A Probabilistic Analysis of Simplified Cluedo with Storm: The Birthday Cake Case

Ezio Bartocci, Josée Desharnais, Peter Lindner, Ana Sokolova

Abstract: We present a family of probabilistic models of a simplified version of the Cluedo game. In this version of the game, instead of a murder happening, a birthday cake has mysteriously disappeared. The aim of the game is to guess, from the clues that each player will collect while playing, what happened to the cake. The winner is the player that first guesses who has eaten the cake and the room where this has happened. We implemented several probabilistic models of the game encoding different playing strategies as Markov Decision Processes in the Prism language. We investigate these strategies by comparing their effectiveness in winning the game using the Prism and Storm probabilistic model checkers. In particular, we use Prism for statistical results and Storm for exact computation. Since the generated state space is in general huge, we limit our models to only two players resulting in almost 15 billion states to check. We believe that this benchmark could serve to further improve the current state-of-the-art probabilistic model checking.