On partial information retrieval: the unconstrained 100 prisoner problem

TL;DR

This paper explores a generalized version of the 100 Prisoner problem, analyzing various strategies and their success probabilities, with implications for understanding information retrieval processes.

Contribution

It introduces a new unconstrained variant of the problem, defines hybrid strategies, and uses simulations to analyze their effectiveness, providing new insights into strategy performance.

Findings

Most strategies converge to random strategy under certain conditions

Hybrid strategies can outperform classical strategies in some scenarios

Simulation results support conjectures about strategy convergence

Abstract

We consider a generalization of the classical 100 Prisoner problem and its variant, involving empty boxes, whereby winning probabilities for a team depend on the number of attempts, as well as on the number of winners. We call this the unconstrained 100 prisoner problem. After introducing the 3 main classes of strategies, we define a variety of `hybrid' strategies and quantify their winning-efficiency. Whenever analytic results are not available, we make use of Monte Carlo simulations to estimate with high accuracy the winning-probabilities. Based on the results obtained, we conjecture that all strategies, except for the strategy maximizing the winning probability of the classical (constrained) problem, converge to the random strategy under weak conditions on the number of players or empty boxes. We conclude by commenting on the possible applications of our results in understanding processes of information retrieval, such as ``memory'' in living organisms.