Generalized Entropy and Solution Information for Measuring Puzzle Difficulty

Abstract

Metrics for problem difficulty are used by many puzzle generation algorithms, as well as by adaptive algorithms that want to provide players with the puzzles at the correct level of difficulty. A recently proposed general metric, puzzle entropy, combines an analysis of game mechanics with a model of player knowledge in the form of inference rules to predict problem difficulty. The entropy of a puzzle is the amount of information required, given a player’s knowledge about the puzzle, to describe a solution to a puzzle. This paper generalizes the concepts of puzzle entropy and solution information, providing a better foundation for the previous work and creating new algorithms, Minimum Solution Information and Total Solution Information. While functionally very similar to past work, the new algorithm allows knowledge about a puzzle to be represented as a policy, something that can be learned more easily. We then evaluate the impact of policies, inference rules, and player knowledge in the 2016 game, The Witness.