2023年经济学人 桌游里的数学原理

 

    Culture

    文艺版块

    Book review

    书评

    Well played, sir

    这招很漂亮，先生

    Around the World in 80 Games. By Marcus du Sautoy.

    《玩遍世界80种游戏》，马库斯·杜·索托伊著。

    Which are the best properties to buy when playing Monopoly, and how many houses should you build on them?

    在玩大富翁游戏时，哪些地产是最值得买的？你应该在上面建多少房子？

    Which continent should you aim to take over first in Risk?

    玩《战国风云》时，首先应拿下哪个大洲？

    And what is the best strategy when using the doubling cube in backgammon?

    玩十五子棋时，让筹码加倍的最佳策略是什么？

    These are some of the questions considered and answered by Marcus du Sautoy, a British mathematician¹ and Oxford² professor, in his sprightly³, light-hearted history of games and gaming.

    这些都是英国数学家兼牛津大学教授马库斯·杜·索托伊在其风格活泼、内容轻松的游戏和博弈史著作中思考和回答的一些问题。

    The narrative⁴ is organised geographically⁵ as a trip around the world, starting with ancient games from the Middle East—backgammon, the Royal Game of Ur, the Egyptian game of senet—and ending up in Europe with modern games such as Pandemic and Dobble.

    全书按地理位置顺序来叙述，结构类似一场环球旅行，从中东的古代游戏开始--十五子棋、乌尔皇室博弈棋、古埃及桌游塞内特--以欧洲的现代桌游结束，如《瘟疫危机》和《嗒宝》。

    Along the way the author considers many old favourites (Cluedo, Scrabble, Risk), recent arrivals (Wordle, Settlers of Catan) and less familiar games from a wide range of cultures and historical periods, such as the African game of mancala and the Indian card game of ganjifa, whose rules change at night.

    在这一过程中，作者探究了许多受欢迎的老游戏(妙探寻凶、拼字游戏、战国风云)、新出现的游戏(Wordle，卡坦岛)，以及来自其他各种文化和历史时期的人们不太熟悉的游戏，如非洲的播棋和印度纸牌甘吉发，甘吉发的规则在晚上会改变。

    The list is not exhaustive or comprehensive but reflects his own collection.

    书中列举的游戏并不详尽或全面，而是展现了作者的个人收藏。

    It includes a handful of video games (Prince of Persia, Game of Life) and one sport (the Mayan ball game of pitz).

    其中包括几款视频游戏(《波斯王子》《生命游戏》)和一项运动(玛雅人的皮茨球)。

    All this is, of course, really an opportunity for Mr du Sautoy to sprinkle in plenty of mathematical explanations, to provide what he calls “a celebration of the mathematics that swims seductively just below the surface of many of the games I love”.

    当然，对杜·索托伊来说这是一个绝佳的机会，可以在书中加入一些数学解释，表达他所说的“对数学的赞颂，在我喜欢的这许多游戏的表面之下，数学在勾人心神地游动”。

    Playing games, he writes, “overlaps with what I enjoy about mathematics”: the challenge of solving a problem within a set of rules, the need to overcome obstacles and the victorious⁶ “aha” moment when a solution is found.

    他写道，玩游戏“与我对数学的喜爱有重叠之处”：在一套规则内解决问题的挑战性、克服障碍的需要，以及灵光一现找到解答时的胜利之感。

    As well as forays into probability and game theory, he explains dice⁷ rolls in Monopoly using Markov chains; the torus-shaped playing field of video games like Spacewar!; and how the geometries of finite projective planes underpin⁸ the deceptively simple game of Dobble.

    除了简要地提到概率论和博弈论之外，他还用马尔可夫链解释了怎样在大富翁中掷骰子，分析了像《太空大战!》这样的视频游戏的圆形游戏界面，解读了像《嗒宝》这种看似简单的游戏如何以有限射影平面的几何理论为其底层原理。

    And in many cases these explanations provide concrete advice to players.

    在许多情况下，这些解释为玩家提供了具体的建议。

    In Monopoly, says Mr du Sautoy, the best properties to buy are the orange ones, followed by the red ones (and build three houses on them).

    杜·索托伊表示，在《大富翁》中，最值得购买的地产是橙色的，其次是红色的(并要在上面建造三栋房子)。

    In Risk, control of North America has the best risk-reward ratio, generating a good supply of bonus armies while being easy to defend.

    在《战国风云》中，拿下北美能带来最佳的风险回报比，在易于防御的同时还能赢得大量的额外军队。

    In backgammon, accept a double if you think you have more than a 20% chance of winning; offer one if you think you have more than an 80% chance of winning.

    在十五子棋游戏中，如果你认为你有20%以上的获胜机会，就接受筹码加倍，如果你认为你有80%以上的获胜机会，就自己提出筹码加倍。

    Oh, and “tales” is the best starting word in Wordle.

    对了，玩Wordle时第一个单词最好填tales。

    The hybrid⁹ history-travelogue approach is clunky at times, and some of the entries are not games at all, but mini-essays on game-related topics, from biography to psychology¹⁰.

    历史和游记相结合的写法有时略显生硬，有些条目根本不是游戏，而是与游戏相关的超短散文，主题包括传记和心理学等等。

    And despite its high-concept framing, the book can be read in pretty much any order; indeed, the author suggests a game to randomise the order of the chapters.

    虽然这本书有一个高概念框架，但基本上可以不按顺序阅读，作者其实还提出了一个游戏来随机排列章节的顺序。

    (In an appendix, he then works out how many possible options there are, which doubles as an illustration of the technique of proof by induction¹¹.)(在附录中，他计算出有多少种可能的选择，这同时也是对归纳证明法的说明。)Fun, unexpected, operating within fixed¹² but arbitrary rules, producing a range of complex outcomes and offering insights that can be applied¹³ to everyday life—a good game combines all these elements.

    有趣、出乎意料、在固定但任意的规则下运作、产生一系列复杂的结果，并得出可以应用于日常生活的洞见，所有这些元素都是一个好游戏所具备的。

    The same can also be said of this book.

    本书同样具备这些元素。

1 mathematician   

n.数学家

参考例句：

• The man with his back to the camera is a mathematician.背对着照相机的人是位数学家。
• The mathematician analyzed his figures again.这位数学家再次分析研究了他的这些数字。

2 Oxford   

n.牛津（英国城市）

参考例句：

• At present he has become a Professor of Chemistry at Oxford.他现在已是牛津大学的化学教授了。
• This is where the road to Oxford joins the road to London.这是去牛津的路与去伦敦的路的汇合处。

3 sprightly   

adj.愉快的，活泼的

参考例句：

• She is as sprightly as a woman half her age.她跟比她年轻一半的妇女一样活泼。
• He's surprisingly sprightly for an old man.他这把年纪了，还这么精神，真了不起。

4 narrative   

n.叙述，故事；adj.叙事的，故事体的

参考例句：

• He was a writer of great narrative power.他是一位颇有记述能力的作家。
• Neither author was very strong on narrative.两个作者都不是很善于讲故事。

5 geographically   

adv.地理学上，在地理上，地理方面

参考例句：

• Geographically, the UK is on the periphery of Europe. 从地理位置上讲，英国处于欧洲边缘。 来自辞典例句
• All these events, however geographically remote, urgently affected Western financial centers. 所有这些事件，无论发生在地理上如何遥远的地方，都对西方金融中心产生紧迫的影响。 来自名作英译部分

6 victorious   

adj.胜利的，得胜的

参考例句：

• We are certain to be victorious.我们定会胜利。
• The victorious army returned in triumph.获胜的部队凯旋而归。

7 dice   

n.骰子；vt.把（食物）切成小方块，冒险

参考例句：

• They were playing dice.他们在玩掷骰子游戏。
• A dice is a cube.骰子是立方体。

8 underpin   

v.加固，支撑

参考例句：

• China needs regional stability to underpin its continued economic growth.中国需要地区稳定来巩固其持续的经济增长。
• These developments are underpinned by solid progress in heavy industry.重工业的稳固发展为这些进展打下了基础。

9 hybrid   

n.(动，植）杂种，混合物

参考例句：

• That is a hybrid perpetual rose.那是一株杂交的四季开花的蔷薇。
• The hybrid was tall,handsome,and intelligent.那混血儿高大、英俊、又聪明。

10 psychology   

n.心理，心理学，心理状态

参考例句：

• She has a background in child psychology.她受过儿童心理学的教育。
• He studied philosophy and psychology at Cambridge.他在剑桥大学学习哲学和心理学。

11 induction   

n.感应，感应现象

参考例句：

• His induction as a teacher was a turning point in his life.他就任教师工作是他一生的转折点。
• The magnetic signals are sensed by induction coils.磁信号由感应线圈所检测。

12 fixed   

adj.固定的，不变的，准备好的；(计算机)固定的

参考例句：

• Have you two fixed on a date for the wedding yet?你们俩选定婚期了吗？
• Once the aim is fixed,we should not change it arbitrarily.目标一旦确定，我们就不应该随意改变。

13 applied   

adj.应用的；v.应用，适用

参考例句：

• She plans to take a course in applied linguistics.她打算学习应用语言学课程。
• This cream is best applied to the face at night.这种乳霜最好晚上擦脸用。