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The Left Center Right Dice Game Without the Center.

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Title: The Left Center Right Dice Game Without the Center.
Authors: May, Rus1 (AUTHOR) r.may@moreheadstate.edu, Vogelpohl, Jacob1,2 (AUTHOR) jt.vogelpohl@uky.edu
Source: College Mathematics Journal. Sep2026, Vol. 57 Issue 4, p236-244. 9p.
Subject Terms: *Dice games, *Mathematical analysis, *Probability theory, *Sparse matrices, *Mathematical expansion, *Time
Abstract: This article focuses on the mathematical analysis of a variant of the Left Center Right (LCR) Dice Game called the Left Right (LR) Dice Game, where moves to the center pot are forbidden and the game ends only when one player accumulates all chips. Using generating functions and sparse linear systems, the authors develop a framework to compute probabilities of winning for each player and the expected duration of the LR game measured in turns or rolls. The study reveals that the LR game typically lasts much longer than the original LCR game, with expected durations growing superlinearly in the number of players and chips, and that players’ chances of winning depend nonuniformly on their positions relative to the first roller. The article also discusses computational challenges for larger games and suggests extensions to analyze the full LCR game using similar methods. [Extracted from the article]
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  Data: The Left Center Right Dice Game Without the Center.
– Name: Author
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  Data: <searchLink fieldCode="AR" term="%22May%2C+Rus%22">May, Rus</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> r.may@moreheadstate.edu</i><br /><searchLink fieldCode="AR" term="%22Vogelpohl%2C+Jacob%22">Vogelpohl, Jacob</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> jt.vogelpohl@uky.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22College+Mathematics+Journal%22">College Mathematics Journal</searchLink>. Sep2026, Vol. 57 Issue 4, p236-244. 9p.
– Name: Subject
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  Data: *<searchLink fieldCode="DE" term="%22Dice+games%22">Dice games</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br />*<searchLink fieldCode="DE" term="%22Probability+theory%22">Probability theory</searchLink><br />*<searchLink fieldCode="DE" term="%22Sparse+matrices%22">Sparse matrices</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+expansion%22">Mathematical expansion</searchLink><br />*<searchLink fieldCode="DE" term="%22Time%22">Time</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: This article focuses on the mathematical analysis of a variant of the Left Center Right (LCR) Dice Game called the Left Right (LR) Dice Game, where moves to the center pot are forbidden and the game ends only when one player accumulates all chips. Using generating functions and sparse linear systems, the authors develop a framework to compute probabilities of winning for each player and the expected duration of the LR game measured in turns or rolls. The study reveals that the LR game typically lasts much longer than the original LCR game, with expected durations growing superlinearly in the number of players and chips, and that players’ chances of winning depend nonuniformly on their positions relative to the first roller. The article also discusses computational challenges for larger games and suggests extensions to analyze the full LCR game using similar methods. [Extracted from the article]
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1080/07468342.2026.2632525
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      – Code: eng
        Text: English
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        PageCount: 9
        StartPage: 236
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      – SubjectFull: Dice games
        Type: general
      – SubjectFull: Mathematical analysis
        Type: general
      – SubjectFull: Probability theory
        Type: general
      – SubjectFull: Sparse matrices
        Type: general
      – SubjectFull: Mathematical expansion
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      – SubjectFull: Time
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      – TitleFull: The Left Center Right Dice Game Without the Center.
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            NameFull: May, Rus
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            NameFull: Vogelpohl, Jacob
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            – D: 01
              M: 09
              Text: Sep2026
              Type: published
              Y: 2026
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            – TitleFull: College Mathematics Journal
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