Ten Times Eighteen

• Item type: Journal(1)
• 公開日: 2015-05-15
• タイトル: Ten Times Eighteen
• タイトル / 言語: en
• タイトル: Ten Times Eighteen
• 言語: eng
• キーワード / 主題Scheme: Other
• キーワード / 主題: [特集：娯楽の離散数理] dice rolling game, expected score maximization, dynamic programming, computational complexity
• 資源タイプ / 資源タイプ識別子: http://purl.org/coar/resource_type/c_6501
• 資源タイプ: journal article
• 著者所属: Friedrich Schiller University
• 著者所属(英): en
• 著者所属(英): Friedrich Schiller University
• 著者名: Sebastian, Bocker
• 著者名(英): Sebastian, Bocker
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: We consider the following simple game: We are given a table with ten slots indexed one to ten. In each of the ten rounds of the game, three dice are rolled and the numbers are added. We then put this number into any free slot. For each slot, we multiply the slot index with the number in this slot, and add up the products. The goal of the game is to maximize this score. In more detail, we play the game many times, and try to maximize the sum of scores or, equivalently, the expected score. We present a strategy to optimally play this game with respect to the expected score. We then modify our strategy so that we need only polynomial time and space. Finally, we show that knowing all ten rolls in advance, results in a relatively small increase in score. Although the game has a random component and requires a non-trivial strategy to be solved optimally, this strategy needs only polynomial time and space.; ------------------------------; This is a preprint of an article intended for publication Journal of; Information Processing(JIP). This preprint should not be cited. This; article should be cited as: Journal of Information Processing Vol.23(2015) No.3 (online); DOI http://dx.doi.org/10.2197/ipsjjip.23.258; ------------------------------
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: We consider the following simple game: We are given a table with ten slots indexed one to ten. In each of the ten rounds of the game, three dice are rolled and the numbers are added. We then put this number into any free slot. For each slot, we multiply the slot index with the number in this slot, and add up the products. The goal of the game is to maximize this score. In more detail, we play the game many times, and try to maximize the sum of scores or, equivalently, the expected score. We present a strategy to optimally play this game with respect to the expected score. We then modify our strategy so that we need only polynomial time and space. Finally, we show that knowing all ten rolls in advance, results in a relatively small increase in score. Although the game has a random component and requires a non-trivial strategy to be solved optimally, this strategy needs only polynomial time and space.; ------------------------------; This is a preprint of an article intended for publication Journal of; Information Processing(JIP). This preprint should not be cited. This; article should be cited as: Journal of Information Processing Vol.23(2015) No.3 (online); DOI http://dx.doi.org/10.2197/ipsjjip.23.258; ------------------------------
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AN00116647
• 書誌情報: 情報処理学会論文誌; 巻 56, 号 5, 発行日 2015-05-15
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 1882-7764