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DOI: 10.4230/LIPIcs.CP.2024.1

Solving Patience and Solitaire Games with Good Old Fashioned AI (Invited Talk)

Authors: Ian P. Gent

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

Abstract

While games like Chess, Checkers and Go have been the subject of extensive research in AI for decades, there has been comparatively little study of single player card games. These games are generally called "Patience" in British English and "Solitaire" in US English, and have been popular for hundreds of years and remain so today. In fact, our ignorance of the winnability percentage of just one such game - "Klondike" - has been described as "one of the embarrassments of applied mathematics" by the distinguished statistician Persi Diaconis. I will talk about "Solvitaire", a program to solve patience games given a simple JSON description of the rules of the game and the initial layout. We have used Solvitaire to determine the winnability percentage of dozens different single-player card games with a 95% confidence interval of ± 0.1% or better. For example, we now know the winnability of Klondike as 81.945% ± 0.084% (in the "thoughtful" variant where the player knows the rank and suit of all cards), a 30-fold reduction in confidence interval over the best previous result. The vast majority of results we obtained with Solvitaire are either entirely new or represent significant improvements on previous knowledge. Solvitaire is very much a "Good Old Fashioned AI" approach to solving patience games, without using Machine Learning or Neural networks. It uses exhaustive depth-first search to explore all possible ways that a game could possibly be won, ensuring that games reported unwinnable really are so. This can involve searching extraordinary seach spaces with depths in the millions even including cases where unwinnability is proven. Numerous techniques imported from AI search play an important role in making this search practicable. Particularly important ones are: the use of a transposition tables; the exploitation of symmetry in search; the use of dominances to force certain moves to be made when it is safe to do so; and the use of streamliners. Solvitaire does have some games it performs poorly on, where exhaustive search is unable to prove that no win is possible but an alternative simple proof is in fact available. I will also talk about using constraint models do this, leading to slight improvements in some variants of Klondike but dramatic improvements in others. This talk will include personal anecdotes, explaining for example why it is dedicated to my mother Margaret Gent (1923-2021) for her patience in teaching me to love the game of patience.

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Ian P. Gent. Solving Patience and Solitaire Games with Good Old Fashioned AI (Invited Talk). In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gent:LIPIcs.CP.2024.1,
  author =	{Gent, Ian P.},
  title =	{{Solving Patience and Solitaire Games with Good Old Fashioned AI}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.1},
  URN =		{urn:nbn:de:0030-drops-206863},
  doi =		{10.4230/LIPIcs.CP.2024.1},
  annote =	{Keywords: AI Search, Solitaire and Patience Games}
}

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DOI: 10.4230/LIPIcs.CP.2022.18

A Framework for Generating Informative Benchmark Instances

Authors: Nguyen Dang, Özgür Akgün, Joan Espasa, Ian Miguel, and Peter Nightingale

Published in: LIPIcs, Volume 235, 28th International Conference on Principles and Practice of Constraint Programming (CP 2022)

Abstract

Benchmarking is an important tool for assessing the relative performance of alternative solving approaches. However, the utility of benchmarking is limited by the quantity and quality of the available problem instances. Modern constraint programming languages typically allow the specification of a class-level model that is parameterised over instance data. This separation presents an opportunity for automated approaches to generate instance data that define instances that are graded (solvable at a certain difficulty level for a solver) or can discriminate between two solving approaches. In this paper, we introduce a framework that combines these two properties to generate a large number of benchmark instances, purposely generated for effective and informative benchmarking. We use five problems that were used in the MiniZinc competition to demonstrate the usage of our framework. In addition to producing a ranking among solvers, our framework gives a broader understanding of the behaviour of each solver for the whole instance space; for example by finding subsets of instances where the solver performance significantly varies from its average performance.

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Nguyen Dang, Özgür Akgün, Joan Espasa, Ian Miguel, and Peter Nightingale. A Framework for Generating Informative Benchmark Instances. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dang_et_al:LIPIcs.CP.2022.18,
  author =	{Dang, Nguyen and Akg\"{u}n, \"{O}zg\"{u}r and Espasa, Joan and Miguel, Ian and Nightingale, Peter},
  title =	{{A Framework for Generating Informative Benchmark Instances}},
  booktitle =	{28th International Conference on Principles and Practice of Constraint Programming (CP 2022)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-240-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{235},
  editor =	{Solnon, Christine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2022.18},
  URN =		{urn:nbn:de:0030-drops-166479},
  doi =		{10.4230/LIPIcs.CP.2022.18},
  annote =	{Keywords: Instance generation, Benchmarking, Constraint Programming}
}

Document

DOI: 10.4230/LIPIcs.CP.2022.38

Selecting SAT Encodings for Pseudo-Boolean and Linear Integer Constraints

Authors: Felix Ulrich-Oltean, Peter Nightingale, and James Alfred Walker

Published in: LIPIcs, Volume 235, 28th International Conference on Principles and Practice of Constraint Programming (CP 2022)

Abstract

Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the literature with widely varying performance, and the problem of selecting suitable encodings for a given problem instance is not trivial. We explore the problem of selecting encodings for pseudo-Boolean and linear constraints using a supervised machine learning approach. We show that it is possible to select encodings effectively using a standard set of features for constraint problems; however we obtain better performance with a new set of features specifically designed for the pseudo-Boolean and linear constraints. In fact, we achieve good results when selecting encodings for unseen problem classes. Our results compare favourably to AutoFolio when using the same feature set. We discuss the relative importance of instance features to the task of selecting the best encodings, and compare several variations of the machine learning method.

Cite as

Felix Ulrich-Oltean, Peter Nightingale, and James Alfred Walker. Selecting SAT Encodings for Pseudo-Boolean and Linear Integer Constraints. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 38:1-38:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ulricholtean_et_al:LIPIcs.CP.2022.38,
  author =	{Ulrich-Oltean, Felix and Nightingale, Peter and Walker, James Alfred},
  title =	{{Selecting SAT Encodings for Pseudo-Boolean and Linear Integer Constraints}},
  booktitle =	{28th International Conference on Principles and Practice of Constraint Programming (CP 2022)},
  pages =	{38:1--38:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-240-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{235},
  editor =	{Solnon, Christine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2022.38},
  URN =		{urn:nbn:de:0030-drops-166670},
  doi =		{10.4230/LIPIcs.CP.2022.38},
  annote =	{Keywords: Constraint programming, SAT encodings, machine learning, global constraints, pseudo-Boolean constraints, linear constraints}
}

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Solving Patience and Solitaire Games with Good Old Fashioned AI (Invited Talk)

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A Framework for Generating Informative Benchmark Instances

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Selecting SAT Encodings for Pseudo-Boolean and Linear Integer Constraints

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