Dynamics of gambling. Origins of randomness in mechanical systems
Randomness is typically studied using dice, coins and roulettes. These are rigid bodies whose equations are the deterministic Newton-Euler equations. This book addresses the following question: How can a rigid body produce a pseudo-random outcome? The obtained result is that due to the high (but finite) sensitivity to initial conditions it is practically impossible (at least for the time being) to predict the outcome. Pseudo-randomness in mechanical systems can be understood using nonlinear dynamics as temporal sensitivity to the initial conditions generated by the non-smoothness properties of such systems. This book consists of five chapters. Chapter one gives the definition of gambling and gaming. A brief history of gambling is given. Fair mechanical randomizers (coin, dice and roulette) are introduced. Chapter two gives the equations of motion for rigid bodies. In chapter three Newton-Euler equations are used to describe the mechanical randomizers. The influences of air resistance and impacts are described. In chapter four the experimental observations and numerical results of Newton-Euler equations for the mechanical randomizers are presented. The authors argue that the system is fully deterministic and that any realistic uncertainty in the initial conditions will lead to uncertainty in the outcome. In chapter five it is argued that the mechanical randomizer systems have non-smoothness which causes uncertainties. An explanation is given of why practically small uncertainties in the initial conditions of mechanical randomizers approximates the random process. These results are not expected to be used to make a fortune in a casino.
scientific article; zbMATH DE number 5652710