Searching Solitaire in Real Time

This article presents a new real-time heuristic search method for planning problems with distinct stages. Our multistage nested rollout algorithm allows the user to apply separate heuristics at each stage of the search process and tune the search magnitude for each stage. We propose a searchtree compression that reveals a new state representation for the games of Klondike Solitaire and Thoughtful Solitaire, a version of Klondike Solitaire in which the location of all cards is known. Moreover, we present a Thoughtful Solitaire solver based on these methods that can determine over 80% of Thoughtful Solitaire games in less than 4 seconds. Finally, we demonstrate empirically that no less than 82% and no more than 91.44% of Klondike Solitaire games have winning solutions, leaving less than 10% of games unresolved.