A Note on Mathematics of Sugoroku and its Extended Games with Educational objectives

Sugoroku is a traditional game. There are various types of extended games of sugoroku, including extended games with deterministic events and rewards, and extended games with action selection and probabilistic rewards. Sugoroku and its extended games are used in various educational fields. In order...

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Bibliographic Details
Published inJournal of Biomedical Fuzzy Systems Association Vol. 25; no. 1; pp. 33 - 44
Main Author MAEDA, Yasunari
Format Journal Article
LanguageJapanese
Published Biomedical Fuzzy Systems Association 10.06.2023
Subjects
educational objective
extended game
mathematical engineering
maximum expected total rewards
sugoroku
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Summary:Sugoroku is a traditional game. There are various types of extended games of sugoroku, including extended games with deterministic events and rewards, and extended games with action selection and probabilistic rewards. Sugoroku and its extended games are used in various educational fields. In order to create effective games based on educational objectives, studies based on mathematical engineering such as the expected number of dice rolls from the start to the goal and the maximum expected total rewards in extended games with action selection are necessary. But there are only a few studies based on mathematical engineering, especially on expected total rewards. In this study, computation methods for the expected total rewards in some extended games are studied. The effectiveness of the proposed methods is shown by some computation examples. In previous research, the validity of the reward setting cannot be confirmed until after the game is played. However, it can be confirmed in advance with the proposed method. This research is a basic research, and future extended research is required.
ISSN:1345-1537
2424-2578
DOI:10.24466/jbfsa.25.1_33