ダーツ01ゲーム最適戦略  [in Japanese] Optimal Strategies for 301 Darts Game  [in Japanese]

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Author(s)

    • 西谷 崇志 NISHITANI Takashi
    • 早稲田大学 理工学部 電気・情報生命工学科 Dept. of Electrical Engineering and Bioscience, School of Science and Engineering, Waseda University
    • 原 慎平 HARA Shinpei
    • 早稲田大学大学院理工学研究科 電気・情報生命専攻 Dept. of Electrical Engineering and Bioscience, Graduate School of Advanced Science and Engineering, Waseda University
    • 井上 真郷 INOUE Masato
    • 早稲田大学 理工学部 電気・情報生命工学科 Dept. of Electrical Engineering and Bioscience, School of Science and Engineering, Waseda University

Abstract

本研究ではダーツ01(301)ゲームを対象に研究を行った。ダーツゲームは状態遷移確率がプレイヤーのスキルに依存する不確定ゲームであるため、未だその戦略的側面についてはあまり詳しく研究されていない。本研究ではプレイヤーが狙った点からダーツが二次元正規分布に従って当たるとするモデルで解析を行った。また、01ゲームの状態遷移には様々な経路が存在する点に着目し、動的計画法を用いることでプレイヤーのスキルに応じて平均的に最も少ないラウンド数で終了条件を満たす戦略を得ることに成功した。また、対戦相手が前述の戦略をとるものと仮定した上での、勝率を最大化する戦略も求め、結果を得た。本手法はより一般的な501ゲームにも容易に適用可能である。We investigated the 301 darts game. The strategic aspects of this game have not been fully studied yet due to the complexity of its state transition equations depending on players' skills. In this research, we adopted a simple model of two-dimensional Gaussian distribution for the gap between targeted point and actual hit point. Then, we analyzed this game by using the dynamic programming techniques because it has numerous transition pathways. As the results, we successfully obtained the optimal strategy which minimizes the expected number of rounds needed to reach the goal. Besides, we also successfully obtained the optimal strategy which maximizes the probability of the winning assuming the opponent player adopting the above strategy. Our analysis method can be easily applied for more popular 501 darts game.

We investigated the 301 darts game. The strategic aspects of this game have not been fully studied yet due to the complexity of its state transition equations depending on players' skills. In this research, we adopted a simple model of two-dimensional Gaussian distribution for the gap between targeted point and actual hit point. Then, we analyzed this game by using the dynamic programming techniques because it has numerous transition pathways. As the results, we successfully obtained the optimal strategy which minimizes the expected number of rounds needed to reach the goal. Besides, we also successfully obtained the optimal strategy which maximizes the probability of the winning assuming the opponent player adopting the above strategy. Our analysis method can be easily applied for more popular 501 darts game.

Journal

  • 研究報告ゲーム情報学(GI)

    研究報告ゲーム情報学(GI) 2009(27(2009-GI-21)), 101-108, 2009-03-02

    Information Processing Society of Japan (IPSJ)

References:  1

  • <no title>

    BELLMAN R.

    Dynamic Programming, 1957

    Cited by (1)

Codes

  • NII Article ID (NAID)
    110007162353
  • NII NACSIS-CAT ID (NCID)
    AA11362144
  • Text Lang
    JPN
  • Article Type
    Technical Report
  • ISSN
    09196072
  • NDL Article ID
    10201697
  • NDL Source Classification
    ZM13(科学技術--科学技術一般--データ処理・計算機)
  • NDL Call No.
    Z14-1121
  • Data Source
    CJP  NDL  NII-ELS  IPSJ 
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