Clues About Bluffing in Clue: Is Conventional Wisdom Wise?

We have used the board game Clue as a pedagogical tool in our course on Artificial Intelligence to teach formal logic through the development of logic-based computational game-playing agents. The development of game-playing agents allows us to experimentally test many game-play strategies and we have encountered some surprising results that refine “conventional wisdom” for playing Clue. In this paper we consider the effect of the oft-used strategy wherein a player uses their own cards when making suggestions (i.e., “bluffing”) early in the game to mislead other players or to focus on acquiring a particular kind of knowledge. We begin with an intuitive argument against this strategy together with a quantitative probabilistic analysis of this strategy’s cost to a player that both suggest “bluffing” should be detrimental to winning the game. We then present our counter-intuitive simulation results from playing computational agents that “bluff” against those that do not that show “bluffing” to be beneficial. We conclude with a nuanced assessment of the cost and benefit of “bluffing” in Clue that shows the strategy, when used correctly, to be beneficial and, when used incorrectly, to be detrimental

Line bundles on rigid varieties and Hodge symmetry

We prove several related results on the low-degree Hodge numbers of proper smooth rigid analytic varieties over non-archimedean fields. Our arguments rely on known structure theorems for the relevant Picard varieties, together with recent advances in p-adic Hodge theory. We also define a rigid analytic Albanese naturally associated with any smooth proper rigid space.Comment: 9 pages, comments welcom

On pp-adic LL-functions for Hilbert modular forms

We construct $p$-adic $L$-functions associated with $p$-refined cohomological cuspidal Hilbert modular forms over any totally real field under a mild hypothesis. Our construction is canonical, varies naturally in $p$-adic families, and does not require any small slope or non-criticality assumptions on the $p$-refinement. The main new ingredients are an adelic definition of a canonical map from overconvergent cohomology to a space of locally analytic distributions on the relevant Galois group and a smoothness theorem for certain eigenvarieties at critically refined points.Comment: 88 page