This is joint work with Charlie Blake.

Abstract:

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 ‘solitaire’ or ‘patience’ 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 to within 0.10% (in the ‘thoughtful’ variant where the player knows the location of all cards). This is a 30-fold reduction in confidence interval, and almost all our results are either entirely new or represent significant improvements on previous knowledge.

Speaker Bio:

Ian Gent is professor of Computer Science at the University of St Andrews. His mother taught him to play patience and herself showed endless patience when he “helped” her by taking complete control of the game. A program to play a patience game was one of the programs he wrote on his 1982 Sinclair Spectrum now on the wall outside his office.