The most famous single-player card game is 'Klondike', but our ignorance of its winnability percentage has been called "one of the embarrassments of applied mathematics". Klondike is just one of many single-player card games, generically called 'patience' or 'solitaire' games, for which players have long wanted to know how likely a particular game is to be winnable for a random deal. A number of different games have been studied empirically in the academic literature and by non-academic enthusiasts. Here we show that a single general purpose Artificial Intelligence program, called "Solvitaire", can be used to determine the winnability percentage of approximately 30 different single-player card games with a 95\% confidence interval of +/- 0.1\% or better. For example, we report the winnability of Klondike as 81.956% +/- 0.096% (in the 'thoughtful' variant where the player knows the location of all cards), a 30-fold reduction in confidence interval over the best previous result. Almost all our results are either entirely new or represent significant improvements on previous knowledge.

Machine learning is traditionally formalized and researched as the study of learning concepts and decision functions from labeled examples, requiring a representation that encodes information about the domain of the decision function to be learned. We are interested in providing a way for a human teacher to interact with an automated learner using natural instructions, thus allowing the teacher to communicate the relevant domain expertise to the learner without necessarily knowing anything about the internal representations used in the learning process. In this paper we suggest to view the process of learning a decision function as a natural language lesson interpretation problem instead of learning from labeled examples. This interpretation of machine learning is motivated by human learning processes, in which the learner is given a lesson describing the target concept directly, and a few instances exemplifying it. We introduce a learning algorithm for the lesson interpretation problem that gets feedback from its performance on the final task, while learning jointly (1) how to interpret the lesson and (2) how to use this interpretation to do well on the final task. his approach alleviates the supervision burden of traditional machine learning by focusing on supplying the learner with only human-level task expertise for learning. We evaluate our approach by applying it to the rules of the Freecell solitaire card game. We show that our learning approach can eventually use natural language instructions to learn the target concept and play the game legally. Furthermore, we show that the learned semantic interpreter also generalizes to previously unseen instructions.

Herein, we employ a genetic algorithm (GA) to obtaining solvers for both the difficult FreeCell puzzle and the slidingtile Discrete puzzles, also known as single-player games, are puzzle. Note that although from a computationalcomplexity an excellent problem domain for artificial intelligence research, point of view the Rush Hour puzzle is harder because they can be parsimoniously described yet (unless NP PSPACE), search spaces induced by typical instances are often hard to solve (Pearl 1984). A well-known, highly of FreeCell tend to be substantially larger than those popular example within the domain of discrete puzzles is the of Rush Hour, and thus far more difficult to solve. This is card game of FreeCell. Another highly popular game is the evidenced by the failure of standard search methods to solve sliding-tile puzzle, the traditional versions of which are the FreeCell, as opposed to their success in solving all 6x6 Rush 15-puzzle (4X4) and the 24-puzzle (5X5). State-of-the-art Hour problems without requiring any heuristics (Hauptman heuristics allow for fast solutions of arbitrary instances of et al. 2009).

We use genetic programming to evolve highly successful solvers for two puzzles: Rush Hour and FreeCell. Many NP-Complete puzzles have remained relatively neglected by researchers (see (Kendall, Parkes, and Spoerer 2008) for a review).