论文标题
骰子随机三重的概率是瞬时的
The probability that a random triple of dice is transitive
论文作者
论文摘要
$ n $侧面的模具是$ n $ n $ tup的积极整数。我们说如果对$（i，j）$（i，j）$的数量，$ a_i> b_j $大于$ a_i，j）$ a_i y_i <b_j $ a_i> b_j $大于$ a_i> b_j $。我们表明，对于随机$ n $侧面骰子的自然型号，如果$ a，b $和$ c $是三个随机骰子，那么考虑到$ a $ beats $ c $的概率，鉴于$ a $ a $ beats $ b $和$ b $ beats $ c $ k $ ky约为1/2。换句话说，$ a $ a $ beats $ b $和$ b $ beats $ c $的信息几乎没有影响$ a $ a $ beats $ c $的可能性。这证明了康里，加布巴德，格兰特，刘和莫里森的陈述，以构想不同的模型。
An $n$-sided die is an $n$-tuple of positive integers. We say that a die $(a_1,\dots,a_n)$ beats a die $(b_1,\dots,b_n)$ if the number of pairs $(i,j)$ such that $a_i>b_j$ is greater than the number of pairs $(i,j)$ such that $a_i<b_j$. We show that for a natural model of random $n$-sided dice, if $A, B$ and $C$ are three random dice then the probability that $A$ beats $C$ given that $A$ beats $B$ and $B$ beats $C$ is approximately 1/2. In other words, the information that $A$ beats $B$ and $B$ beats $C$ has almost no effect on the probability that $A$ beats $C$. This proves a statement that was conjectured by Conrey, Gabbard, Grant, Liu and Morrison for a different model.
