Pseudo Random Coins Show More Heads Than Tails

TL;DR

This paper demonstrates that pseudo-random number generators tend to produce more heads than tails in simulated coin tosses, revealing an inherent bias linked to their algebraic structure, which affects their use in Monte Carlo methods.

Contribution

The paper analytically and empirically shows that common pseudo-random generators are biased, particularly favoring heads over tails, due to their algebraic properties.

Findings

Pseudo random coins show a bias towards heads.

Popular generators fail to imitate a fair coin accurately.

Bias is linked to the role of zero in finite fields.

Abstract

Tossing a coin is the most elementary Monte Carlo experiment. In a computer the coin is replaced by a pseudo random number generator. It can be shown analytically and by exact enumerations that popular random number generators are not capable of imitating a fair coin: pseudo random coins show more heads than tails. This bias explains the empirically observed failure of some random number generators in random walk experiments. It can be traced down to the special role of the value zero in the algebra of finite fields.