A choiceless box game paradox

TL;DR

This paper introduces a variant of the box game paradox where players predict unknown real numbers with high accuracy without any information, highlighting the necessity of choice in solving the original problem.

Contribution

It presents a choiceless version of the box game paradox and demonstrates the importance of choice in the original problem's solution.

Findings

Players can predict unknown real numbers with near-perfect accuracy without information.

Choice is shown to be essential for solving the original box game paradox.

Further variations of the game are analyzed.

Abstract

We identify a choiceless variation of the box game paradox, in which players predict unknown real numbers with near-perfect accuracy despite lacking any useful information. We also verify that choice is necessary in the solution of the original problem and consider some further variations of the game.