How to Generalize Janken - Rock-Paper-Scissors-King-Flea
How to Generalize Janken - Rock-Paper-Scissors-King-Flea
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如何概括 Janken - 石头剪刀布国王跳蚤
DOI：
10.1007/978-3-642-45281-9_8
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Hiro Ito
中科院分区：
文献类型：
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作者：
Hiro Ito
扬肯是一个非常简单的游戏，在日本通常被用作掷硬币的游戏，起源于中国，世界各地都有很多变种。Janken的一个变体可以用锦标赛来表示，其中一个顶点对应一个符号，而弧线(x，y)表示符号x击败符号Signy。然而，并不是所有的锦标赛都定义了有用的简肯变体，也就是说，一些简肯变体可能包括一个无用的手势，这在任何情况下都严格低于另一个手势。我们首先证明了对于除2和4以外的任何正整数，我们可以构造一个没有无用符号的Janken变型。接下来，我们介绍了一种利用出度差和入度差的变化来度量简肯变种娱乐性的方法。在这一衡量标准下，我们表明，如果且仅当它对应于J·W·W·穆恩在1993年定义的锦标赛之一时，Janken变体在有符号的变体中具有最好的娱乐性。根据这些结果，我们提出了一个简肯变体“King-fles-janken”，它是有五个符号的变体中最有趣的一个。
Janken, which is a very simple game and it is usually used as a coin-toss in Japan, originated in China, and many variants are seen throughout the world. A variant of janken can be represented by a tournament, where a vertex corresponds a sign and an arc (x,y) means signxdefeats signy. However, not all tournaments define useful janken variants, i.e., some janken variants may include a useless sign, which is strictly inferior than another sign in any case. We first shows that for any positive integernexcept 2 and 4, we can construct a janken variant withnsigns without useless signs. Next we introduces a measure of amusement of janken variants by using the variation of the difference of out-degree and in-degree. Under this measure, we show that a janken variant has the best amusement among ones withnsigns if and only if it corresponds to one of the tournaments defined by J. W. Moon in 1993. Following these results, we present a janken variant “King-fles-janken,” which is the best amusing janken variant among ones with five signs.