skip to main content
10.1145/3402942.3402963acmotherconferencesArticle/Chapter ViewAbstractPublication PagesfdgConference Proceedingsconference-collections
short-paper

Applications of Graph Theory and Probability in the Board Game Ticket to Ride

Published: 17 September 2020 Publication History

Abstract

In the board game Ticket to Ride, players race to claim routes and connect cities on a map of the U.S. In this work, we identify winning strategies for and potential improvements to Ticket to Ride by applying probabilistic and graph-theoretic concepts. We find that longer routes are overvalued, presenting a simple winning strategy for opportunistic players. The scoring scheme we propose—based on indicator random variables—prevents exploitation from this strategy and improves the competitive nature of the game. Using a variety of game data visualizations, we also investigate why players who connect particular pairs of cities perform better than others. In addition, we build a statistical model from the effective resistance of the game’s underlying graph structure to suggest how to choose the best pairs of cities.

Supplementary Material

a65-witter-supplement (a65-witter-supplement.pdf)
Slide presentation

References

[1]
Stephen D Abbott and Matt Richey. 1997. Take a Walk on the Boardwalk. The College Mathematics Journal 28, 3 (1997), 162–171.
[2]
Wen-Chih Chang, Yan-Da Chiu, and Mao-Fan Li. 2008. Learning Kruskal’s Algorithm, Prim’s Algorithm and Dijkstra’s Algorithm by Board Game. In International Conference on Web-based Learning. Springer, 275–284.
[3]
Michael Cornelius. 1986. An Historical Background to Some Mathematical Games. Mathematics in School 15, 1 (1986), 47–49.
[4]
Fernando de Mesentier Silva, Scott Lee, Julian Togelius, and Andy Nealen. 2017. AI as Evaluator: Search Driven Playtesting of Modern Board Games. In AAAI Workshops.
[5]
Fernando de Mesentier Silva, Scott Lee, Julian Togelius, and Andy Nealen. 2017. AI-based Playtesting of Contemporary Board Games. In Proceedings of the 12th International Conference on the Foundations of Digital Games. ACM, 13.
[6]
Fernando de Mesentier Silva, Scott Lee, Julian Togelius, and Andy Nealen. 2018. Evolving Maps and Decks for Ticket to Ride. In Proceedings of the 13th International Conference on the Foundations of Digital Games. ACM, 48.
[7]
Peter Drake and Kelvin Sung. 2011. Teaching Introductory Programming with Popular Board Games. In Proceedings of the 42nd ACM Technical Symposium on Computer Science Education. ACM, 619–624.
[8]
Wendy Ellens, FM Spieksma, P Van Mieghem, A Jamakovic, and RE Kooij. 2011. Effective Graph Resistance. Linear Algebra Appl. 435, 10 (2011), 2491–2506.
[9]
Darren Lim. 2007. Taking Students out for a Ride: Using a Board Game to Teach Graph Theory. ACM SIGCSE Bulletin 39, 1 (2007), 367–371.
[10]
Alexander Lyford, Thomas Rahr, Tina Chen, and Benjamin Kovach. 2019. Using Camels to Teach Probability and Expected Value. Teaching Statistics 41, 1 (2019), 18–24.
[11]
Fa-Yueh Wu. 2004. Theory of Resistor Networks: the Two-point Resistance. Journal of Physics A: Mathematical and General 37, 26 (2004), 6653.

Cited By

View all
  • (2024)Analysis, Generation, and Validation of New Boards for the Game Micro RobotsApplied Sciences10.3390/app1420941614:20(9416)Online publication date: 15-Oct-2024
  • (2021)The Application of Graph Theory in the Strategy Board Game “Crossing the Desert”Advances in Applied Mathematics10.12677/AAM.2021.10724810:07(2369-2377)Online publication date: 2021

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Other conferences
FDG '20: Proceedings of the 15th International Conference on the Foundations of Digital Games
September 2020
804 pages
ISBN:9781450388078
DOI:10.1145/3402942
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 17 September 2020

Permissions

Request permissions for this article.

Check for updates

Qualifiers

  • Short-paper
  • Research
  • Refereed limited

Conference

FDG '20

Acceptance Rates

Overall Acceptance Rate 152 of 415 submissions, 37%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)65
  • Downloads (Last 6 weeks)3
Reflects downloads up to 16 Jan 2025

Other Metrics

Citations

Cited By

View all
  • (2024)Analysis, Generation, and Validation of New Boards for the Game Micro RobotsApplied Sciences10.3390/app1420941614:20(9416)Online publication date: 15-Oct-2024
  • (2021)The Application of Graph Theory in the Strategy Board Game “Crossing the Desert”Advances in Applied Mathematics10.12677/AAM.2021.10724810:07(2369-2377)Online publication date: 2021

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

HTML Format

View this article in HTML Format.

HTML Format

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media