Explore the Underlying Mathematical Logic of Various Games and the Existence or Non-Existence of Mathematically Calculated Winning Strategies

Yating Xiang; Yuhuan Chen; Yuhan Li

doi:10.18686/ijmss.v6i6.3994

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Explore the Underlying Mathematical Logic of Various Games and the Existence or Non-Existence of Mathematically Calculated Winning Strategies

Yating Xiang

Yuhuan Chen

Yuhan Li

International Journal of Mathematics and Systems Science 2023, 6(6), 3994; https://doi.org/10.18686/ijmss.v6i6.3994

Submitted：05 Jan 2024

Accepted：05 Jan 2024

Published：05 Jan 2024

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Abstract

This paper delves into the intricate relationship between games and the mathematical structures that govern them. By exploring both traditional board games and modern video games, we assess the extent to which mathematical logic plays a pivotal role in determining gameplay and strategies. A central theme is the quest for winning strategies: their existence, their mathematical underpinnings, and their limitations. Through case studies of games like chess and poker, the study elucidates the balance between deterministic gameplay and the unpredictable nature of certain game elements.This comprehensive study offers a bridge between game theory, mathematical logic, and the practical world of gaming.

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References

[1] Soldano C, Luz Y, Arzarello F, et al. Technology-based inquiry in geometry: Semantic games through the lens of variation[J]. Edu_x005fcational studies in mathematics, 2019, 100: 7-23.

[2] Hearn RA, Demaine ED. Games, puzzles, and computation[M]. CRC Press, 2009.

[3] PUBG Corporation. (2017). Player Unknown’s Battlegrounds [Video game]. PUBG Corporation.

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