\AE quitas: Two-Player Counterfeit Coin Games
Kyle Burke, Tanya Khovanova, Joshua Lee, Richard J. Nowakowski, Amelia, Rowland, Craig Tennenhouse

TL;DR
This paper analyzes two-player games involving identifying a counterfeit coin through strategic weighings, providing solutions for various game configurations and characterizing winning strategies.
Contribution
It introduces a comprehensive analysis of counterfeit coin games, including winning positions and Grundy numbers for different game variants.
Findings
Characterization of winning positions for various game setups
Calculation of Grundy numbers for different game variants
Strategies for optimal play in counterfeit coin games
Abstract
We discuss games involving a counterfeit coin. Given one counterfeit coin among a number of otherwise identical coins, two players with full knowledge of the fake coin take turns weighing coins on a two-pan scale, under the condition that on every turn they reveal some information to an Observer with limited prior knowledge about the coins. We study several games depending on the types of the counterfeit coin, the end-game condition, and the availability of extra genuine coins. We present the winning positions and the Grundy numbers for these games.
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Taxonomy
TopicsGambling Behavior and Treatments · Art History and Market Analysis
