A Mathematical Analysis of Tilt

Elly Do; David Richeson; Barry Tesman

doi:10.2478/rmm-2025-0007

.blurhash-client-img { display: none !important; }

A Mathematical Analysis of Tilt

Recreational Mathematics Magazine

Volume 12 (2025): Issue 20 (June 2025)

By: Elly Do, David Richeson and Barry Tesman

Open Access

|Jun 2025

Abstract

The logic game Tilt has 40 challenge cards labeled beginner, intermediate, advanced, and expert. In this article, we use mathematics to analyze the game and use various techniques to measure its difficulty. We create a digraph for each game’s possible configurations and use the graph’s properties to determine its difficulty. We also imagine random gameplay and use the theory of absorbing Markov chains to analyze the difficulty of the game.

References

[AB72] Robert B. Ash and Richard L. Bishop. Monopoly as a Markov process. Mathematics Magazine, 45(1):26–29, Jan 1972. URL: https://doi.org/10.1080%2F0025570x.1972.11976187, doi:10.1080/0025570x.1972.11976187.
Search in Google Scholar Back to article
[AKS93] S. C. Althoen, L. King, and K. Schilling. How long is a game of Snakes and Ladders? The Mathematical Gazette, 77(478):71–76, Mar 1993. URL: http://www.jstor.org/stable/3619261.
Search in Google Scholar Back to article
[AR97] Stephen D. Abbott and Matt Richey. Take a walk on the boardwalk. The College Mathematics Journal, 28(3):162–171, May 1997. URL: https://doi.org/10.1080%2F07468342.1997.11973857, doi:10.1080/07468342.1997.11973857.
Search in Google Scholar Back to article
[CG14] Darcie Connors and Darren Glass. Chutes and Ladders with large spinners. College Mathematics Journal, 45(4):289–295, 2014.
Search in Google Scholar Back to article
[CRV15] Alissa S. Crans, Robert J. Rovetti, and Jessica Vega. Solving the KO Labyrinth. Mathematics Magazine, 88(1):27–36, Feb 2015. URL: https://doi.org/10.4169%2Fmath.mag.88.1.27, doi:10.4169/math.mag.88.1.27.
Search in Google Scholar Back to article
[DD01] Persi Diaconis and Rick Durrett. Chutes and Ladders in Markov chains. J. Theor. Prob., 14(3):899–926, 2001. doi:10.1023/A:1017509611178.
Search in Google Scholar Back to article
[LR12] Evgeny Lakshtanov and Vera Roshchina. On finiteness in the card game of War. The American Mathematical Monthly, 119(4):318–232, April 2012. URL: https://doi.org/10.4169%2Famer.math.monthly.119.04.318, doi: 10.4169/amer.math.monthly.119.04.318.
Search in Google Scholar Back to article
[Osb03] Jason A. Osborne. Markov chains for the RISK board game revisited. Mathematics Magazine, 76(2):129–135, Apr 2003. URL: https://doi.org/10.1080%2F0025570x.2003.11953165, doi:10.1080/0025570x.2003.11953165.
Search in Google Scholar Back to article
[PW15] Pamela Pierce and Robert Wooster. Conquer the world with Markov chains. Math Horizons, 22(4):18–21, Apr 2015. URL: https://doi.org/10.4169%2Fmathhorizons.22.4.18, doi:10.4169/mathhorizons.22.4.18.
Search in Google Scholar Back to article
[Rob76] Fred S. Roberts. Discrete mathematical models with applications to social, biological, and environmental problems. Prentice Hall, Englewood Cliffs, N.J., 1976.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/rmm-2025-0007 | Journal eISSN: 2182-1976

Journal RSS Feed

Language: English

Page range: 121 - 136

Published on: Jun 26, 2025

Published by: Ludus Association

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Related subjects:

Mathematics,

General mathematics

© 2025 Elly Do, David Richeson, Barry Tesman, published by Ludus Association
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 12 (2025): Issue 20 (June 2025)