The Winnability of Klondike Solitaire and Many Other Patience Games

Abstract

Our ignorance of the winnability percentage of the game in the Windows Solitaire program, more properly called 'Klondike', has been described as "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. 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 45 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.