蛇和梯子和不及物性，或者数学家在他们的时间做什么
Snakes and Ladders and Intransitivity, or what mathematicians do in their time off
摘要：
这篇娱乐性的数学文章表明，蛇和梯子的游戏是不传递的：平方69比79有一个获胜的优势，79反过来又击败了73，73击败了69。游戏的分析是马尔可夫链、不同种类的模拟和大小偏差抽样的一个很好的说明。将其与“不及物骰子”联系起来，说明了名字的力量，以及与同事合作的乐趣。当抽签不算的时候，我们展示一个不传递骰子的最小例子，一个骰子只有一个“面”，两个骰子各有两个面。
英文摘要：
This recreational mathematics article shows that the game of Snakes and Ladders is intransitive: square 69 has a winning edge over 79, which in turn beats 73, which beats 69. Analysis of the game is a nice illustration of Markov chains, simulations of different sorts, and size-biased sampling. Connecting this to "intransitive dice" illustrates the power of a name, and the joy of working with colleagues. When draws do not count, we show a minimal example of intransitive dice, with one die having just a single "face" and two dice each having two faces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
