Three problems for the clairvoyant demon
Geoffrey Grimmett
TL;DR
This paper explores three probability problems involving infinite coin toss sequences, framing them as dependent percolation issues, and investigates what a clairvoyant demon could achieve in these scenarios.
Contribution
It introduces three new problems related to infinite coin sequences and dependent percolation, analyzing the capabilities of a clairvoyant demon in these contexts.
Findings
Identification of the three problems' structure
Insights into the demon’s potential actions
Connections to dependent percolation theory
Abstract
A number of tricky problems in probability are discussed, having in common one or more infinite sequences of coin tosses, and a representation as a problem in dependent percolation. Three of these problems are of `Winkler' type, that is, they ask about what can be achieved by a clairvoyant demon.
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Taxonomy
TopicsTheology and Philosophy of Evil