside? After all, for all practical purposes the motion is described by the laws of deterministic classical mechanics. Therefore the undisputed status of dice as random number generators calls for a careful analysis. This paper is an attempt in that direction. As a simplified model of a dice a barbell with two marked masses at its tips and only two final positions is…

## 16 Citations

Simple model for dice loading

- Physics
- 2010

Dice tossing is commonly believed to be random. However, throwing a fair cube is a dissipative process that is well described by deterministic classical mechanics. In Nagler and Richter (2008 Phys.…

Weldon's Dice, Automated

- Mathematics
- 2009

Walter Frank Raphael Weldon’s data on 26,306 rolls of 12 dice have been a source of fascination since their publication in Karl Pearson’s seminal paper introducing the !2 goodness-of-fit statistic in…

Weldon ’ s Data on Dice : 26 , 306 Throws of 12 Dice

- Mathematics
- 2009

Walter Frank Raphael Weldon’s data on 26,306 rolls of 12 dice have been a source of fascination since their publication in Karl Pearson’s seminal paper introducing the 2 goodness-of-fit statistic in…

Probability and dynamics in the toss of a non-bouncing thick coin

- Physics
- 2010

When a thick cylindrical coin is tossed in the air and lands without bouncing on an inelastic substrate, it ends up on its face or its side. We account for the rigid body dynamics of spin and…

Probability, geometry, and dynamics in the toss of a thick coin

- Physics
- 2011

When a thick cylindrical coin is tossed in the air and lands without bouncing on an inelastic substrate, it ends up on its face or its side. We account for the rigid body dynamics of spin and…

Randomness at large numbers: Experimental proof in coin toss and prime number

- Mathematics
- 2019

Randomness is a central concept to statistics and physics. Here, we conduct experimental investigations with a coin toss and prime number to show experimental evidence that tossing coins and finding…

The three-dimensional dynamics of the die throw.

- PhysicsChaos
- 2012

It is argued that non-smoothness of the system plays a key role in the occurrence of dynamical uncertainties and gives the explanation why for practically small uncertainties in the initial conditions a mechanical randomizer approximates the random process.

Randomness in a Galton board from the viewpoint of predictability: sensitivity and statistical bias of output states.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

A simple dynamical model inspired by the Galton board is analyzed, and it is shown that it is possible to determine the radii of scatterers corresponding to a given predictability criterion, specified as a statistical bias, and a given uncertainty of initial conditions.

How Does God Play Dice

- Physics
- 2010

Albert Einstein is reported to have said that “God does not play dice with the universe.” This was prompted by the peculiarities of quantum mechanics. He didn’t like the way quantum mechanics dealt…

Unpredictable as dice: analyzing riddled basin structures in a passive dynamic walker

- Mathematics2019 International Symposium on Micro-NanoMechatronics and Human Science (MHS)
- 2019

This paper shows that a locomotion dynamics of a simple biped robot has the final state sensitivity and suggests that, in some sets of parameter region, the behavior of a robot becomes unpredictable as a dice, which is qualitatively different from other parameter set in its nature.

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